Low-rank and discriminate block diagonal representation via projection reconstruction for image classification

The primary objective of subspace learning in image classification is to group samples into distinct subspaces that share similar visual features. However, learning a representation coefficient matrix with a block-diagonal structure, which ideally aligns with individual classes, is often challenging due to noise, outliers, and other complexities in image data, potentially degrading classification accuracy. To address these issues, this paper introduces a novel approach called Low-Rank and Discriminative Block Diagonal Representation (LDBDR) to preserve the essential block-diagonal structure in classification tasks. Specifically, LDBDR utilizes projection and orthogonal recovery matrices to construct a reconstruction space that deeply captures the intrinsic structure and key feature details of image data, enhancing both robustness and discriminability in the learned representations. By incorporating a block-diagonal regularizer, LDBDR enforces this structure directly within the representation matrix, leading to significant improvements in classification performance. On various publicly available image datasets, LDBDR demonstrates superior classification accuracy compared to other state-of-the-art methods, showcasing the approach's effectiveness and resilience against challenging data conditions.