Handling Time

When performing feature engineering with temporal data, carefully selecting the data that is used for any calculation is paramount. By annotating entities with a time index column and providing a cutoff time during feature calculation, Featuretools will automatically filter out any data after the cutoff time before running any calculations.

What is the Time Index?

The time index is the column in the data that specifies when the data in each row became known. For example, let’s examine a table of customer transactions:

In [1]: import featuretools as ft

In [2]: es = ft.demo.load_mock_customer(return_entityset=True, random_seed=0)

In [3]: es['transactions'].df.head()
Out[3]: 
     transaction_id  session_id    transaction_time  amount product_id
298             298           1 2014-01-01 00:00:00  127.64          5
2                 2           1 2014-01-01 00:01:05  109.48          2
308             308           1 2014-01-01 00:02:10   95.06          3
116             116           1 2014-01-01 00:03:15   78.92          4
371             371           1 2014-01-01 00:04:20   31.54          3

In this table, there is one row for every transaction and a transaction_time column that specifies when the transaction took place. This means that transaction_time is the time index because it indicates when the information in each row became known and available for feature calculations.

However, not every datetime column is a time index. Consider the customers entity:

In [4]: es['customers'].df
Out[4]: 
   customer_id           join_date date_of_birth zip_code
5            5 2010-07-17 05:27:50    1984-07-28    60091
4            4 2011-04-08 20:08:14    2006-08-15    60091
1            1 2011-04-17 10:48:33    1994-07-18    60091
3            3 2011-08-13 15:42:34    2003-11-21    13244
2            2 2012-04-15 23:31:04    1986-08-18    13244

Here, we have two time columns, join_date and date_of_birth. While either column might be useful for making features, the join_date should be used as the time index because it indicates when that customer first became available in the dataset.

Important

The time index is defined as the first time that any information from a row can be used. If a cutoff time is specified when calculating features, rows that have a later value for the time index are automatically ignored.

What is the Cutoff Time?

The cutoff_time specifies the last point in time that a row’s data can be used for a feature calculation. Any data after this point in time will be filtered out before calculating features.

For example, let’s consider a dataset of timestamped customer transactions, where we want to predict whether customers 1, 2 and 3 will spend $500 between 04:00 on January 1 and the end of the day. When building features for this prediction problem, we need to ensure that no data after 04:00 is used in our calculations.

retail cutoff time diagram

We pass the cutoff time to featuretools.dfs() or featuretools.calculate_feature_matrix() using the cutoff_time argument like this:

In [5]: fm, features = ft.dfs(entityset=es,
   ...:                       target_entity='customers',
   ...:                       cutoff_time=pd.Timestamp("2014-1-1 04:00"),
   ...:                       instance_ids=[1,2,3],
   ...:                       cutoff_time_in_index=True)
   ...: 

In [6]: fm
Out[6]: 
                                zip_code  COUNT(sessions)  NUM_UNIQUE(sessions.device) MODE(sessions.device)  SUM(transactions.amount)  STD(transactions.amount)  MAX(transactions.amount)  SKEW(transactions.amount)  MIN(transactions.amount)  MEAN(transactions.amount)  COUNT(transactions)  NUM_UNIQUE(transactions.product_id)  MODE(transactions.product_id)  DAY(date_of_birth)  DAY(join_date)  YEAR(date_of_birth)  YEAR(join_date)  MONTH(date_of_birth)  MONTH(join_date)  WEEKDAY(date_of_birth)  WEEKDAY(join_date)  SUM(sessions.MIN(transactions.amount))  SUM(sessions.MEAN(transactions.amount))  SUM(sessions.NUM_UNIQUE(transactions.product_id))  SUM(sessions.STD(transactions.amount))  SUM(sessions.MAX(transactions.amount))  SUM(sessions.SKEW(transactions.amount))  STD(sessions.MIN(transactions.amount))  STD(sessions.MEAN(transactions.amount))  STD(sessions.COUNT(transactions))  STD(sessions.NUM_UNIQUE(transactions.product_id))  STD(sessions.SUM(transactions.amount))  STD(sessions.MAX(transactions.amount))  STD(sessions.SKEW(transactions.amount))  MAX(sessions.MIN(transactions.amount))  MAX(sessions.MEAN(transactions.amount))  MAX(sessions.COUNT(transactions))  MAX(sessions.NUM_UNIQUE(transactions.product_id))  MAX(sessions.SUM(transactions.amount))  MAX(sessions.STD(transactions.amount))  MAX(sessions.SKEW(transactions.amount))  SKEW(sessions.MIN(transactions.amount))  SKEW(sessions.MEAN(transactions.amount))  SKEW(sessions.COUNT(transactions))  SKEW(sessions.NUM_UNIQUE(transactions.product_id))  SKEW(sessions.SUM(transactions.amount))  SKEW(sessions.STD(transactions.amount))  SKEW(sessions.MAX(transactions.amount))  MIN(sessions.MEAN(transactions.amount))  MIN(sessions.COUNT(transactions))  MIN(sessions.NUM_UNIQUE(transactions.product_id))  MIN(sessions.SUM(transactions.amount))  MIN(sessions.STD(transactions.amount))  MIN(sessions.MAX(transactions.amount))  MIN(sessions.SKEW(transactions.amount))  MEAN(sessions.MIN(transactions.amount))  MEAN(sessions.MEAN(transactions.amount))  MEAN(sessions.COUNT(transactions))  MEAN(sessions.NUM_UNIQUE(transactions.product_id))  MEAN(sessions.SUM(transactions.amount))  MEAN(sessions.STD(transactions.amount))  MEAN(sessions.MAX(transactions.amount))  MEAN(sessions.SKEW(transactions.amount))  NUM_UNIQUE(sessions.MODE(transactions.product_id))  NUM_UNIQUE(sessions.DAY(session_start))  NUM_UNIQUE(sessions.YEAR(session_start))  NUM_UNIQUE(sessions.MONTH(session_start))  NUM_UNIQUE(sessions.WEEKDAY(session_start))  MODE(sessions.MODE(transactions.product_id))  MODE(sessions.DAY(session_start))  MODE(sessions.YEAR(session_start))  MODE(sessions.MONTH(session_start))  MODE(sessions.WEEKDAY(session_start))  NUM_UNIQUE(transactions.sessions.customer_id)  NUM_UNIQUE(transactions.sessions.device)  MODE(transactions.sessions.customer_id) MODE(transactions.sessions.device)
customer_id time                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         
1           2014-01-01 04:00:00    60091                4                            3                tablet                   4958.19                 42.309717                    139.23                  -0.006928                      5.81                  74.002836                   67                                    5                              4                  18              17                 1994             2011                     7                 4                       0                   6                                   27.62                               304.601700                                                 20                              169.572874                                  540.04                                -0.505043                                1.285833                                10.426572                           5.678908                                                0.0                              271.917637                                5.027226                                 0.500353                                    8.74                                85.469167                                 25                                                  5                                 1613.93                               46.905665                                 0.234349                                 1.452325                                 -0.233453                            1.614843                                                0.0                                  1.197406                                 1.235445                                -0.451371                                64.557200                                 12                                                  5                                 1025.63                               39.825249                                  129.00                                -0.830975                                    6.905                                 76.150425                               16.75                                                  5                                 1239.5475                                42.393218                                 135.0100                                 -0.126261                                                  3                                         1                                         1                                          1                                            1                                             4                                  1                                2014                                    1                                      2                                              1                                         3                                        1                             tablet
2           2014-01-01 04:00:00    13244                4                            2               desktop                   4150.30                 39.289512                    146.81                  -0.134786                     12.07                  84.700000                   49                                    5                              4                  18              15                 1986             2012                     8                 4                       0                   6                                  105.24                               340.791792                                                 20                              157.262738                                  569.29                                 0.045171                               20.424007                                 8.983533                           3.862210                                                0.0                              307.743859                                3.470527                                 0.324809                                   56.46                                96.581000                                 16                                                  5                                 1320.64                               47.935920                                 0.295458                                 1.815491                                  0.651941                           -0.169238                                                0.0                                 -0.823347                                -0.966834                                 0.459305                                76.813125                                  8                                                  5                                  634.84                               27.839228                                  138.38                                -0.455197                                   26.310                                 85.197948                               12.25                                                  5                                 1037.5750                                39.315685                                 142.3225                                  0.011293                                                  3                                         1                                         1                                          1                                            1                                             2                                  1                                2014                                    1                                      2                                              1                                         2                                        2                            desktop
3           2014-01-01 04:00:00    13244                1                            1                tablet                    941.87                 47.264797                    146.31                   0.618455                      8.19                  62.791333                   15                                    5                              1                  21              13                 2003             2011                    11                 8                       4                   5                                    8.19                                62.791333                                                  5                               47.264797                                  146.31                                 0.618455                                     NaN                                      NaN                                NaN                                                NaN                                     NaN                                     NaN                                      NaN                                    8.19                                62.791333                                 15                                                  5                                  941.87                               47.264797                                 0.618455                                      NaN                                       NaN                                 NaN                                                NaN                                       NaN                                      NaN                                      NaN                                62.791333                                 15                                                  5                                  941.87                               47.264797                                  146.31                                 0.618455                                    8.190                                 62.791333                               15.00                                                  5                                  941.8700                                47.264797                                 146.3100                                  0.618455                                                  1                                         1                                         1                                          1                                            1                                             1                                  1                                2014                                    1                                      2                                              1                                         1                                        3                             tablet

