Optimal Discriminative Projection for Sparse Representation-Based Classification via Bilevel Optimization

Abstract

Recently, sparse representation-based classification (SRC) has been widely studied and has produced state-of-the-art results in various classification tasks. Learning useful and computationally convenient representations from complex redundant and highly variable visual data is crucial for the success of SRC. However, how to find the best feature representation to work with SRC remains an open question. In this paper, we present a novel discriminative projection learning approach with the objective of seeking a projection matrix such that the learned low-dimensional representation can fit SRC well and that it has well discriminant ability. More specifically, we formulate the learning algorithm as a bilevel optimization problem, where the optimization includes an $\ell _{1}$ -norm minimization problem in its constraints. Through the bilevel optimization model, the relationship between sparse representation and the desired feature projection can be explicitly exploited during the learning process. Therefore, SRC can achieve a better performance in the transformed subspace. The optimization model can be solved by using a stochastic gradient ascent algorithm, and the desired gradient is computed using implicit differentiation. Furthermore, our method can be easily extended to learn a dictionary. The extensive experimental results on a series of benchmark databases show that our method outperforms many state-of-the-art algorithms.