Unsupervised feature selection based on robust self-representative dictionary pair learning with application to aluminum electrolysis

The purpose of feature selection is to remove the irrelevant and redundant features, and find the compact representation of the original features with good generalization ability in the high-dimensional data. In practical applications, a large number of high-dimensional data lead to the curse of dimensionality. Besides, the real data are much more complex, which is characterized by redundant, less labeled data and containing noise and outliers. To eliminate these unfavourable factors, an unsupervised feature selection method based on robust self-representative dictionary pair learning is proposed and applied to classification. The method does not require data labels, and uses representation coefficients to model the clustering structure and data distribution. The synthetical dictionary is used for data reconstruction, and the analytical dictionary is designed to analytically code data and assign probabilities to data features. Then, sparse regularization constraint is applied to the analytical dictionary to ensure robustness against noise and outliers in the data. Meanwhile, a regularized self-representative weight strategy is proposed, which uses the self-representative weight matrix to enhance the significance of important features. The effectiveness of the proposed method is verified by experiments on the benchmark datasets and the anode current data in aluminum electrolysis.