Discriminative latent subspace learning with adaptive metric learning

Least squares regression (LSR) has been widely used in the field of pattern recognition. However, LSR-based classifier still suffers from the following issues. One is that it focuses only on the dependency between the input data and the output targets, while overlooking the local structure of instances. Another one is that using binary labels as the regression targets is too strict to fully exploit the discriminative information of the data. To address these issues, we propose a novel multiclass classification method called discriminative latent subspace learning with adaptive metric learning (DLSAML). Specifically, DLSAML adaptively learns a metric matrix for the residuals between inputs and outputs, driving smaller distances between instances of the same class and larger distances between instances of different classes in the output space. To solve the second problem, latent representations are learnt guided by the pairwise label relations as the regression targets, allowing for more flexible use of discriminative information in the data. As a combination of these two techniques, the interactive optimization of the projection matrix and metric matrix allows DLSAML to fully exploit the structural and supervised information of the data to obtain a more discriminative latent subspace for multiclass classification. Extensive experiments on several benchmark datasets have demonstrated the effectiveness of the proposed method.