Fair Principal Component Analysis and Filter Design

Gad Zalcberg*, Ami Wiesel

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


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.

Original languageAmerican English
Article number9496158
Pages (from-to)4835-4842
Number of pages8
JournalIEEE Transactions on Signal Processing
StatePublished - 2021

Bibliographical note

Publisher Copyright:
© 1991-2012 IEEE.


  • Dimensionality reduction
  • PCA
  • SDP
  • fairness
  • normalized tight frame


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