Discussion of “Influential feature PCA for high dimensional clustering”
Tommaso Cai, Linjun Zhang · The Annals of Statistics · 2016
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 [5] under mild conditions and compare it with the proposed IF-PCA method.We then discuss the dependent case where the covariance matrix is not necessarily diagonal.To be consistent, we will follow the same notation used in the present paper.