Even though the entityset contains the complete transaction history for each customer, only data with a time index up to and including the cutoff time was used to calculate the features above.

Using a Cutoff Time DataFrame

Oftentimes, the training examples for machine learning will come from different points in time. To specify a unique cutoff time for each row of the resulting feature matrix, we can pass a dataframe where the first column is the instance id and the second column is the corresponding cutoff time.

Note

Only the first two columns are used to calculate features. Any additional columns passed through are appended to the resulting feature matrix. This is typically used to pass through machine learning labels to ensure that they stay aligned with the feature matrix.

In [7]: cutoff_times = pd.DataFrame()

In [8]: cutoff_times['customer_id'] = [1, 2, 3, 1]

In [9]: cutoff_times['time'] = pd.to_datetime(['2014-1-1 04:00',
   ...:                              '2014-1-1 05:00',
   ...:                              '2014-1-1 06:00',
   ...:                              '2014-1-1 08:00'])
   ...: 

In [10]: cutoff_times['label'] = [True, True, False, True]

In [11]: cutoff_times
Out[11]: 
   customer_id                time  label
0            1 2014-01-01 04:00:00   True
1            2 2014-01-01 05:00:00   True
2            3 2014-01-01 06:00:00  False
3            1 2014-01-01 08:00:00   True

In [12]: fm, features = ft.dfs(entityset=es,
   ....:                       target_entity='customers',
   ....:                       cutoff_time=cutoff_times,
   ....:                       cutoff_time_in_index=True)
   ....: 

