Low Dimensional Subspace Finding Via Size-Reducing Dictionary Learning
Bogdan Dumitrescu, University Politehnica of Bucharest
Paul Irofti, University Politehnica of Bucharest

We present a dictionary learning algorithm that aims to reduce the size of the dictionary to a parsimonious value during the learning process. The sparse coding step uses a weighted Orthogonal Matching Pursuit favoring atoms that enter more representations. The dictionary update step optimizes a regularized error, encouraging the apparition of zero rows in the representation matrix; the corresponding unused atoms are eliminated. The algorithm is extended to the case of incomplete data. Besides dictionary learning, the algorithm is also shown to be useful for finding low-dimensional subspaces. Such versatility is a feature with little precedent. Numerical examples show good convergence properties.