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Supplied that the vast majority of variation is in the initial k PCs, the approximation is sweet, but it's however an approximations, Whilst the MD is exact.
Should you change the scale within your variables, then the covariance matrix also adjustments. For those who measure MD by using the new covariance matrix to measure the new (rescaled) data, you receive the identical respond to as in case you made use of the first covariance matrix to evaluate the initial knowledge.
In both equally of these purposes, you employ the Mahalanobis length together with the chi-sq. distribution perform to draw conclusions.
Following, as described in the posting 'Detecting outliers in SAS: Component three: Multivariate locale and scatter', I might foundation my outlier detection within the significant values on the chi-squared distribution.
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By resolving the 1-D problem, I normally get a better idea of the multivariate difficulty. The next point I check out is to grasp/solve the challenge for multivariate data that have a diagonal covariance matrix σ^2 I.
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