Computational neuroscience between machine learning and topology

The field of computational neuroscience and neuroimaging is showing a great interest in the application of statistical and mathematical techniques to represent and study complex brain structures. Neural data is complicated and, as the field of brain connectomics has developed, new techniques to represent and analyze the human connectome to obtain a description of the brain's structural and functional connections emerged. There exist different imaging techniques to acquire measurements of brain structure and activity, such as electroencephalography, magnetoencephalography, calcium imaging or functional magnetic resonance imaging. One of the main challenges in neuroscience consists in understanding the global brain organization and the correlation that exists among different brain measurements. Network theory and analysis is often used to address these kinds of problems, as the functional or structural connectivity between each pair of brain regions can be expressed, in matrix form, in terms of the correlation between the time series data or the morphometric feature vectors of the two regions in question. These matrices, called connectivity matrices, can be investigated to analyze network-level properties of the brain and can reveal biomarkers of subjects' clinical traits. In this work, we use structural data to construct morphometric similarity matrices based on inter-regional similarity of multiple morphometric features measured using multimodal MRI. We first investigate strengths and short-comings of different measures of correlation used to construct these matrices: correlation, partial correlation or more complex geometrical models such as the tangent space parametrization and the Riemannian geometry. Then, we investigate the application of predictive models on one side and of topological data analysis on the other side. The former refers to the use of machine learning pipelines that link the structural connectomes to the prediction of a target phenotype addressing both classification and regression tasks. Dealing with very high-dimensional datasets, we also inspect both data-driven and hypothesis-driven dimensionality reduction techniques. The latter consists in inspecting the geometric relations in the data using topological data analysis techniques and focusing on persistent homology to detect statistical differences among the groups. In this way, we can show the potentiality of this tool as an alternative for data analysis and, comparing the obtained results, we can demonstrate its powerfulness in the understanding of data and the detection of important differences among subgroups even in cases in which traditional Machine Learning techniques are not able to find signals and meaningful results.