Density-based clustering: A 'landscape view' of multi-channel neural data for inference and dynamic complexity analysis

TL;DR

This paper introduces a density-based clustering method for multi-channel neural data, enabling efficient analysis of neural dynamics, metastable states, and complexity, with applications to neural network models and real spiking networks.

Contribution

It develops a novel clustering approach using mean-shift for neural data, and extends learning and complexity analysis techniques for multi-modular spiking networks.

Findings

Effective clustering of neural states in high-dimensional space.

Improved inference of synaptic couplings from neural activity.

Demonstration of complexity measures related to neural adaptation effects.

Abstract

Simultaneous recordings from N electrodes generate N-dimensional time series that call for efficient representations to expose relevant aspects of the underlying dynamics. Binning the time series defines neural activity vectors that populate the N-dimensional space as a density distribution, especially informative when the neural dynamics performs a noisy path through metastable states (often a case of interest in neuroscience); this makes clustering in the N-dimensional space a natural choice. We apply a variant of the 'mean-shift' algorithm to perform such clustering, and validate it on an Hopfield network in the glassy phase, in which metastable states are uncorrelated from memory attractors. The neural states identified as clusters' centroids are then used to define a parsimonious parametrization of the synaptic matrix, which allows a significant improvement in inferring the synaptic couplings from neural activities. We next consider the more realistic case of a multi-modular spiking network, with spike-frequency adaptation (SFA) inducing history-dependent effects; we develop a procedure, inspired by Boltzmann learning but extending its domain of application, to learn inter-module synaptic couplings so that the spiking network reproduces a prescribed pattern of spatial correlations. After clustering the activity generated by multi-modular spiking networks, we represent their multi-dimensional dynamics as the symbolic sequence of the clusters' centroids, which naturally lends itself to complexity estimates that provide information on memory effects like those induced by SFA. To obtain a relative complexity measure we compare the Lempel-Ziv complexity of the actual centroid sequence to the one of Markov processes sharing the same transition probabilities between centroids; as an illustration, we show that the dependence of such relative complexity on the time scale of SFA.