Iterative re-weighted L1-norm principal-component analysis

Abstract

We consider the problem of principal-component analysis of a given set of data samples. When the data set contains faulty measurements/outliers, the performance of classic L2 principal-component analysis (L2-PCA) deteriorates drastically. Instead, L1 principal-component analysis (L1-PCA) offers outlier resistance due to the L1-norm maximization criterion it adopts to compute the principal subspace. In this work, we present an iterative re-weighted L1-PCA method (IRW L1-PCA) that generates a sequence of Li-norm subspaces. In each iteration, the data set comformity of each sample is measured by the L1 subspace calculated in the previous iteration and used to weigh the data sample before the L1 subspace update. The approach automatically suppresses outliers in each iteration resulting in increasingly accurate subspace calculation. We provide convergence analysis and compare the proposed algorithm against benchmark algorithms in the literature. Experimental studies demonstrate the superiority of the proposed IRW L1-PCA procedure.