In [13]: fm
Out[13]: 
                                zip_code  COUNT(sessions)  NUM_UNIQUE(sessions.device) MODE(sessions.device)  SUM(transactions.amount)  STD(transactions.amount)  MAX(transactions.amount)  SKEW(transactions.amount)  MIN(transactions.amount)  MEAN(transactions.amount)  COUNT(transactions)  NUM_UNIQUE(transactions.product_id)  MODE(transactions.product_id)  DAY(date_of_birth)  DAY(join_date)  YEAR(date_of_birth)  YEAR(join_date)  MONTH(date_of_birth)  MONTH(join_date)  WEEKDAY(date_of_birth)  WEEKDAY(join_date)  SUM(sessions.MIN(transactions.amount))  SUM(sessions.MEAN(transactions.amount))  SUM(sessions.NUM_UNIQUE(transactions.product_id))  SUM(sessions.STD(transactions.amount))  SUM(sessions.MAX(transactions.amount))  SUM(sessions.SKEW(transactions.amount))  STD(sessions.MIN(transactions.amount))  STD(sessions.MEAN(transactions.amount))  STD(sessions.COUNT(transactions))  STD(sessions.NUM_UNIQUE(transactions.product_id))  STD(sessions.SUM(transactions.amount))  STD(sessions.MAX(transactions.amount))  STD(sessions.SKEW(transactions.amount))  MAX(sessions.MIN(transactions.amount))  MAX(sessions.MEAN(transactions.amount))  MAX(sessions.COUNT(transactions))  MAX(sessions.NUM_UNIQUE(transactions.product_id))  MAX(sessions.SUM(transactions.amount))  MAX(sessions.STD(transactions.amount))  MAX(sessions.SKEW(transactions.amount))  SKEW(sessions.MIN(transactions.amount))  SKEW(sessions.MEAN(transactions.amount))  SKEW(sessions.COUNT(transactions))  SKEW(sessions.NUM_UNIQUE(transactions.product_id))  SKEW(sessions.SUM(transactions.amount))  SKEW(sessions.STD(transactions.amount))  SKEW(sessions.MAX(transactions.amount))  MIN(sessions.MEAN(transactions.amount))  MIN(sessions.COUNT(transactions))  MIN(sessions.NUM_UNIQUE(transactions.product_id))  MIN(sessions.SUM(transactions.amount))  MIN(sessions.STD(transactions.amount))  MIN(sessions.MAX(transactions.amount))  MIN(sessions.SKEW(transactions.amount))  MEAN(sessions.MIN(transactions.amount))  MEAN(sessions.MEAN(transactions.amount))  MEAN(sessions.COUNT(transactions))  MEAN(sessions.NUM_UNIQUE(transactions.product_id))  MEAN(sessions.SUM(transactions.amount))  MEAN(sessions.STD(transactions.amount))  MEAN(sessions.MAX(transactions.amount))  MEAN(sessions.SKEW(transactions.amount))  NUM_UNIQUE(sessions.MODE(transactions.product_id))  NUM_UNIQUE(sessions.DAY(session_start))  NUM_UNIQUE(sessions.YEAR(session_start))  NUM_UNIQUE(sessions.MONTH(session_start))  NUM_UNIQUE(sessions.WEEKDAY(session_start))  MODE(sessions.MODE(transactions.product_id))  MODE(sessions.DAY(session_start))  MODE(sessions.YEAR(session_start))  MODE(sessions.MONTH(session_start))  MODE(sessions.WEEKDAY(session_start))  NUM_UNIQUE(transactions.sessions.customer_id)  NUM_UNIQUE(transactions.sessions.device)  MODE(transactions.sessions.customer_id) MODE(transactions.sessions.device)  label
customer_id time                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                
1           2014-01-01 04:00:00    60091                4                            3                tablet                   4958.19                 42.309717                    139.23                  -0.006928                      5.81                  74.002836                   67                                    5                              4                  18              17                 1994             2011                     7                 4                       0                   6                                   27.62                               304.601700                                                 20                              169.572874                                  540.04                                -0.505043                                1.285833                                10.426572                           5.678908                                                0.0                              271.917637                                5.027226                                 0.500353                                    8.74                                85.469167                                 25                                                  5                                 1613.93                               46.905665                                 0.234349                                 1.452325                                 -0.233453                            1.614843                                                0.0                                  1.197406                                 1.235445                                -0.451371                                64.557200                                 12                                                  5                                 1025.63                               39.825249                                  129.00                                -0.830975                                  6.90500                                 76.150425                               16.75                                                  5                                 1239.5475                                42.393218                                135.01000                                 -0.126261                                                  3                                         1                                         1                                          1                                            1                                             4                                  1                                2014                                    1                                      2                                              1                                         3                                        1                             tablet   True
2           2014-01-01 05:00:00    13244                5                            2               desktop                   5155.26                 38.047944                    146.81                  -0.121811                     12.07                  83.149355                   62                                    5                              4                  18              15                 1986             2012                     8                 4                       0                   6                                  127.06                               418.096407                                                 25                              190.987775                                  688.14                                -0.269747                               17.801322                                 8.543351                           3.361547                                                0.0                              266.912832                               10.919023                                 0.316873                                   56.46                                96.581000                                 16                                                  5                                 1320.64                               47.935920                                 0.295458                                 1.959531                                  1.082192                           -0.379092                                                0.0                                 -0.667256                                -0.213518                                -1.814717                                76.813125                                  8                                                  5                                  634.84                               27.839228                                  118.85                                -0.455197                                 25.41200                                 83.619281                               12.40                                                  5                                 1031.0520                                38.197555                                137.62800                                 -0.053949                                                  4                                         1                                         1                                          1                                            1                                             2                                  1                                2014                                    1                                      2                                              1                                         2                                        2                            desktop   True
3           2014-01-01 06:00:00    13244                4                            2               desktop                   2867.69                 40.349758                    146.31                   0.318315                      6.65                  65.174773                   44                                    5                              1                  21              13                 2003             2011                    11                 8                       4                   5                                  126.66                               290.968018                                                 16                              119.136697                                  493.07                                 0.860577                               40.508892                                16.540737                           7.118052                                                2.0                              417.557763                               22.808351                                 0.500999                                   91.76                                91.760000                                 17                                                  5                                  944.85                               47.264797                                 0.618455                                 1.874170                                  0.201588                           -1.330938                                               -2.0                                 -1.977878                                 1.722323                                -1.060639                                55.579412                                  1                                                  1                                   91.76                               35.704680                                   91.76                                -0.289466                                 31.66500                                 72.742004                               11.00                                                  4                                  716.9225                                39.712232                                123.26750                                  0.286859                                                  2                                         1                                         1                                          1                                            1                                             1                                  1                                2014                                    1                                      2                                              1                                         2                                        3                            desktop  False
1           2014-01-01 08:00:00    60091                8                            3                mobile                   9025.62                 40.442059                    139.43                   0.019698                      5.81                  71.631905                  126                                    5                              4                  18              17                 1994             2011                     7                 4                       0                   6                                   78.59                               582.193117                                                 40                              312.745952                                 1057.97                                -0.476122                                6.954507                                13.759314                           4.062019                                                0.0                              279.510713                                7.322191                                 0.589386                                   26.36                                88.755625                                 25                                                  5                                 1613.93                               46.905665                                 0.640252                                 2.440005                                 -0.424949                            1.946018                                                0.0                                  0.778170                                -0.312355                                -0.780493                                50.623125                                 12                                                  5                                  809.97                               30.450261                                  118.90                                -1.038434                                  9.82375                                 72.774140                               15.75                                                  5                                 1128.2025                                39.093244                                132.24625                                 -0.059515                                                  4                                         1                                         1                                          1                                            1                                             4                                  1                                2014                                    1                                      2                                              1                                         3                                        1                             mobile   True

We can now see that every row of the feature matrix is calculated at the corresponding time in the cutoff time dataframe. Because we calculate each row at a different time, it is possible to have a repeat customer. In this case, we calculated the feature vector for customer 1 at both 04:00 and 08:00.

Training Window

By default, all data up to and including the cutoff time is used. We can restrict the amount of historical data that is selected for calculations using a “training window.”

