A topological classifier to characterize brain states: When shape matters more than variance

Despite the remarkable accuracies attained by machine learning classifiers to separate complex datasets in a supervised fashion, most of their operation falls short to provide an informed intuition about the structure of data, and, what is more important, about the phenomena being characterized by the given datasets. By contrast, topological data analysis (TDA) is devoted to study the shape of data clouds by means of persistence descriptors and provides a quantitative characterization of specific topological features of the dataset under scrutiny. In this article we introduce a novel TDA-based classifier that works on the principle of assessing quantifiable changes on topological metrics caused by the addition of new input to a subset of data. We used this classifier with a high-dimensional electro-encephalographic (EEG) dataset recorded from eleven participants during a decision-making experiment in which three motivational states were induced through a manipulation of social pressure. After processing a band-pass filtered version of EEG signals, we calculated silhouettes from persistence diagrams associated with each motivated state, and classified unlabeled signals according to their impact on each reference silhouette. Our results show that in addition to providing accuracies within the range of those of a nearest neighbour classifier, the TDA classifier provides formal intuition of the structure of the dataset as well as an estimate of its intrinsic dimension. Towards this end, we incorporated dimensionality reduction methods to our procedure and found that the accuracy of our TDA classifier is generally not sensitive to explained variance but rather to shape, contrary to what happens with most machine learning classifiers.