Bi-Level Spectral Feature Selection.

Unsupervised feature selection (UFS) aims to learn an indicator matrix relying on some characteristics of the high-dimensional data to identify the features to be selected. However, traditional unsupervised methods perform only at the feature level, i.e., they directly select useful features by feature ranking. Such methods do not pay any attention to the interaction information with other tasks such as classification, which severely degrades their feature selection performance. In this article, we propose an UFS method which also takes into account the classification level, and selects features that perform well both in clustering and classification. To achieve this, we design a bi-level spectral feature selection (BLSFS) method, which combines classification level and feature level. More concretely, at the classification level, we first apply the spectral clustering to generate pseudolabels, and then train a linear classifier to obtain the optimal regression matrix. At the feature level, we select useful features via maintaining the intrinsic structure of data in the embedding space with the learned regression matrix from the classification level, which in turn guides classifier training. We utilize a balancing parameter to seamlessly bridge the classification and feature levels together to construct a unified framework. A series of experiments on 12 benchmark datasets are carried out to demonstrate the superiority of BLSFS in both clustering and classification performance.