Here’s an example of using a two hour training window:

In [14]: window_fm, window_features = ft.dfs(entityset=es,
   ....:                                     target_entity="customers",
   ....:                                     cutoff_time=cutoff_times,
   ....:                                     cutoff_time_in_index=True,
   ....:                                     training_window="2 hour")
   ....: 

In [15]: window_fm
Out[15]: 
                                zip_code  COUNT(sessions)  NUM_UNIQUE(sessions.device) MODE(sessions.device)  SUM(transactions.amount)  STD(transactions.amount)  MAX(transactions.amount)  SKEW(transactions.amount)  MIN(transactions.amount)  MEAN(transactions.amount)  COUNT(transactions)  NUM_UNIQUE(transactions.product_id)  MODE(transactions.product_id)  DAY(date_of_birth)  DAY(join_date)  YEAR(date_of_birth)  YEAR(join_date)  MONTH(date_of_birth)  MONTH(join_date)  WEEKDAY(date_of_birth)  WEEKDAY(join_date)  SUM(sessions.MIN(transactions.amount))  SUM(sessions.MEAN(transactions.amount))  SUM(sessions.NUM_UNIQUE(transactions.product_id))  SUM(sessions.STD(transactions.amount))  SUM(sessions.MAX(transactions.amount))  SUM(sessions.SKEW(transactions.amount))  STD(sessions.MIN(transactions.amount))  STD(sessions.MEAN(transactions.amount))  STD(sessions.COUNT(transactions))  STD(sessions.NUM_UNIQUE(transactions.product_id))  STD(sessions.SUM(transactions.amount))  STD(sessions.MAX(transactions.amount))  STD(sessions.SKEW(transactions.amount))  MAX(sessions.MIN(transactions.amount))  MAX(sessions.MEAN(transactions.amount))  MAX(sessions.COUNT(transactions))  MAX(sessions.NUM_UNIQUE(transactions.product_id))  MAX(sessions.SUM(transactions.amount))  MAX(sessions.STD(transactions.amount))  MAX(sessions.SKEW(transactions.amount))  SKEW(sessions.MIN(transactions.amount))  SKEW(sessions.MEAN(transactions.amount))  SKEW(sessions.COUNT(transactions))  SKEW(sessions.NUM_UNIQUE(transactions.product_id))  SKEW(sessions.SUM(transactions.amount))  SKEW(sessions.STD(transactions.amount))  SKEW(sessions.MAX(transactions.amount))  MIN(sessions.MEAN(transactions.amount))  MIN(sessions.COUNT(transactions))  MIN(sessions.NUM_UNIQUE(transactions.product_id))  MIN(sessions.SUM(transactions.amount))  MIN(sessions.STD(transactions.amount))  MIN(sessions.MAX(transactions.amount))  MIN(sessions.SKEW(transactions.amount))  MEAN(sessions.MIN(transactions.amount))  MEAN(sessions.MEAN(transactions.amount))  MEAN(sessions.COUNT(transactions))  MEAN(sessions.NUM_UNIQUE(transactions.product_id))  MEAN(sessions.SUM(transactions.amount))  MEAN(sessions.STD(transactions.amount))  MEAN(sessions.MAX(transactions.amount))  MEAN(sessions.SKEW(transactions.amount))  NUM_UNIQUE(sessions.MODE(transactions.product_id))  NUM_UNIQUE(sessions.DAY(session_start))  NUM_UNIQUE(sessions.YEAR(session_start))  NUM_UNIQUE(sessions.MONTH(session_start))  NUM_UNIQUE(sessions.WEEKDAY(session_start))  MODE(sessions.MODE(transactions.product_id))  MODE(sessions.DAY(session_start))  MODE(sessions.YEAR(session_start))  MODE(sessions.MONTH(session_start))  MODE(sessions.WEEKDAY(session_start))  NUM_UNIQUE(transactions.sessions.customer_id)  NUM_UNIQUE(transactions.sessions.device)  MODE(transactions.sessions.customer_id) MODE(transactions.sessions.device)  label
customer_id time                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                
1           2014-01-01 04:00:00    60091                2                            2               desktop                   2077.66                 43.772157                    139.09                  -0.187686                      5.81                  76.950370                   27                                    5                              4                  18              17                 1994             2011                     7                 4                       0                   6                                   12.59                               155.604500                                                 10                               86.730914                                  271.81                                -0.604638                                0.685894                                10.842658                           2.121320                                           0.000000                               18.667619                                4.504270                                 0.747633                                    6.78                                85.469167                                 15                                                  5                                 1052.03                               46.905665                                 0.226337                                      NaN                                       NaN                                 NaN                                                NaN                                       NaN                                      NaN                                      NaN                                70.135333                                 12                                                  5                                 1025.63                               39.825249                                  132.72                                -0.830975                                 6.295000                                 77.802250                           13.500000                                           5.000000                               1038.830000                                43.365457                               135.905000                                 -0.302319                                                  2                                         1                                         1                                          1                                            1                                             1                                  1                                2014                                    1                                      2                                              1                                         2                                        1                            desktop   True
2           2014-01-01 05:00:00    13244                3                            2               desktop                   2605.61                 36.077146                    146.81                  -0.198611                     12.07                  84.051935                   31                                    5                              4                  18              15                 1986             2012                     8                 4                       0                   6                                   90.35                               253.240615                                                 15                              109.500185                                  404.04                                -0.110009                               23.329038                                10.587085                           2.516611                                           0.000000                              203.331699                               14.342521                                 0.242542                                   56.46                                96.581000                                 13                                                  5                                 1004.96                               47.935920                                 0.130019                                 1.397956                                  1.659252                            0.585583                                           0.000000                                 -1.660092                                 1.121470                                -1.083626                                77.304615                                  8                                                  5                                  634.84                               27.839228                                  118.85                                -0.314918                                30.116667                                 84.413538                           10.333333                                           5.000000                                868.536667                                36.500062                               134.680000                                 -0.036670                                                  3                                         1                                         1                                          1                                            1                                             1                                  1                                2014                                    1                                      2                                              1                                         2                                        2                            desktop   True
3           2014-01-01 06:00:00    13244                3                            1               desktop                   1925.82                 37.130891                    128.26                   0.110145                      6.65                  66.407586                   29                                    5                              1                  21              13                 2003             2011                    11                 8                       4                   5                                  118.47                               228.176684                                                 11                               71.871900                                  346.76                                 0.242122                               45.761028                                18.557570                           8.082904                                           2.309401                              477.281339                               20.648490                                 0.580573                                   91.76                                91.760000                                 17                                                  5                                  944.85                               36.167220                                 0.531588                                 1.566223                                 -1.081879                           -0.722109                                          -1.732051                                 -1.705607                                      NaN                                -1.721498                                55.579412                                  1                                                  1                                   91.76                               35.704680                                   91.76                                -0.289466                                39.490000                                 76.058895                            9.666667                                           3.666667                                641.940000                                35.935950                               115.586667                                  0.121061                                                  2                                         1                                         1                                          1                                            1                                             1                                  1                                2014                                    1                                      2                                              1                                         1                                        3                            desktop  False
1           2014-01-01 08:00:00    60091                3                            2                mobile                   3124.15                 38.952172                    139.43                   0.047120                      5.91                  66.471277                   47                                    5                              4                  18              17                 1994             2011                     7                 4                       0                   6                                   24.61                               198.984750                                                 15                              107.128899                                  384.44                                -0.003438                                3.016195                                19.935229                           0.577350                                           0.000000                              330.655558                               10.415432                                 0.906666                                   11.62                                88.755625                                 16                                                  5                                 1420.09                               44.354104                                 0.640252                                 1.443486                                  1.344879                           -1.732051                                           0.000000                                  1.606791                                 1.612576                                 0.846298                                50.623125                                 15                                                  5                                  809.97                               30.450261                                  118.90                                -1.038434                                 8.203333                                 66.328250                           15.666667                                           5.000000                               1041.383333                                35.709633                               128.146667                                 -0.001146                                                  3                                         1                                         1                                          1                                            1                                             1                                  1                                2014                                    1                                      2                                              1                                         2                                        1                             mobile   True

