A multi-class structured dictionary learning method using discriminant atom selection
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A multi‑class structured dictionary learning method using discriminant atom selection Roman E. Rolon1 · Leandro E. Di Persia1 · Ruben D. Spies2 · Hugo L. Rufiner1 Received: 19 October 2018 / Accepted: 3 November 2020 © Springer-Verlag London Ltd., part of Springer Nature 2020
Abstract In the last decade, traditional dictionary learning methods have been successfully applied to various pattern classification tasks. Although these methods produce sparse representations of signals which are robust against distortions and missing data, such representations quite often turn out to be unsuitable if the final objective is signal classification. In order to overcome, or at least to attenuate, such a weakness, several new methods which incorporate discriminant information into sparse-inducing models have emerged in recent years. In particular, methods for discriminant dictionary learning have shown to be more accurate than the traditional ones, which are only focused on minimizing the total representation error. In this work, we present both a novel multi-class discriminant measure and an innovative dictionary learning method. For a given dictionary, this new measure, which takes into account not only when a particular atom is used for representing signals coming from a certain class and the magnitude of its corresponding representation coefficient, but also the effect that such an atom has in the total representation error, is capable of efficiently quantifying the degree of discriminability of each one of the atoms. On the other hand, the new dictionary construction method yields dictionaries which are highly suitable for multi-class classification tasks. Our method was tested with two widely used databases for handwritten digit recognition and for object recognition, and compared with three state-of-the-art classification methods. The results show that our method significantly outperforms the other three achieving good recognition rates and additionally, reducing the computational cost of the classifier. Keywords Multi-class discriminant measure · Structured dictionary learning · Sparse coding · Handwritten digit recognition · Object recognition
1 Introduction Sparse representation of signals is considered a very powerful signal processing technique which has drawn massive interest in recent years mainly due to its success in solving * Roman E. Rolon [email protected] Leandro E. Di Persia [email protected] Ruben D. Spies rspies@santafe‑conicet.gov.ar Hugo L. Rufiner [email protected] 1
Instituto de Investigación en Señales, Sistemas e Inteligencia Computacional, sinc(i) (FICH/UNL-CONICET), Santa Fe, Argentina
Instituto de Matemática Aplicada del Litoral, IMAL (FIQ/UNL-CONICET), Santa Fe, Argentina
2
a wide variety of problems in different fields such as biomedical signal processing [1, 2], computer vision [3] and image analysis [4], including image denoising [5], color image restoration [6] and image classification [7]. Roughly speaking, the problem of sparse
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