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Computing Robust Principal Components by A* Search

Principal Component Analysis (PCA) is a classical dimensionality reduction technique that computes a low rank representation of the data. Recent studies have shown how to compute this low rank representation from most of the data, excluding a small amount of outlier data. We describe an algorithm that solves this problem by applying a variant of the A* algorithm to search for the outliers. The results obtained by our algorithm are optimal, and more accurate than the current state of the art. This comes at the cost of running time, which is typically slower than the current state of the art. We also describe a related variant of the A* algorithm that runs much faster and produces a solution that is guaranteed to be near the optimal.