We can see that that the counts for the same feature are lower after we shorten the training window:

In [16]: fm[["COUNT(transactions)"]]
Out[16]: 
                                 COUNT(transactions)
customer_id time                                    
1           2014-01-01 04:00:00                   67
2           2014-01-01 05:00:00                   62
3           2014-01-01 06:00:00                   44
1           2014-01-01 08:00:00                  126

In [17]: window_fm[["COUNT(transactions)"]]
Out[17]: 
                                 COUNT(transactions)
customer_id time                                    
1           2014-01-01 04:00:00                   27
2           2014-01-01 05:00:00                   31
3           2014-01-01 06:00:00                   29
1           2014-01-01 08:00:00                   47

Setting a Last Time Index

The training window in Featuretools limits the amount of past data that can be used while calculating a particular feature vector. A row in the entity is filtered out if the value of its time index is either before or after the training window. This works for entities where a row occurs at a single point in time. However, a row can sometimes exist for a duration.

For example, a customer’s session has multiple transactions which can happen at different points in time. If we are trying to count the number of sessions a user has in a given time period, we often want to count all the sessions that had any transaction during the training window. To accomplish this, we need to not only know when a session starts, but also when it ends. The last time that an instance appears in the data is stored as the last_time_index of an Entity. We can compare the time index and the last time index of the sessions entity above:

In [18]: es['sessions'].df['session_start'].head()
Out[18]: 
1   2014-01-01 00:00:00
2   2014-01-01 00:17:20
3   2014-01-01 00:28:10
4   2014-01-01 00:44:25
5   2014-01-01 01:11:30
Name: session_start, dtype: datetime64[ns]

In [19]: es['sessions'].last_time_index.head()
Out[19]: 
1   2014-01-01 00:16:15
2   2014-01-01 00:27:05
3   2014-01-01 00:43:20
4   2014-01-01 01:10:25
5   2014-01-01 01:22:20
Name: last_time, dtype: datetime64[ns]

Featuretools can automatically add last time indexes to every Entity in an Entityset by running EntitySet.add_last_time_indexes(). If a last_time_index has been set, Featuretools will check to see if the last_time_index is after the start of the training window. That, combined with the cutoff time, allows DFS to discover which data is relevant for a given training window.

Approximating Features by Rounding Cutoff Times

For each unique cutoff time, Featuretools must perform operations to select the data that’s valid for computations. If there are a large number of unique cutoff times relative to the number of instances for which we are calculating features, the time spent filtering data can add up. By reducing the number of unique cutoff times, we minimize the overhead from searching for and extracting data for feature calculations.

One way to decrease the number of unique cutoff times is to round cutoff times to an earlier point in time. An earlier cutoff time is always valid for predictive modeling — it just means we’re not using some of the data we could potentially use while calculating that feature. So, we gain computational speed by losing a small amount of information.

To understand when an approximation is useful, consider calculating features for a model to predict fraudulent credit card transactions. In this case, an important feature might be, “the average transaction amount for this card in the past”. While this value can change every time there is a new transaction, updating it less frequently might not impact accuracy.

Note

The bank BBVA used approximation when building a predictive model for credit card fraud using Featuretools. For more details, see the “Real-time deployment considerations” section of the white paper describing the work involved.

The frequency of approximation is controlled using the approximate parameter to featuretools.dfs() or featuretools.calculate_feature_matrix(). For example, the following code would approximate aggregation features at 1 day intervals:

fm = ft.calculate_feature_matrix(features=features,
                                 entityset=es_transactions,
                                 cutoff_time=ct_transactions,
                                 approximate="1 day")

In this computation, features that can be approximated will be calculated at 1 day intervals, while features that cannot be approximated (e.g “what is the destination of this flight?”) will be calculated at the exact cutoff time.

Secondary Time Index

It is sometimes the case that information in a dataset is updated or added after a row has been created. This means that certain columns may actually become known after the time index for a row. Rather than drop those columns to avoid leaking information, we can create a secondary time index to indicate when those columns become known.

The Flights entityset is a good example of a dataset where column values in a row become known at different times. Each trip is recorded in the trip_logs entity, and has many times associated with it.

In [20]: es_flight = ft.demo.load_flight(nrows=100)
Downloading data ...

