  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.
