In Andrew Ng's Machine Learning Coursera Class, he covers anomaly detection in multiple dimensions for both independent univariate Gaussians and multivariate Gaussians, the latter being more costly than the former.

Would running independent anomaly detection after orthogonalizing the data produce the same results as a multivariate anomaly detection? Is PCA too costly for this to ever be worthwhile (assuming it works at all)?

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#### Best Answer

No. PCA is performed on the multivariate case as well (there is an inverse of a covariance matrix in the formula), but it measures the distance from the mean using all dimensions. By looking at each axis individually (I am assuming thats what you mean when you say independent anamoly detection) you will miss anomalies that come about as a result of two or more dimensions acting awry.