Topology preservation under dimensionality reduction during neural manifold discovery

Abstract

[en] One of the main challenges that neuroscience faces nowadays is to understand how the brain represents different stimuli. This involves dealing with large amounts of data, which are usually high-dimensional and have to be processed to unveil how they are related with the associated cognitive processes. This work describes methods to preserve the topology of recorded data when their dimensionality is reduced, using predictions from neural coding theory. Relevant dimensionality reduction techniques are exposed, along with a couple of examples where persistent homology is crucial to discriminate the resulting neural manifold from being a circle or a torus. It is impossible to infer this from dimensionality reduction alone. Thus, to combine both techniques is essential for the manifold’s parameterization and the subsequent variable decoding to be successful.