In [21]: es_flight
Out[21]: 
Entityset: Flight Data
  Entities:
    trip_logs [Rows: 100, Columns: 21]
    flights [Rows: 13, Columns: 9]
    airlines [Rows: 1, Columns: 1]
    airports [Rows: 6, Columns: 3]
  Relationships:
    trip_logs.flight_id -> flights.flight_id
    flights.carrier -> airlines.carrier
    flights.dest -> airports.dest

In [22]: es_flight['trip_logs'].df.head(3)
Out[22]: 
    trip_log_id        flight_id date_scheduled  scheduled_dep_time  scheduled_arr_time            dep_time            arr_time  dep_delay  taxi_out  taxi_in  arr_delay  scheduled_elapsed_time  air_time  distance  carrier_delay  weather_delay  national_airspace_delay  security_delay  late_aircraft_delay  canceled  diverted
30           30  AA-494:RSW->CLT     2016-09-03 2017-01-01 13:14:00 2017-01-01 15:05:00 2017-01-01 13:03:00 2017-01-01 14:53:00      -11.0      12.0     10.0      -12.0           6660000000000      88.0     600.0            0.0            0.0                      0.0             0.0                  0.0       0.0       0.0
38           38  AA-495:ATL->PHX     2016-09-03 2017-01-01 11:30:00 2017-01-01 15:40:00 2017-01-01 11:24:00 2017-01-01 15:41:00       -6.0      28.0      5.0        1.0          15000000000000     224.0    1587.0            0.0            0.0                      0.0             0.0                  0.0       0.0       0.0
46           46  AA-495:CLT->ATL     2016-09-03 2017-01-01 09:25:00 2017-01-01 10:42:00 2017-01-01 09:23:00 2017-01-01 10:39:00       -2.0      18.0      8.0       -3.0           4620000000000      50.0     226.0            0.0            0.0                      0.0             0.0                  0.0       0.0       0.0

For every trip log, the time index is date_scheduled, which is when the airline decided on the scheduled departure and arrival times, as well as what route will be flown. We don’t know the rest of the information about the actual departure/arrival times and the details of any delay at this time. However, it is possible to know everything about how a trip went after it has arrived, so we can use that information at any time after the flight lands.

Using a secondary time index, we can indicate to Featuretools which columns in our flight logs are known at the time the flight is scheduled, plus which are known at the time the flight lands.

flight secondary time index diagram

In Featuretools, when creating the entity, we set the secondary time index to be the arrival time like this:

es = ft.EntitySet('Flight Data')
arr_time_columns = ['arr_delay', 'dep_delay', 'carrier_delay', 'weather_delay',
                    'national_airspace_delay', 'security_delay',
                    'late_aircraft_delay', 'canceled', 'diverted',
                    'taxi_in', 'taxi_out', 'air_time', 'dep_time']

es.entity_from_dataframe('trip_logs',
                         data,
                         index='trip_log_id',
                         make_index=True,
                         time_index='date_scheduled',
                         secondary_time_index={'arr_time': arr_time_columns})

By setting a secondary time index, we can still use the delay information from a row, but only when it becomes known.

Hint

It’s often a good idea to use a secondary time index if your entityset has inline labels. If you know when the label would be valid for use, it’s possible to automatically create very predictive features using historical labels.

Flight Predictions

Let’s make some features at varying times using the flight example described above. Trip 14 is a flight from CLT to PHX on January 31, 2017 and trip 92 is a flight from PIT to DFW on January 1. We can set any cutoff time before the flight is scheduled to depart, emulating how we would make the prediction at that point in time.

We set two cutoff times for trip 14 at two different times: one which is more than a month before the flight and another which is only 5 days before. For trip 92, we’ll only set one cutoff time, three days before it is scheduled to leave.

flight cutoff time diagram

Our cutoff time dataframe looks like this:

In [23]: ct_flight = pd.DataFrame()

In [24]: ct_flight['trip_log_id'] = [14, 14, 92]

In [25]: ct_flight['time'] = pd.to_datetime(['2016-12-28',
   ....:                                     '2017-1-25',
   ....:                                     '2016-12-28'])
   ....: 

In [26]: ct_flight['label'] = [True, True, False]

In [27]: ct_flight
Out[27]: 
   trip_log_id       time  label
0           14 2016-12-28   True
1           14 2017-01-25   True
2           92 2016-12-28  False

Now, let’s calculate the feature matrix:

In [28]: fm, features = ft.dfs(entityset=es_flight,
   ....:                       target_entity='trip_logs',
   ....:                       cutoff_time=ct_flight,
   ....:                       cutoff_time_in_index=True,
   ....:                       agg_primitives=["max"],
   ....:                       trans_primitives=["month"],)
   ....: 

In [29]: fm[['flight_id', 'label', 'flights.MAX(trip_logs.arr_delay)', 'MONTH(scheduled_dep_time)']]
Out[29]: 
                              flight_id  label  flights.MAX(trip_logs.arr_delay)  MONTH(scheduled_dep_time)
trip_log_id time                                                                                           
14          2016-12-28  AA-494:CLT->PHX   True                               NaN                          1
            2017-01-25  AA-494:CLT->PHX   True                              33.0                          1
92          2016-12-28  AA-496:PIT->DFW  False                               NaN                          1

Let’s understand the output:

  1. A row was made for every id-time pair in ct_flight, which is returned as the index of the feature matrix.

  2. The output was sorted by cutoff time. Because of the sorting, it’s often helpful to pass in a label with the cutoff time dataframe so that it will remain sorted in the same fashion as the feature matrix. Any additional columns beyond id and cutoff_time will not be used for making features.

  3. The column flights.MAX(trip_logs.arr_delay) is not always defined. It can only have any real values when there are historical flights to aggregate. Notice that, for trip 14, there wasn’t any historical data when we made the feature a month in advance, but there were flights to aggregate when we shortened it to 5 days. These are powerful features that are often excluded in manual processes because of how hard they are to make.

Creating and Flattening a Feature Tensor

The make_temporal_cutoffs() function generates a series of equally spaced cutoff times from a given set of cutoff times and instance ids.

This function can be paired with DFS to create and flatten a feature tensor rather than making multiple feature matrices at different delays.

The function takes in the the following parameters:

  • instance_ids (list, pd.Series, or np.ndarray): A list of instances.

  • cutoffs (list, pd.Series, or np.ndarray): An associated list of cutoff times.

  • window_size (str or pandas.DateOffset): The amount of time between each cutoff time in the created time series.

  • start (datetime.datetime or pd.Timestamp): The first cutoff time in the created time series.

  • num_windows (int): The number of cutoff times to create in the created time series.

Only two of the three options window_size, start, and num_windows need to be specified to uniquely determine an equally-spaced set of cutoff times at which to compute each instance.

If your cutoff times are the ones used above:

In [30]: cutoff_times
Out[30]: 
   customer_id                time  label
0            1 2014-01-01 04:00:00   True
1            2 2014-01-01 05:00:00   True
2            3 2014-01-01 06:00:00  False
3            1 2014-01-01 08:00:00   True

Then passing in window_size='1h' and num_windows=2 makes one row an hour over the last two hours to produce the following new dataframe. The result can be directly passed into DFS to make features at the different time points.

