Discussion of “ Influential Feature Pca for High Dimensional Clustering ”

We would like to congratulate the authors for an interesting paper and a novel proposal for clustering high-dimensional Gaussian mixtures with a diagonal covariance matrix. The proposed two-stage procedure first selects features based on the Kolmogorov-Smirnov statistics and then applies a spectral clustering method to the post-selected data. A rigorous theoretical analysis for the clustering error is given and the results are supported by a competitive performance in numerical studies. The following discussion is divided into two parts. We will discuss a clustering method based on the sparse principal component analysis (SPCA) method proposed in [4] under mild conditions and compare it with the proposed IF-PCA method. We then discuss the dependent case where the covariance matrix Σ is not necessarily diagonal. To be consistent, we will follow the same notations used in the present paper.