Self-representation graph feature selection method for classification

Abstract

This paper proposed a novel feature selection method that includes a self-representation loss function, a graph regularization term and an ${l_{2,1}}$-norm regularization term. Different from traditional least square loss function which focuses on achieving the minimal regression error between the class labels and their corresponding predictions, the proposed self-representation loss function pushes to represent each feature with a linear combination of its relevant features, aim at effectively selecting representative features and ensuring the robustness to outliers. The graph regularization terms include two kinds of inherent information, i.e., the relationship between samples (the sample–sample relation for short) and the relationship between features (the feature–feature relation for short). The feature–feature relation reflects the similarity between two features and preserves the relation into the coefficient matrix, while the sample–sample relation reflects the similarity between two samples and preserves the relation into the coefficient matrix. The ${l_{2,1}}$-norm regularization term is used to conduct feature selection, aim at selecting the features, which satisfies the characteristics mentioned above. Furthermore, we put forward a new optimization method to solve our objective function. Finally, we feed reduced data into support vector machine (SVM) to conduct classification on real datasets. The experimental results showed that the proposed method has a better performance comparing with state-of-the-art methods, such as k nearest neighbor, ridge regression, SVM and so on.