In [31]: temporal_cutoffs = ft.make_temporal_cutoffs(cutoff_times['customer_id'],
   ....:                                             cutoff_times['time'],
   ....:                                             window_size='1h',
   ....:                                             num_windows=2)
   ....: 

In [32]: temporal_cutoffs
Out[32]: 
                 time  instance_id
0 2014-01-01 03:00:00            1
1 2014-01-01 04:00:00            1
2 2014-01-01 04:00:00            2
3 2014-01-01 05:00:00            2
4 2014-01-01 05:00:00            3
5 2014-01-01 06:00:00            3
6 2014-01-01 07:00:00            1
7 2014-01-01 08:00:00            1

In [33]: fm, features = ft.dfs(entityset=es,
   ....:                       target_entity='customers',
   ....:                       cutoff_time=temporal_cutoffs,
   ....:                       cutoff_time_in_index=True)
   ....: 

In [34]: fm
Out[34]: 
                                zip_code  COUNT(sessions)  NUM_UNIQUE(sessions.device) MODE(sessions.device)  SUM(transactions.amount)  STD(transactions.amount)  MAX(transactions.amount)  SKEW(transactions.amount)  MIN(transactions.amount)  MEAN(transactions.amount)  COUNT(transactions)  NUM_UNIQUE(transactions.product_id)  MODE(transactions.product_id)  DAY(date_of_birth)  DAY(join_date)  YEAR(date_of_birth)  YEAR(join_date)  MONTH(date_of_birth)  MONTH(join_date)  WEEKDAY(date_of_birth)  WEEKDAY(join_date)  SUM(sessions.MIN(transactions.amount))  SUM(sessions.MEAN(transactions.amount))  SUM(sessions.NUM_UNIQUE(transactions.product_id))  SUM(sessions.STD(transactions.amount))  SUM(sessions.MAX(transactions.amount))  SUM(sessions.SKEW(transactions.amount))  STD(sessions.MIN(transactions.amount))  STD(sessions.MEAN(transactions.amount))  STD(sessions.COUNT(transactions))  STD(sessions.NUM_UNIQUE(transactions.product_id))  STD(sessions.SUM(transactions.amount))  STD(sessions.MAX(transactions.amount))  STD(sessions.SKEW(transactions.amount))  MAX(sessions.MIN(transactions.amount))  MAX(sessions.MEAN(transactions.amount))  MAX(sessions.COUNT(transactions))  MAX(sessions.NUM_UNIQUE(transactions.product_id))  MAX(sessions.SUM(transactions.amount))  MAX(sessions.STD(transactions.amount))  MAX(sessions.SKEW(transactions.amount))  SKEW(sessions.MIN(transactions.amount))  SKEW(sessions.MEAN(transactions.amount))  SKEW(sessions.COUNT(transactions))  SKEW(sessions.NUM_UNIQUE(transactions.product_id))  SKEW(sessions.SUM(transactions.amount))  SKEW(sessions.STD(transactions.amount))  SKEW(sessions.MAX(transactions.amount))  MIN(sessions.MEAN(transactions.amount))  MIN(sessions.COUNT(transactions))  MIN(sessions.NUM_UNIQUE(transactions.product_id))  MIN(sessions.SUM(transactions.amount))  MIN(sessions.STD(transactions.amount))  MIN(sessions.MAX(transactions.amount))  MIN(sessions.SKEW(transactions.amount))  MEAN(sessions.MIN(transactions.amount))  MEAN(sessions.MEAN(transactions.amount))  MEAN(sessions.COUNT(transactions))  MEAN(sessions.NUM_UNIQUE(transactions.product_id))  MEAN(sessions.SUM(transactions.amount))  MEAN(sessions.STD(transactions.amount))  MEAN(sessions.MAX(transactions.amount))  MEAN(sessions.SKEW(transactions.amount))  NUM_UNIQUE(sessions.MODE(transactions.product_id))  NUM_UNIQUE(sessions.DAY(session_start))  NUM_UNIQUE(sessions.YEAR(session_start))  NUM_UNIQUE(sessions.MONTH(session_start))  NUM_UNIQUE(sessions.WEEKDAY(session_start))  MODE(sessions.MODE(transactions.product_id))  MODE(sessions.DAY(session_start))  MODE(sessions.YEAR(session_start))  MODE(sessions.MONTH(session_start))  MODE(sessions.WEEKDAY(session_start))  NUM_UNIQUE(transactions.sessions.customer_id)  NUM_UNIQUE(transactions.sessions.device)  MODE(transactions.sessions.customer_id) MODE(transactions.sessions.device)
customer_id time                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         
1           2014-01-01 03:00:00    60091                3                            3               desktop                   3932.56                 42.769602                    139.23                   0.140387                      5.81                  71.501091                   55                                    5                              1                  18              17                 1994             2011                     7                 4                       0                   6                                   20.84                               219.132533                                                 15                              129.747625                                  400.95                                 0.325932                                1.571507                                10.255607                           5.773503                                                0.0                              283.551883                                5.178021                                 0.210827                                    8.74                                84.440000                                 25                                                  5                                 1613.93                               46.905665                                 0.234349                                 1.552040                                  1.173675                            1.732051                                                0.0                                  0.685199                                 0.763052                                 0.782152                                64.557200                                 15                                                  5                                 1052.03                               40.187205                                  129.00                                -0.134754                                 6.946667                                 73.044178                           18.333333                                                  5                               1310.853333                                43.249208                               133.650000                                  0.108644                                                  3                                         1                                         1                                          1                                            1                                             1                                  1                                2014                                    1                                      2                                              1                                         3                                        1                             mobile
            2014-01-01 04:00:00    60091                4                            3                tablet                   4958.19                 42.309717                    139.23                  -0.006928                      5.81                  74.002836                   67                                    5                              4                  18              17                 1994             2011                     7                 4                       0                   6                                   27.62                               304.601700                                                 20                              169.572874                                  540.04                                -0.505043                                1.285833                                10.426572                           5.678908                                                0.0                              271.917637                                5.027226                                 0.500353                                    8.74                                85.469167                                 25                                                  5                                 1613.93                               46.905665                                 0.234349                                 1.452325                                 -0.233453                            1.614843                                                0.0                                  1.197406                                 1.235445                                -0.451371                                64.557200                                 12                                                  5                                 1025.63                               39.825249                                  129.00                                -0.830975                                 6.905000                                 76.150425                           16.750000                                                  5                               1239.547500                                42.393218                               135.010000                                 -0.126261                                                  3                                         1                                         1                                          1                                            1                                             4                                  1                                2014                                    1                                      2                                              1                                         3                                        1                             tablet
2           2014-01-01 04:00:00    13244                4                            2               desktop                   4150.30                 39.289512                    146.81                  -0.134786                     12.07                  84.700000                   49                                    5                              4                  18              15                 1986             2012                     8                 4                       0                   6                                  105.24                               340.791792                                                 20                              157.262738                                  569.29                                 0.045171                               20.424007                                 8.983533                           3.862210                                                0.0                              307.743859                                3.470527                                 0.324809                                   56.46                                96.581000                                 16                                                  5                                 1320.64                               47.935920                                 0.295458                                 1.815491                                  0.651941                           -0.169238                                                0.0                                 -0.823347                                -0.966834                                 0.459305                                76.813125                                  8                                                  5                                  634.84                               27.839228                                  138.38                                -0.455197                                26.310000                                 85.197948                           12.250000                                                  5                               1037.575000                                39.315685                               142.322500                                  0.011293                                                  3                                         1                                         1                                          1                                            1                                             2                                  1                                2014                                    1                                      2                                              1                                         2                                        2                            desktop
