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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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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 (, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The Creative Commons Public Domain Dedication waiver ( 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 (Suppl 1), P255 (2015).

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