5. Multi-label data stratification¶

With the development of more complex multi-label transformation methods the community realizes how much the quality of classification depends on how the data is split into train/test sets or into folds for parameter estimation. More questions appear on stackoverflow or crossvalidated concerning methods for multi-label stratification.

For many reasons, described here and here traditional single-label approaches to stratifying data fail to provide balanced data set divisions which prevents classifiers from generalizing information.

Some train/test splits don’t include evidence for a given label at all in the train set. others disproportionately put even as much as 70% of label pair evidence in the test set, leaving the train set without proper evidence for generalizing conditional probabilities for label relations.

You can also watch a great video presentation from ECML 2011 which explains this in depth:

On the Stratification of Multi-Label Data Grigorios Tsoumakas

Scikit-multilearn provides an implementation of iterative stratification which aims to provide well-balanced distribution of evidence of label relations up to a given order. To see what it means, let’s load up some data. We’ll be using the scene data set, both in divided and undivided variants, to illustrate the problem.

In [263]:

from skmultilearn.dataset import load_dataset
X,y, _, _ = load_dataset('scene', 'undivided')

scene:undivided - exists, not redownloading

Let’s look at how many examples are available per label combination:

In [264]:

from skmultilearn.model_selection.measures import get_combination_wise_output_matrix

In [265]:

Counter(combination for row in get_combination_wise_output_matrix(y.A, order=2) for combination in row)

Out[265]:

Counter({(0, 0): 427,
         (0, 3): 1,
         (0, 4): 38,
         (0, 5): 19,
         (1, 1): 364,
         (2, 2): 397,
         (2, 3): 24,
         (2, 4): 14,
         (3, 3): 433,
         (3, 4): 76,
         (3, 5): 6,
         (4, 4): 533,
         (4, 5): 1,
         (5, 5): 431})

Let’s load up the original division, to see how the set was split into train/test data in 2004, before multi-label stratification methods appeared.

In [266]:

_, original_y_train, _, _ = load_dataset('scene', 'train')
_, original_y_test, _, _ = load_dataset('scene', 'test')

scene:train - exists, not redownloading
scene:test - exists, not redownloading

In [267]:

import pandas as pd

In [268]:

pd.DataFrame({
    'train': Counter(str(combination) for row in get_combination_wise_output_matrix(original_y_train.A, order=2) for combination in row),
    'test' : Counter(str(combination) for row in get_combination_wise_output_matrix(original_y_test.A, order=2) for combination in row)
}).T.fillna(0.0)

Out[268]:

In [269]:

original_y_train.shape[0], original_y_test.shape[0]

Out[269]:

(1211, 1196)

We can see that the split size is nearly identical, yet some label combination evidence is well balanced between the splits. While this is a toy case on a small data set, such phenomena are common in larger datasets. We would like to fix this.

Let’s load the iterative stratifier and divided the set again.

In [270]:

from skmultilearn.model_selection import iterative_train_test_split

In [278]:

X_train, y_train, X_test, y_test = iterative_train_test_split(X, y, test_size = 0.5)

In [279]:

pd.DataFrame({
    'train': Counter(str(combination) for row in get_combination_wise_output_matrix(y_train.A, order=2) for combination in row),
    'test' : Counter(str(combination) for row in get_combination_wise_output_matrix(y_test.A, order=2) for combination in row)
}).T.fillna(0.0)

Out[279]:

We can see that the new division is much more balanced.