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## Technical Report Details

 Date 12-10-2010 Number DISI-TR-10-06 Title PADDLE: Proximal Algorithm for Dual Dictionaries LEarning Authors Curzio Basso, Matteo Santoro, Alessandro Verri, Silvia Villa Bibtex Entry E-mail curzio.basso@disi.unige.it Link http://www.disi.unige.it/person/BassoC/pubs/basso10tr.pdf Abstract Recently, considerable research efforts have been devoted to the design of methods to learn from data overcomplete dictionaries for sparse coding. However, learned dictionaries require the solution of an optimization problem for coding new data. In order to overcome this drawback, we propose an algorithm aimed at learning both a dictionary and its dual: a linear mapping directly performing the coding. By leveraging on proximal methods, our algorithm jointly minimizes the reconstruction error of the dictionary and the coding error of its dual; the sparsity of the representation is induced by an $\ell_1$-based penalty on its coefﬁcients. The results obtained on synthetic data and real images show that the algorithm is capable of recovering the expected dictionaries. Furthermore, on a benchmark dataset, we show that the image features obtained from the dual matrix yield state-of-the-art classiﬁcation performance while being much less computational intensive.
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