呂融昇 || A Geometric Algorithm for Contrastive PCA in High Dimension || 2022/12/15 ||
Dimensional reduction is useful in exploratory data analysis. In many applications, the interesting features of “target” dataset may be obscured by high variance component from “background” dataset. In this situation, we hope to find the subspace that contains variance enriched in target dataset relative to background dataset. Contrastive PCA (cPCA) (Abid et al., 2018) is proposed for this setting. Usually the cPCA is solved by eigenvalue decomposition. However, it becomes impractical for high dimensional data. To the best of our knowledge, there is no computationally feasible algorithm for high dimensional cPCA. In this talk, we propose a geometric line search algorithm for it. Convergence analysis is provided. Numerical experiments are conducted to show its empirical performance.