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Sparse and spurious: dictionary learning with noise and outliers (2014)
| Citations: | 2 - 0 self |
BibTeX
@MISC{Jenatton14sparseand,
author = {Rodolphe Jenatton and Francis Bach},
title = {Sparse and spurious: dictionary learning with noise and outliers},
year = {2014}
}
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Abstract
A popular approach within the signal processing and machine learning communities consists in mod-elling signals as sparse linear combinations of atoms selected from a learned dictionary. While this paradigm has led to numerous empirical successes in various fields ranging from image to audio process-ing, there have only been a few theoretical arguments supporting these evidences. In particular, sparse coding, or sparse dictionary learning, relies on a non-convex procedure whose local minima have not been fully analyzed yet. In this paper, we consider a probabilistic model of sparse signals, and show that, with high probability, sparse coding admits a local minimum around the reference dictionary generating the signals. Our study takes into account the case of over-complete dictionaries, noisy signals, and possible outliers, thus extending previous work limited to noiseless settings and/or under-complete dictionaries. The analysis we conduct is non-asymptotic and makes it possible to understand how the key quantities of the problem, such as the coherence or the level of noise, can scale with respect to the dimension of the signals, the number of atoms, the sparsity and the number of observations. 1
Keyphrases
dictionary learning local minimum noiseless setting over-complete dictionary high probability theoretical argument various field noisy signal previous work non-convex procedure key quantity signal processing under-complete dictionary mod-elling signal sparse dictionary learning possible outlier sparse linear combination probabilistic model machine learning community numerous empirical success popular approach sparse signal learned dictionary sparse coding
