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

Area of Science:

• Neuroscience
• Data Science
• Computational Mathematics

Background:

• Supervised machine learning excels at classification but often lacks interpretability regarding data structure and underlying phenomena.
• Topological Data Analysis (TDA) quantitatively characterizes data shape using persistence descriptors, offering insights into complex datasets.

Purpose of the Study:

• Introduce a novel TDA-based classifier for analyzing complex datasets.
• Assess the classifier's performance and interpretability using electro-encephalographic (EEG) data from a decision-making experiment.

Main Methods:

• Developed a TDA classifier based on quantifying topological metric changes with new data inputs.
• Applied the classifier to high-dimensional EEG data from participants experiencing different motivational states.
• Calculated persistence diagram silhouettes for each state and classified unlabeled signals based on silhouette impact.

Main Results:

• The TDA classifier achieved accuracies comparable to nearest neighbor classifiers.
• The TDA approach provided formal intuition about the dataset's structure and intrinsic dimensionality.
• Classifier accuracy remained stable across varying dimensions after incorporating variance-based dimensionality reduction.

Conclusions:

• TDA offers a powerful, interpretable alternative to traditional machine learning for complex data analysis.
• The novel TDA classifier demonstrates potential for uncovering hidden structures and phenomena in high-dimensional data.
• The method's robustness to dimensionality reduction highlights its suitability for diverse datasets.