  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.
