Linear Discriminative Learning for Image Classification

In this paper, we propose a linear discriminative learning model called adaptive locality-based weighted collaborative representation (ALWCR) that formulates the image classification task as an optimization problem to reduce the reconstruction error between the query sample and its computed linear representation. The optimal linear representation for a query image is obtained by using the weighted regularized linear regression approach which incorporates intrinsic locality structure and feature variance between data into representation. The resultant representation increases the discrimination ability for correct classification. The proposed ALWCR method can be considered an extension of the collaborative representation- (CR-) based classification approach which is an alternative to the sparse representation- (SR-) based classification method. ALWCR improved the discriminant ability for classification as compared with CR original formulation and overcomes the limitations that arose due to a small training sample size and low feature dimension. Experimental results obtained using various feature dimensions on well-known publicly available face and digit datasets have verified the competitiveness of the proposed method against competing image classification methods.