From: rif@mit.edu   
      
   "Michael"  writes:   
      
   > 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?   
   > >   
      
   Assuming the underlying pdf is completely known is probably not a good   
   assumption.  If it's true, use the feature transformation of   
   projecting your multidimensional x to the single vector p(c_1 | x)   
   (easily found via Bayes rule and the prior on the classes), which will   
   then contain all the information you need to do optimal discrimination   
   (if your loss function is just number of misclassified points,   
   classify based on p(c_1 | x) > .5).   
      
   My point is that discrimination is hard only because the underlying   
   pdf is never completely known.  In fact, it's not even well-known,   
   because doing density estimation in high dimensions is tough.   
      
   Are you actually interested in projections for their own sake, do you   
   need dimensionality reduction, or do you really just want to   
   discriminate?   
      
   rif   
      
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