Structurally incoherent adaptive weighted low-rank matrix decomposition for image classification

To address image classification challenges caused by noisy disturbances, we propose a new algorithm called structurally incoherent adaptive weighted low-rank matrix decomposition (SIAWLR). This method divides the raw image matrix into a low-rank denoised matrix, which retains all the information of images, and a sparse error matrix that captures the noise components. The incorporation of structural incoherence in the low-rank matrix and the utilization of adaptive weights in the error matrix significantly enhance the classification performance. To solve the SIAWLR, we propose an integrated algorithm consisting of two steps. Firstly, we employ the augmented lagrangian alternating direction method (ALADM) (Shen et al., Optim Methods Softw 29(2), 239-263, 2014) to solve the SIAWLR. Subsequently, we classify the images based on the obtained low-rank matrix. In comparison to other methods, SIAWLR exhibits computational attractiveness as it requires fewer parameters, often determined through cross validation. We conduct experiments comparing the proposed method with four other methods on three datasets. The experimental results consistently demonstrate that SIAWLR outperforms the other methods in terms of classification accuracy.