CLASSICALLY

Classifier Comparison and Feature Analysis Tools in Python

A python package for the evaluation of classification performance.

Installation

Classically is published on PyPi so you can install it with pip.

>>> python -m pip install classically

Applications

Critical Difference Diagram

A main application is the comparison of categorized paired metric data, e.g. accuracy results of different classification methods in machine learning. Therefore Classically implements the critical difference diagram (described in [1]).

Example

Imagine that we have five different classification methods tested on 14 different datasets. Every classifiers returns an accuracy result on each test set in the corresponding dataset. We collect the results in a table like this:

Classifier
A	0.60	0.81	0.62	0.19	0.93	0.54	0.53	0.41	0.21	0.97	0.32	0.82	0.38	0.75
B	0.33	0.68	0.43	0.23	0.90	0.43	0.32	0.20	0.22	0.86	0.21	0.82	0.41	0.73
C	0.25	0.64	0.40	0.10	0.85	0.39	0.31	0.19	0.18	0.90	0.23	0.78	0.43	0.71
D	0.64	0.84	0.60	0.26	0.95	0.60	0.36	0.37	0.19	0.95	0.44	0.84	0.41	0.84
E	0.37	0.68	0.47	0.18	0.88	0.37	0.27	0.25	0.24	0.79	0.25	0.83	0.36	0.64

We load this table in a numpy array of shape (5, 14) and call the function classically.critical_difference_diagram. The resulting plot can be seen below.

Markings on this number line represent the average ranks of one classifier based on his accuracy over all datasets. The lowest rank corresponds to the highest accuracy. Classifiers are connected by a horizontal line if they do not have a significant difference. This significance is based on post-hoc Wilcoxon signed rank tests for each pair of classifiers.

Therefore, it seems like classifier D is the best choice for the overall classification task. It works best on the 14 chosen datasets, altough it's not the best classfier for every single dataset on its own. But we can also see, that there is no significant (alpha=0.05) difference in the accuracy results of classifier D and A. If D would be much more computationally expensive than A, then we should consider choosing A as the better classifier.

Scatter Matrix

For an in-depth comparison of the classifiers on single datasets a special type of scatter matrix that is designed to compare multiple categories of data can be found in Classically.

Example

For a more elaborate decision in the example above we could directly compare the best three classifiers A, B and D using the function classically.scatter_comparison.

Points above the diagonal line represent datasets that are better classified by the method in the upper left corner. A horizontal and vertical line indicates the mean accuracy of the corresponding classifier. A solid line marks the higher mean. A choice can now be easily made for the comparison of classifier A and B as well as B and D. We also see that D is better than A in mean accuracy but that A has a big advantage on one dataset that is well beyond the diagonal line for five percent difference. The datasets could now be further analyzed by, for example, looking at the number of training and test instances. An option for setting the opacity value of points in the scatterplots accordingly is available.

Feature Score

Evaluating the importance of features in data can be very helpful in reducing the dimensionality of the feature space. While principal component analysis transforms original features into new ones, it can also be used to creating a ranking of those features. Classically is able to compute the feature score for a given dataset.

Example

We can analyze the importance of the four features in the well-known IRIS dataset by using the method classically.plot_feature_score.

The plot shows the normalized feature score. The 'most important' feature based on that score is 'petal length (cm)'. All other features then have a relatively low score, e.g. sepal length's score is about 80% lower. The red markings show the accuracy results of a ridge classifier where only the first n features (in descending score order) are used (n gets incremented with each step on the x-axis).

References

[1] Demšar, Janez (2006). "Statistical comparisons of classifiers over multiple data sets." The Journal of Machine learning research 7, 1-30.