Clustering high-dimensional data via feature selection.

High-dimensional clustering analysis is a challenging problem in statistics and machine learning, with broad applications such as the analysis of microarray data and RNA-seq data. In this paper, we propose a new clustering procedure called spectral clustering with feature selection (SC-FS), where we first obtain an initial estimate of labels via spectral clustering, then select a small fraction of features with the largest R-squared with these labels, that is, the proportion of variation explained by group labels, and conduct clustering again using selected features. Under mild conditions, we prove that the proposed method identifies all informative features with high probability and achieves the minimax optimal clustering error rate for the sparse Gaussian mixture model. Applications of SC-FS to four real-world datasets demonstrate its usefulness in clustering high-dimensional data.