For any system, how do we decide as to which characteristics will be appropriate for the construction of the Mahalanobis space? Since the applicability of the distance measure calculation and subsequently the isolation of faults relies on the appropriate selection of characteristics, is there any technique that allows us to identify those characteristics - any practical experience, any algorithm, or any trick?
I am not sure what you mean by "characteristics" here. I suppose you mean the covariance matrix used in Mahalanobis distance calculation.
Suppose we have a set of observed points from a multivariant distribution. Now we are going to calculate the Mahalanobis distance between two points from the same distribution.
Then the covariance matrix is simply the covariance matrix calculated from the observed points. Please notice that here, we are assuming that both the two points and the observed points are from the same distribution.
If the two points are from different distributions, or the two points are from a distribution that is different from the observed points, or the observed points are not available at all, then calculating the Mahalanobis distance does not make any sense.
In practice, if the observed points are not available, we can select a covariance matrix based on prior knowledge. If the prior knowledge is not available neither, then we can simply assume the covariance matrix is an identity matrix. In the last case, it degrades to the Euclidean distance.
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