Robust Principal Component Analysis using Density Power Divergence

Principal component analysis (PCA) is a widely employed statistical tool used primarilyfor dimensionality reduction. However, it is known to be adversely affected by the presenceof outlying observations in the sample, which is quite common. Robust PCA methodsusing M-estimators have theoretical benefits, but their robustness drop substantially forhigh dimensional data. On the other end of the spectrum, robust PCA algorithms solv-ing principal component pursuit or similar optimization problems have high breakdown,but lack theoretical richness and demand high computational power compared to the M-estimators. We introduce a novel robust PCA estimator based on the minimum densitypower divergence estimator. This combines the theoretical strength of the M-estimatorsand the minimum divergence estimators with a high breakdown guarantee regardless ofdata dimension. We present a computationally efficient algorithm for this estimate. Ourtheoretical findings are supported by extensive simulations and comparisons with existingrobust PCA methods. We also showcase the proposed algorithm's applicability on twobenchmark data sets and a credit card transactions data set for fraud detection.