Spherical Principal Component Analysis

Kai Liu, Qiuwei Li, Hua Wang, Gongguo Tang

SDM - 2019

Principal Component Analysis (PCA) is one of the most important methods to handle high dimensional data. However, most of the studies on PCA aim to minimize the loss after projection, which usually measure the Euclidean distance, though in some fields, angle distance is known to be more important and critical for analysis. In this paper, we propose a method by adding constraints on factors to unify the Euclidean distance and angle distance. However, due to the nonconvexity of the objective and constraints, the optimized solution is not easy to obtain. We propose an alternating linearized minimization method to solve it with provable convergence rate and guarantee. Experiments on synthetic data and real-world datasets have validated the effectiveness of our method and demonstrated its advantages over state-of-art clustering methods.


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Liu, Kai, et al. "Spherical Principal Component Analysis." Proceedings of the 2019 SIAM International Conference on Data Mining. Society for Industrial and Applied Mathematics, 2019.
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  title={Spherical Principal Component Analysis},
  author={Liu, Kai and Li, Qiuwei and Wang, Hua and Tang, Gongguo},
  booktitle={Proceedings of the 2019 SIAM International Conference on Data Mining},