Mean Squared Error vs. Frame Potential for Unsupervised Variable Selection

Abstract

Forward Selection Component Analysis (FSCA) provides a pragmatic solution to the NP-hard unsupervised variable selection problem, but is not guaranteed to be optimal due to the multi-modal nature of the mean squared error (MSE) selection metric used. Frame potential (FP) is a metric that has recently been shown to yield near-optimal greedy sensor selection performance for linear inverse problems. This paper explores if FP offers similar benefits in the unsupervised variable selection context. In addition, the backward elimination counterpart of FSCA is introduced for the first time (BECA) and compared with forward and backward FP based variable selection on a number of simulated and real world datasets. It is concluded that FP does not improve on FSCA and that while BECA yields comparable results to FSCA it is not a competitive alternative due to its much higher computational complexity.