L 2,1-norm-based sparse principle component analysis with trace norm regularised term

Principal component analysis (PCA) is the most widely used unsupervised dimensionality reduction approach. However, most PCA based on the squared reconstruction errors assume that all training samples have been centred, which make them not robust to outliers or noises in the samples and will depress their performance of classification accuracy. On the other hand, when there are various correlations in the training samples, the l 1-norm regularisation encounters instability problems. To address the above problems, the authors propose a novel L 2,1-norm-based sparse PCA with the trace norm regularised term (abbreviated to OMSPCA-L21-TN) to learn the optimal projection matrix and optimal mean simultaneously, where the objective function in model consists of the L 2,1-norm-based reconstruction error and the trace-norm-based regularised term of the projection vectors involved the sample matrix. Thus, not only can the authors’ method obtain the sparse features and reduce the effect of noise and outliers but also be adaptive to the correlation of the training samples. An effective optimisation solution is also given. The experimental results on some publicly available datasets demonstrate that the proposed approach is feasible and effective.