Statistical mechanics of dictionary learning

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 system...

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Bibliographic Details
Published in:Europhysics letters 2013-07, Vol.103 (2), p.28008
Main Authors: Sakata, Ayaka, Kabashima, Yoshiyuki
Format: Article
Language:English
Subjects:
75.10.Nr
89.20.Ff
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Summary: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.
ISSN:0295-5075
1286-4854
DOI:10.1209/0295-5075/103/28008