XPost: comp.ai.neural-nets   
   From: ted.dunning@gmail.com   
      
   Actually, centering and scaling aren't all that big of a deal; most NN   
   training algorithms can handle a few mis-scaled or offset inputs pretty   
   reasonably.  It is a good idea to scale and offset, but it isn't all   
   that terribly important.   
      
   It is generally more helpful to use the empirical distribution of the   
   inputs to non-linearly rescale inputs to more conventional   
   distributions.  This particularly helps when inputs have multiple size   
   scales, but the nature of the scales is not particularly clear.  By   
   scaling by the empirical distribution and then converting the resulting   
   (approximately) uniformly distributed value using an inverse normal   
   cumulative distribution to an approximately normally distributed value.   
      
   Once input redistribution is done, it can also be helpful to transform   
   all inputs by first clustering the data and then using the distances to   
   all of the cluster centroids instead of (or in addition to) the   
   original inputs.  These distances may best be described in terms of   
   probabilities by assuming each cluster is itself normally distributed.   
   EM based clustering algorithms are particularly good for this.   
      
   These are non-linear transformations which can be difficult to   
   characterize theoretically, but the practical import in certain   
   problems can be substantial.   
      
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