Sparsity Score: a Novel Graph-Preserving Feature Selection Method

As thousands of features are available in many pattern recognition and machine learning applications, feature selection remains an important task to ̄nd the most compact representation of the original data. In the literature, although a number of feature selection methods have been developed, most of them focus on optimizing speci ̄c objective functions. In this paper, we ̄rst propose a general graph-preserving feature selection framework where graphs to be preserved vary in speci ̄c de ̄nitions, and show that a number of existing ̄lter-type feature selection algorithms can be uni ̄ed within this framework. Then, based on the proposed framework, a new ̄lter-type feature selection method called sparsity score (SS) is proposed. This method aims to preserve the structure of a pre-de ̄ned l1 graph that is proven robust to data noise. Here, the modi ̄ed sparse representation based on an l1-norm minimization problem is used to determine the graph adjacency structure and corresponding a±nity weight matrix simultaneously. Furthermore, a variant of SS called supervised SS (SuSS) is also proposed, where the l1 graph to be preserved is constructed by using only data points from the same class. Experimental results of clustering and classi ̄cation tasks on a series of benchmark data sets show that the proposed methods can achieve better performance than conventional ̄lter-type feature selection methods.