An L1 criterion for dictionary learning by subspace identification

Florent Jaillet (1) , Rémi Gribonval (1) , Mark D. Plumbley (2) , Hadi Zayyani (3)

1 METISS - Speech and sound data modeling and processing
2 Centre for Digital Music
3 EE department of SUT [Tehran] - Department of Electrical Engineering [Tehran]

We propose an ℓ1 criterion for dictionary learning for sparse signal representation. Instead of directly searching for the dictionary vectors, our dictionary learning approach identifies vectors that are orthogonal to the subspaces in which the training data concentrate. We study conditions on the coefficients of training data that guarantee that ideal normal vectors deduced from the dictionary are local optima of the criterion. We illustrate the behavior of the criterion on a 2D example, showing that the local minima correspond to ideal normal vectors when the number of training data is sufficient. We conclude by describing an algorithm that can be used to optimize the criterion in higher dimension.

Mots clés: Sparse representation; dictionary learning; non-convex optimization

Domaines: Traitement du signal et de l'image [eess.SP]; Traitement du signal et de l'image [eess.SP]

Florent Jaillet, Rémi Gribonval, Mark D. Plumbley, Hadi Zayyani. An L1 criterion for dictionary learning by subspace identification. Acoustics, Speech and Signal Processing, IEEE Conference on (ICASSP'10), Mar 2010, Dallas, United States. pp.5482--5485. ⟨hal-00474328⟩