Fair Principal Component Analysis and Filter Design

Gad Zalcberg, Ami Wiesel

פרסום מחקרי: פרסום בכתב עתמאמרביקורת עמיתים

תקציר

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.

שפה מקוריתאנגלית אמריקאית
מספר המאמר9496158
עמודים (מ-עד)4835-4842
מספר עמודים8
כתב עתIEEE Transactions on Signal Processing
כרך69
מזהי עצם דיגיטלי (DOIs)
סטטוס פרסוםפורסם - 2021

ASJC Scopus subject areas

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