Statistical Mechanics of Dictionary Learning
This addresses a theoretical bottleneck in dictionary learning for researchers and practitioners, though it is incremental as it builds on existing statistical mechanics methods.
The paper tackles the problem of determining the minimum training set size needed for successful dictionary learning, finding that it is much smaller than previously estimated, which supports practical applications.
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.