Title（标题）：High-dimensional sparse PCA and sparse SVD

Speaker（汇报人）：Prof.Zongming Ma Department of Statistics, University of Pennsylvania

Time（功夫）：2011年7月5日（周二）上午10:30 — 11:30

Place（地址）：北京大学理科一号楼（数学学院）1418教室

Abstract（提要）：For high-dimensional data, it is often desirable to reduce the dimensionality by projection onto a low-dimensional principal subspace. However, classical PCA usually cannot find the subspace consistently in high dimensions. In this talk, we present a new principal subspace estimation method based on iterative thresholding. For a class of spiked covariance models with sparsity constraints, it consistently, and even optimally, estimates the subspace.

Interestingly, a similar breakdown phenomenon is observed when classical SVD is applied to recover high-dimensional low-rank matrices with noisy entries. However, if there are bases in which we have sparse representations of both the left and right singular vectors, the iterative thresholding idea again leads to a near-optimal estimation scheme for the low-rank structure.

About the speaker（汇报人介绍）：

北京大学统计科学中心