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Sparse coding and dictionary learning for spike trains to find spatio-temporal patterns

In biological neural networks, it is widely accepted that the spikes are the fundamental building blocks of information representation [1]. In contrast, whether such building blocks exist at a higher level in terms of time and in a population of neurons is a topic of ongoing debate. One approach for finding candidates for such building blocks is to seek for frequently appearing spike patterns in a population. These sequences are often called spatio-temporal patterns, cell assemblies, or unitary events [24]. They could metaphorically be considered as an ``alphabet'' of neural information processing [5, 6]. Some patterns have already been found and are related to functional roles such as memory consolidation and gating of sensory inputs [7, 8].

One difficulty in finding spatio-temporal patterns arises from observed spike trains being a superposition of multiple patterns. In signal processing, one commonly used method for decomposing the signal into patterns is dictionary learning for sparse coding [911]. Sparse coding expresses the input signal as a linear combination of a few template vectors taken from a matrix called a dictionary or codebook. In terms of linear algebra, sparse coding corresponds to finding a sparse vector x, which fulfills y = Dx, where y is the observed signal vector and D is a dictionary. When the dimension of × is much larger than that of y, it is possible to find sparse x. Each column of D is called an atom, which represents a template vector. A good dictionary decomposes the most of the observed signals into a small set of template vectors. In other words, D must sparsify not just one input vector y but many others as well. This is represented by using matrix Y whose column vectors are observed signals. In this case, sparse coding is represented by equation Y = DX. The goal is to find sparse matrix × given Y and D. Whether input matrix Y can be transformed into sparse × or not depends on dictionary D. The goodness of D depends on Y. The task of finding optimal D given Y is called dictionary learning. In this work sparse coding and dictionary learning were applied for finding spatio-temporal patterns from multivariate spike trains. Spike trains were transformed to vectors using binning, that is, converted to vectors of short-time firing rates. The methods were tested using different bin sizes. The results obtained for biological data showed possible candidates of spatio-temporal patterns in neural activity.

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Acknowledgement

This work was supported in part by JSPS KAKENHI Grant Numbers 21700121, 25280110, and 25540159.

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Correspondence to Taro Tezuka.

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This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated.

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Tezuka, T. Sparse coding and dictionary learning for spike trains to find spatio-temporal patterns. BMC Neurosci 16, P255 (2015). https://doi.org/10.1186/1471-2202-16-S1-P255

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Keywords

  • Building Block
  • Firing Rate
  • Spike Train
  • Sparse Matrix
  • Memory Consolidation