            2014-01-01 05:00:00    13244                5                            2               desktop                   5155.26                 38.047944                    146.81                  -0.121811                     12.07                  83.149355                   62                                    5                              4                  18              15                 1986             2012                     8                 4                       0                   6                                  127.06                               418.096407                                                 25                              190.987775                                  688.14                                -0.269747                               17.801322                                 8.543351                           3.361547                                                0.0                              266.912832                               10.919023                                 0.316873                                   56.46                                96.581000                                 16                                                  5                                 1320.64                               47.935920                                 0.295458                                 1.959531                                  1.082192                           -0.379092                                                0.0                                 -0.667256                                -0.213518                                -1.814717                                76.813125                                  8                                                  5                                  634.84                               27.839228                                  118.85                                -0.455197                                25.412000                                 83.619281                           12.400000                                                  5                               1031.052000                                38.197555                               137.628000                                 -0.053949                                                  4                                         1                                         1                                          1                                            1                                             2                                  1                                2014                                    1                                      2                                              1                                         2                                        2                            desktop
3           2014-01-01 05:00:00    13244                2                            2               desktop                   1886.72                 41.199361                    146.31                   0.637074                      6.65                  58.960000                   32                                    5                              1                  21              13                 2003             2011                    11                 8                       4                   5                                   14.84                               118.370745                                                 10                               83.432017                                  273.05                                 1.150043                                1.088944                                 5.099599                           1.414214                                                0.0                                2.107178                               13.838080                                 0.061424                                    8.19                                62.791333                                 17                                                  5                                  944.85                               47.264797                                 0.618455                                      NaN                                       NaN                                 NaN                                                NaN                                       NaN                                      NaN                                      NaN                                55.579412                                 15                                                  5                                  941.87                               36.167220                                  126.74                                 0.531588                                 7.420000                                 59.185373                           16.000000                                                  5                                943.360000                                41.716008                               136.525000                                  0.575022                                                  1                                         1                                         1                                          1                                            1                                             1                                  1                                2014                                    1                                      2                                              1                                         2                                        3                            desktop
            2014-01-01 06:00:00    13244                4                            2               desktop                   2867.69                 40.349758                    146.31                   0.318315                      6.65                  65.174773                   44                                    5                              1                  21              13                 2003             2011                    11                 8                       4                   5                                  126.66                               290.968018                                                 16                              119.136697                                  493.07                                 0.860577                               40.508892                                16.540737                           7.118052                                                2.0                              417.557763                               22.808351                                 0.500999                                   91.76                                91.760000                                 17                                                  5                                  944.85                               47.264797                                 0.618455                                 1.874170                                  0.201588                           -1.330938                                               -2.0                                 -1.977878                                 1.722323                                -1.060639                                55.579412                                  1                                                  1                                   91.76                               35.704680                                   91.76                                -0.289466                                31.665000                                 72.742004                           11.000000                                                  4                                716.922500                                39.712232                               123.267500                                  0.286859                                                  2                                         1                                         1                                          1                                            1                                             1                                  1                                2014                                    1                                      2                                              1                                         2                                        3                            desktop
1           2014-01-01 07:00:00    60091                7                            3                tablet                   7605.53                 41.018896                    139.43                   0.149908                      5.81                  69.141182                  110                                    5                              4                  18              17                 1994             2011                     7                 4                       0                   6                                   66.97                               493.437492                                                 35                              280.421418                                  931.86                                 0.562312                                7.470707                                13.123365                           4.386125                                                0.0                              273.713405                                7.441648                                 0.471955                                   26.36                                85.469167                                 25                                                  5                                 1613.93                               46.905665                                 0.640252                                 2.552328                                 -0.282093                            1.927658                                                0.0                                  1.377768                                -0.755846                                -1.277394                                50.623125                                 12                                                  5                                  809.97                               30.450261                                  118.90                                -0.830975                                 9.567143                                 70.491070                           15.714286                                                  5                               1086.504286                                40.060203                               133.122857                                  0.080330                                                  4                                         1                                         1                                          1                                            1                                             1                                  1                                2014                                    1                                      2                                              1                                         3                                        1                             tablet
            2014-01-01 08:00:00    60091                8                            3                mobile                   9025.62                 40.442059                    139.43                   0.019698                      5.81                  71.631905                  126                                    5                              4                  18              17                 1994             2011                     7                 4                       0                   6                                   78.59                               582.193117                                                 40                              312.745952                                 1057.97                                -0.476122                                6.954507                                13.759314                           4.062019                                                0.0                              279.510713                                7.322191                                 0.589386                                   26.36                                88.755625                                 25                                                  5                                 1613.93                               46.905665                                 0.640252                                 2.440005                                 -0.424949                            1.946018                                                0.0                                  0.778170                                -0.312355                                -0.780493                                50.623125                                 12                                                  5                                  809.97                               30.450261                                  118.90                                -1.038434                                 9.823750                                 72.774140                           15.750000                                                  5                               1128.202500                                39.093244                               132.246250                                 -0.059515                                                  4                                         1                                         1                                          1                                            1                                             4                                  1                                2014                                    1                                      2                                              1                                         3                                        1                             mobile