A0463
Title: A geometric algorithm for contrastive principal component analysis in high dimension
Authors: Su-Yun Huang - Academia Sinica (Taiwan)
Shao-Hsuan Wang - National Central University (Taiwan) [presenting]
Abstract: Principal component analysis (PCA) has been widely used in exploratory data analysis. Contrastive PCA, a generalized method of PCA, is a new tool used to capture features of a target dataset relative to a background dataset while preserving the maximum amount of information contained in the data. With high dimensional data, contrastive PCA becomes impractical due to its high computational requirement of forming the contrastive covariance matrix and associated eigenvalue decomposition for extracting leading components. A geometric curvilinear-search method is proposed to solve this problem and provide a convergence analysis. The approach offers significant computational efficiencies. Specifically, it reduces the time complexity from $O(max{n,m}p)$ to a more manageable $O(max{n,m}pr)$, where n, m are the sample sizes of the target data and background data, respectively, p is the data dimension and r is the number of leading components.
