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.
Links
- View publications from Kai Liu
- View publications from Hua Wang
- View publications presented in SDM
- View publications in the project, Mining Brain Imaging Genomics Data for Improved Cognitive Health
- View publications researching Embeddings
- View publications applied to Computer Vision
Cite this paper
MLA
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.
BibTeX
@inproceedings{liu2019spherical,
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},
pages={387--395},
year={2019},
organization={SIAM}
}