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Learning Feature Sparse Principal Subspace
Lai Tian · Feiping Nie · Rong Wang · Xuelong Li

Wed Dec 09 09:00 AM -- 11:00 AM (PST) @ Poster Session 3 #1052

This paper presents new algorithms to solve the feature-sparsity constrained PCA problem (FSPCA), which performs feature selection and PCA simultaneously. Existing optimization methods for FSPCA require data distribution assumptions and are lack of global convergence guarantee. Though the general FSPCA problem is NP-hard, we show that, for a low-rank covariance, FSPCA can be solved globally (Algorithm 1). Then, we propose another strategy (Algorithm 2) to solve FSPCA for the general covariance by iteratively building a carefully designed proxy. We prove (data-dependent) approximation bound and convergence guarantees for the new algorithms. For the spectrum of covariance with exponential/Zipf's distribution, we provide exponential/posynomial approximation bound. Experimental results show the promising performance and efficiency of the new algorithms compared with the state-of-the-arts on both synthetic and real-world datasets.

Author Information

Lai Tian (Northwestern Polytechnical University)
Feiping Nie (University of Texas Arlington)
Rong Wang (Northwestern Polytechnical University)
Xuelong Li (Northwestern Polytechnical Univ.)

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