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A Compressed PCA Subspace Method for Anomaly Detection in High-Dimensional Data

Random projection is widely used as a method of dimension reduction. In recent years, its combination with standard techniques of regression and classification has been explored. Here we examine its use with principal component analysis (PCA) and subspace detection methods. Specifically, we show that, under appropriate conditions, with high probability the magnitude of the residuals of a PCA analysis of randomly projected data behaves comparably to that of the residuals of a similar PCA analysis of the original data. Our results indicate the feasibility of applying subspace-based anomaly detection algorithms to randomly projected data, when the data are high-dimensional but have a covariance of an appropriately compressed nature. We illustrate in the context of computer network traffic anomaly detection.