Iterative Re-weighted L1-Norm Principal-Component Analysis

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 L-2 principal-component analysis (L-2-PCA) deteriorates drastically. Instead, L-1 principal-component analysis (L-1-PCA) offers outlier resistance due to the Li-norm maximization criterion it adopts to compute the principal subspace. In this work, we present an iterative re-weighted L-1-PCA method (IRW L-1-PCA) that generates a sequence of L-1-norm subspaces. In each iteration, the data set comformity of each sample is measured by the L-1 subspace calculated in the previous iteration and used to weigh the data sample before the L-1 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 L-1-PCA procedure.