Statistical Mechanics of Dictionary Learning

Ayaka Sakata; Yoshiyuki Kabashima

doi:10.1209/0295-5075/103/28008

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arXiv · 1203.6178

Statistical Mechanics of Dictionary Learning

Ayaka Sakata·Yoshiyuki Kabashima

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Abstract

Finding a basis matrix (dictionary) by which objective signals are represented sparsely is of major relevance in various scientific and technological fields. We consider a problem to learn a dictionary from a set of training signals. We employ techniques of statistical mechanics of disordered systems to evaluate the size of the training set necessary to typically succeed in the dictionary learning. The results indicate that the necessary size is much smaller than previously estimated, which theoretically supports and/or encourages the use of dictionary learning in practical situations.

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cond-mat.dis-nn cond-mat.stat-mech cs.IT cs.LG math.IT

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Ayaka Sakata, Yoshiyuki Kabashima. 2013-01-25. Statistical Mechanics of Dictionary Learning. https://doi.org/10.1209/0295-5075%2F103%2F28008

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