Fair Principal Component Analysis and Filter Design

We consider Fair Principal Component Analysis (FPCA) and search for a low dimensional subspace that spans multiple target vectors in fair manner. FPCA is defined as non-concave maximization of the worst projected norm within given set. The problem arises filter design signal processing, when incorporating fairness into dimensionality reduction schemes. state art approach to via semidefinite relaxation involves polynomial yet computationally expensive optimization. To allow scalability, we propose address using naive sub-gradient descent. analyze landscape underlying optimization case orthogonal targets. prove benign all local minima are globally optimal. Interestingly, SDR leads sub-optimal solutions this simple case. Finally, discuss equivalence between normalized tight frames.