In the wake of recent advances in experimental methods in neuroscience, the ability to record in-vivo neuronal activity from awake animals has become feasible. The availability of such rich and detailed physiological measurements calls for the development of advanced data analysis tools, as commonly used techniques do not suffice to capture the spatio-temporal network complexity. In this paper, we propose a new hierarchical coupled-geometry analysis that implicitly takes into account the connectivity structures between neurons and the dynamic patterns at multiple time scales. Our approach gives rise to the joint organization of neurons and dynamic patterns in data-driven hierarchical data structures. These structures provide local to global data representations, from local partitioning of the data in flexible trees through a new multiscale metric to a global manifold embedding. The application of our techniques to in-vivo neuronal recordings demonstrate the capability of extracting neuronal activity patterns and identifying temporal trends, associated with particular behavioral events and manipulations introduced in the experiments.
These methods share significant drawbacks, as they are mostly heuristic, providing only an approximation of a largely unknown system, and their quality is often hard to assess @cite_0 . More importantly, they are all prone to the curse of dimensionality". On the one hand, designing a parametric generative model for truly complex high-dimensional data, such as neuronal behavioral recordings, requires considerable flexibility, resulting in a model with a large number of tunable parameters. On the other hand, estimating a large number of parameters, and fitting a predefined class of dynamical models to high-dimensional data, is practically infeasible, thereby leading to poor data representations. Our approach is better designed to deal with dynamical systems and aims to alleviate the shortcomings present in current analysis methods. The proposed framework deviates from common recently used in neuroscience as it makes only very general smoothness assumptions, rather than postulating a-priori specific structural models. In addition, we show that it takes into consideration the high dimensional spatio-temporal neuronal network structure.
@cite_0
2017539895
Most sensory, cognitive and motor functions depend on the interactions of many neurons. In recent years, there has been rapid development and increasing use of technologies for recording from large numbers of neurons, either sequentially or simultaneously. A key question is what scientific insight can be gained by studying a population of recorded neurons beyond studying each neuron individually. Here, we examine three important motivations for population studies: single-trial hypotheses requiring statistical power, hypotheses of population response structure and exploratory analyses of large data sets. Many recent studies have adopted dimensionality reduction to analyze these populations and to find features that are not apparent at the level of individual neurons. We describe the dimensionality reduction methods commonly applied to population activity and offer practical advice about selecting methods and interpreting their outputs. This review is intended for experimental and computational researchers who seek to understand the role dimensionality reduction has had and can have in systems neuroscience, and who seek to apply these methods to their own data.