期刊
IEEE TRANSACTIONS ON SIGNAL PROCESSING
卷 69, 期 -, 页码 4835-4842出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TSP.2021.3099983
关键词
Optimization; Principal component analysis; Linear matrix inequalities; Signal to noise ratio; Signal processing algorithms; Dimensionality reduction; Convergence; Dimensionality reduction; SDP; fairness; normalized tight frame; PCA
资金
- ISF [1339/15]
This paper investigates Fair Principal Component Analysis (FPCA) and proposes addressing it using simple sub-gradient descent. The study shows that the landscape of optimization is benign in the case of orthogonal targets, and all local minima are globally optimal. Interestingly, the SDR approach leads to sub-optimal solutions in this orthogonal case.
We consider Fair Principal Component Analysis (FPCA) and search for a low dimensional subspace that spans multiple target vectors in a fair manner. FPCA is defined as a non-concave maximization of the worst projected target norm within a given set. The problem arises in filter design in signal processing, and when incorporating fairness into dimensionality reduction schemes. The state of the art approach to FPCA is via semidefinite programming followed by rank reduction methods. Instead, we propose to address FPCA using simple sub-gradient descent. We analyze the landscape of the underlying optimization in the case of orthogonal targets. We prove that the landscape is benign and that all local minima are globally optimal. Interestingly, the SDR approach leads to sub-optimal solutions in this orthogonal case. Finally, we discuss the equivalence between orthogonal FPCA and the design of normalized tight frames.
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