Hierarchical Coupled Geometry Analysis for Neuronal Structure and Activity Pattern Discovery

A fundamental goal in neuroscience is to understand how information is represented, stored and modified in cortical networks. New experimental methods in neuroscience not only enable chronic, minimally invasive, recordings of large populations of neurons with cellular level resolution, but also allow recordings from identified neuronal subtypes [1]. The ability to acquire complex large-scale detailed behavioral and neuronal datasets calls for the development of advanced data analysis tools, as commonly used techniques do not suffice to capture the spatiotemporal network complexity. Such a framework should deal effectively with the challenging characteristics of neuronal and behavioral data, namely connectivity structures between neurons and dynamic patterns at multiple timescales. Due to natural and physical constraints, the accessible highdimensional data often exhibit geometric structures and lie on a low-dimensional manifold. Manifold learning is a class of data driven methods; these methods aim to find meaningful geometry-based nonlinear representations that parametrize the manifold underlying the data [2]-[6]. Only very recently have we begun to witness seeds of its applicability to real biological data, and, in particular, to neuroscience (e.g., [7], [8]).