Discriminative Least Squares Regression (DLSR) is an algorithm that utilizes ε-draggings to expand the distance between classes to better solve multi-classification problems. However, this method increases the differences in regression targets within classes during the classification process, and noise in the samples adversely affects its performance. To address the above problems, we propose a novel method called Regularisation Constrained Denoising Discriminant Least Squares Regression (RCDDLSR). Firstly, the idea of matrix decomposition is introduced and sparse constraints are imposed on the noise matrix for noise elimination, thus helping to maintain the manifold structure of the raw data. Secondly, the neighbourhood relationship between samples of the same category is ensured through graph regularisation to avoid overfitting. In addition, we introduce low-rank constraints in the labelling space to better capture the local structure of the regression target within the class. Finally, our experiments show that the method performs better in various types of image datasets compared to other different algorithms.