Important Features PCA for High-Dimensional Clustering

• Activity Number: 190
• Type: Contributed
• Date/Time: Monday, August 10, 2015 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Wanjie Wang* and Jiashun Jin
• Companies: The Wharton School and Carnegie Mellon University
• Keywords: Big Data ; Feature selection ; Spectral Clustering ; Gene microarray ; Sparsity

Abstract

We consider a clustering problem where we observe N feature vectors from K possible classes, each feature vector with length P. The class labels are unknown and the main interest is to estimate them. We are primarily interested in the modern regime that P >> N, where classical clustering methods face challenges. We propose Important Features PCA (IF-PCA) as a new clustering procedure. In IF-PCA, we select a small fraction of features with the largest Kolmogorov-Smirnov (KS) scores, obtain the first (K ?1) left singular vectors of the post-selection normalized data matrix, and then estimate the labels by applying the classical k-means to these singular vectors. The threshold is set in a data-driven fashion by adapting the recent notion of Higher Criticism. As a result, IF-PCA is a tuning free clustering method. IF-PCA is applied to 10 gene microarray data sets. The method has competitive performance in clustering.