From: mlh496@gmail.com   
      
   On Oct 4, 1:41 am, "Xiao Xiong"  wrote:   
   > I have a general question to ask:   
   >   
   > There are a set of supervised training data which belong to two classes   
   > A and B. Each training sample is a multi-dimensional vector and the   
   > covariance matrix of the features are not diagonal, that is the feature   
   > elements are correlated. Assume the underlying pdf is completely known.   
   > We can use two Gaussian mixture models (GMM) for the two classes   
   > separately and build a Bayesian classifer.   
   >   
   > My quesetion is:   
   >   
   > Is it possible to use some kinds of feature transformation method, such   
   > as Linear Discriminative Analysis, to project the features into a new   
   > space for better discriminative power?   
   >   
      
   One way to extract the features from a multi-dimensional normal   
   distribution is to use the Mahalanobis distance.  This can be thought   
   of as a generalization of the z-score to multivariate normal   
   distributions.  If you let m1 and m2 be the Mahalanobis distances for A   
   & B respectively, then your decision rule is:   
      - classify 'x' as A if m1 < m2,   
      - otherwise classify 'x' as B.   
      
   -Michael   
      
   PS: http://en.wikipedia.org/wiki/Mahalanobis_distance   
      
      
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