A Machine Learning Exploration of Topological Data Analysis Applied to Low and High Dimensional fMRI Data

With recent advances in technology, data has become more plentiful and pervasive in many fields. With this increase in data availability, novel data analysis methods are necessary to make sense of underlying patterns within the data. One relatively recent analysis technique is Topological Data Analysis (TDA), which imposes a geometric structure upon a data set, and then uses the “shape” of the structure to describe the data. Machine Learning (ML) is another form of analysis, where a computer can “learn” distinguishing features of data through various algorithms.

We apply TDA to functional magnetic resonance imaging (fMRI) brain scan data. Our data, provided by the Nopoulos Lab at the University of Iowa, contains the fMRI scans of healthy children and children who will develop Huntington’s disease (HD), a neurodegenerative disease that currently has no cure. For each patient, we use the fMRI data to build a model of the brain that measures how different areas of the brain interact. Then, for each model, we compute topological features which describe the “shape” of the model. We compare the topological features of the healthy controls to the features obtained from the children who will develop HD using ML.

We discuss our findings on a “small” data set, where only a few brain regions were studied, as well as exploratory results on “large” data, where we studied the full brain. We also describe the successes and pitfalls of our particular data analysis methods, with the goal of determining the usefulness of TDA combined with ML when applied to fMRI data.