Random projection is widely used as a method of dimension reduction. Inrecent years, its combination with standard techniques of regression andclassification has been explored. Here we examine its use with principalcomponent analysis (PCA) and subspace detection methods. Specifically, we showthat, under appropriate conditions, with high probability the magnitude of theresiduals of a PCA analysis of randomly projected data behaves comparably tothat of the residuals of a similar PCA analysis of the original data. Ourresults indicate the feasibility of applying subspace-based anomaly detectionalgorithms to randomly projected data, when the data are high-dimensional buthave a covariance of an appropriately compressed nature. We illustrate in thecontext of computer network traffic anomaly detection.
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