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

arXiv: https://arxiv.org/abs/2303.04231 · HTML: https://mlsanity.com/paper/2303.04231/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 61 references that are in the map.
- First posted on arXiv 7 Mar 2023.

## Builds on (most cited first, 11 of 11)

- [Deep Neural Networks are Easily Fooled: High Confidence Predictions for Unrecognizable Images](https://mlsanity.com/paper/1412.1897/) (2014)
- [Deep learning to represent sub-grid processes in climate models](https://mlsanity.com/paper/1806.04731/) (2018)
- [A roadmap for the computation of persistent homology](https://mlsanity.com/paper/1506.08903/) (2015)
- [Deep Learning with Topological Signatures](https://mlsanity.com/paper/1707.04041/) (2017)
- [Stochastic Convergence of Persistence Landscapes and Silhouettes](https://mlsanity.com/paper/1312.0308/) (2013)
- [A persistence landscapes toolbox for topological statistics](https://mlsanity.com/paper/1501.00179/) (2014)
- [Adversary Detection in Neural Networks via Persistent Homology](https://mlsanity.com/paper/1711.10056/) (2017)
- [The importance of the whole: topological data analysis for the network neuroscientist](https://mlsanity.com/paper/1806.05167/) (2018)
- [Classification based on Topological Data Analysis](https://mlsanity.com/paper/2102.03709/) (2021)
- [A Topological Data Analysis Based Classifier](https://mlsanity.com/paper/2111.05214/) (2021)
- [Semi-Supervised Machine Learning: a Homological Approach](https://mlsanity.com/paper/2301.11658/) (2023)

## Built on by (most cited first, 1 of 1)

- [Train-Free Segmentation in MRI with Cubical Persistent Homology](https://mlsanity.com/paper/2401.01160/) (2024)

## Abstract (arXiv)

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.