Unsupervised discriminative feature selection in a kernel space via L2,1-norm minimization

Traditional nonlinear feature selection methods map the data from an original space into a kernel space to make the data be separated more easily, then move back to the original feature space to select features. However, the performance of clustering or classification is better in the kernel space, so we are able to select the features directly in the kernel space and get the direct importance of each feature. Motivated by this idea, we propose a novel method for unsupervised feature selection directly in the kernel space. To do this, we utilize local discriminative information to find the best label for each instance with L_2,1-norm minimization, then select the most important features in the kernel space using the labels predicted. Extensive experiments demonstrate the effectiveness of our method.