Learning Feature Sparse Principal Subspace

Lai Tian, Feiping Nie, Rong Wang, Xuelong Li

NeurIPS 2020

/neurips/2020/tian2020neurips-learning-a/

Abstract

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.

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Cite

Text

Tian et al. "Learning Feature Sparse Principal Subspace." Neural Information Processing Systems, 2020.

Markdown

[Tian et al. "Learning Feature Sparse Principal Subspace." Neural Information Processing Systems, 2020.](https://mlanthology.org/neurips/2020/tian2020neurips-learning-a/)

BibTeX

@inproceedings{tian2020neurips-learning-a,
  title     = {{Learning Feature Sparse Principal Subspace}},
  author    = {Tian, Lai and Nie, Feiping and Wang, Rong and Li, Xuelong},
  booktitle = {Neural Information Processing Systems},
  year      = {2020},
  url       = {https://mlanthology.org/neurips/2020/tian2020neurips-learning-a/}
}