Image classification based on weighted nonconvex low-rank and discriminant least squares regression

Classifiers based on least squares regression (LSR) are effective in multi-classification tasks. However, there are two main problems that greatly limit its performance. First of all, most of the existing methods use limited projections and cause a lot of loss of discriminative information, but excessive use of relaxed labels may lead to overfitting. Additionally, the traditional nuclear norm treats the weights of each singular value equally, and cannot fully discuss the influence of different weights on the rank. In order to solve these problems and improve the classification performance, this paper proposes a multi-class image classification method based on weighted nonconvex low-rank and discriminative least squares regression (WNLRDLSR). Specially, using relaxed labels to replace zero-one labels, which allows the margins from different classes of samples to be widened while enhancing the intra-class compactness and similarity, thus making the resulting projections more discriminative; Furthermore, introducing the weighted nonconvex low-rank constraint in the least squares regression model, applying the weighted nonconvex low-rank norm to fully explore the effect of different rank components on the label matrix while being close to the original low-rank hypothesis. Experiments show that it helps to learn more distinguished regression projections to achieve better classification performance. The classification accuracy on different face, object and handwriting datasets are higher than that of the contrastive methods, and experiments show that the proposed WNLRDLSR is superior to many state-of-the-art methods.