Improved Sparse Principal Component Analysis Algorithm based on Non-convex Optimization

Weihao Li

doi:10.54097/vh2hep69

Authors

Weihao Li

DOI:

https://doi.org/10.54097/vh2hep69

Keywords:

Non-convex Optimization, Convex Sparse Principal Component Analysis, Generalized Inverse Lemma of Matrices, Unsupervised Feature Selection

Abstract

Downloads

Download data is not yet available.

References

[1] Nie F, Huang H, Ding C. Low-rank matrix recovery via efficient schatten p-norm minimization[C]. Proceedings of the AAAI Conference on Artificial Intelligence. 2017, 26(1): 655-661.

[2] Wang J, Xie F, Nie F, et al. Unsupervised Adaptive Embedding for Dimensionality Reduction[J]. IEEE Transactions on Neural Networks and Learning Systems, 2021, PP (99): 1-12.

[3] Zhao H, Wang Z, Nie F. A New Formulation of Linear Discriminant Analysis for Robust Dimensionality Reduction[J]. IEEE Transactions on Knowledge and Data Engineering, 2019, 31(4): 629-640.

[4] Ang J C, Mirzal A, Haron H, et al. Supervised, Unsupervised, and Semi-Supervised Feature Selection: A Review on Gene Selection[J]. IEEE/ACM Transactions on Computational Biology & Bioinformatics, 2016, 13(5): 971-989.

[5] Davenport M A, Romberg J. An overview of low-rank matrix recovery from incomplete observations[J]. IEEE Journal of Selected Topics in Signal Processing, 2016, 10(4): 608-622.

[6] Candès E J, Li X, Ma Y, et al. Robust principal component analysis? [J]. Journal of the ACM (JACM), 2011, 58(3): 1-37.

[7] Fan J, Ding L, Chen Y, et al. Factor group-sparse regularization for efficient low-rank matrix recovery[J]. Advances in Neural Information Processing Systems, 2019, 32(14): 78-103.

[8] Chang X, Nie F, Yang Y, et al. Convex sparse PCA for unsupervised feature learning[J]. ACM Transactions on Knowledge Discovery from Data (TKDD), 2016, 11(1): 1-16.

[9] Giampouras P V, Rontogiannis A A, Koutroumbas K D. Robust PCA via alternating iteratively reweighted low-rank matrix factorization[C]. The 2018 25th IEEE International Conference on Image Processing (ICIP). IEEE, 2018: 3383-3387.

[10] Nie F, Hu Z, Li X. Matrix completion based on non-convex low-rank approximation[J]. IEEE Transactions on Image Processing, 2018, 28(5): 2378-2388.

[11] Chi Y, Lu Y M, Chen Y. Nonconvex optimization meets low-rank matrix factorization: An overview[J]. IEEE Transactions on Signal Processing, 2019, 67(20): 5239-5269.

[12] Sun R, Luo Z Q. Guaranteed matrix completion via non-convex factorization[J]. IEEE Transactions on Information Theory, 2016, 62(11): 6535-6579.

[13] Aftab K, Hartley R. Convergence of iteratively re-weighted least squares to robust m-estimators[C]. The 2015 IEEE Winter Conference on Applications of Computer Vision. IEEE, 2015: 480-487.

[14] Abdi H, Williams L J. Principal component analysis[J]. Wiley interdisciplinary reviews: computational statistics, 2010, 2(4): 433-459.

[15] Zhi Xiaobin, Li Yalan. Two-stage Discriminant Embedded Clustering [J]. Journal of Xi'an University of Posts and Telecommunications, 2018, 23(03): 45-51.

[16] Recht B, Fazel M, Parrilo P A. Guaranteed minimum-rank solutions of linear matrix equations via nuclear norm minimization[J]. SIAM review, 2010, 52(3): 471-501.

[17] Wright J, Ganesh A, Rao S, et al. Robust principal component analysis: Exact recovery of corrupted low-rank matrices via convex optimization[J]. Advances in neural information processing systems, 2009, 22: 17-30.

[18] Ornhag M V, Olsson C. A unified optimization framework for low-rank inducing penalties[C]. Proceedings of the IEEE/CVF conference on computer vision and pattern recognition. 2020: 8474-8483.

[19] Zhao T, Wang Z, Liu H. A nonconvex optimization framework for low rank matrix estimation[J]. Advances in Neural Information Processing Systems, 2015, 28(3): 8-21.

[20] Mo D, Lai Z. Robust Jointly Sparse Regression with Generalized Orthogonal Learning for Image Feature Selection[J]. Pattern Recognition, 2019, 93: 164-178.