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(Neural Computation. 2002;14:2269-2316.)
© 2002 The MIT Press

Information-Geometric Measure for Neural Spikes

Hiroyuki Nakahara

hiro{at}brain.riken.go.jp, Laboratory for Mathematical Neuroscience, RIKEN Brain Science Institute, Wako, Saitama, 351-0198, Japan

Shun-ichi Amari

amari{at}brain.riken.go.jp, Laboratory for Mathematical Neuroscience, RIKEN Brain Science Institute, Wako, Saitama, 351-0198, Japan

This study introduces information-geometric measures to analyze neural firing patterns by taking not only the second-order but also higher-order interactions among neurons into account. Information geometry provides useful tools and concepts for this purpose, including the orthogonality of coordinate parameters and the Pythagoras relation in the Kullback-Leibler divergence. Based on this orthogonality, we show a novel method for analyzing spike firing patterns by decomposing the interactions of neurons of various orders. As a result, purely pairwise, triple-wise, and higher-order interactions are singled out. We also demonstrate the benefits of our proposal by using several examples.




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