Spherical Principal Component Analysis
Kai Liu, Qiuwei Li, Hua Wang, Gongguo Tang · Society for Industrial and Applied Mathematics eBooks · 2019
Principal Component Analysis (PCA) is one of the most broadly used methods to analyze high-dimensional data. However, most existing studies on PCA aim to minimize the reconstruction error measured by the Euclidean distance, although in some fields, such as text analysis in information retrieval, analysis using the angle distance is known to be more effective. In this paper, we propose a novel PCA formulation by adding a constraint on the factors to unify the Euclidean distance and the angle distance. Because the objective and constraints are nonconvex, the optimization problem is difficult to solve in general. To tackle the optimization problem, we propose an alternating linearized minimization method with guaranteed convergence and provable convergence rate. Experiments on synthetic data and real-world data sets have validated the effectiveness of our new method and demonstrated its advantages over state-of-art competing methods.