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   Message 620 of 1,954   
   Greg Heath to All   
   Re: Functional approximation in higher d   
   24 Feb 05 04:46:33   
   
   XPost: comp.ai.neural-nets, sci.math.num-analysis, sci.math   
   From: heath@alumni.brown.edu   
      
   With that many inputs, the first order of business after scaling and   
   outlier removal is probably input dimensionality reduction.   
      
   In general, optimal results for classification and regression are   
   obtained when the the I/O transformation is taken into consideration.   
   However, since there is never a free lunch, compromises must be made   
   with the prediction/causality dilema.   
      
   For prediction, one looks for a method of dimensionality reduction that   
   will represent the n-dimensional input by as few as possible m (m < n)   
   independent features without significantly degrading the resulting   
   output. However, often this results in features whose correlation with   
   the output is very difficult for humans to understand.   
      
   For causality, one looks for a method of input variable subset   
   selection that will represent the n-dimensional input by as few as   
   possible p ( p < n) original inputs without significantly degrading   
   the resulting output. However, often the the number of inputs with an   
   understandable correlation with the output is far less than the number   
   needed to obtain a satisfactory output.   
      
   Nonlinear Partial Least Squares (NPLS) is a technique that has been   
   developed to deal with this dilema. I am not familiar with the method,   
   but I think it is equivalent to trying to minimize the weighted sum of   
   mean-square-errors in output and input space. There are free algorithms   
   available via an internet search. Most of them, however, are for Linear   
   PLS.   
      
   I've read that NLPS doesn't appear to have an advantage over NNs.   
   However, since many real-world I/O correlations have a strong linear   
   component, a quick and dirty fling with a free PLS (Linear) algorithm   
   might be fruitful. In the same vein, Linear Principal Component   
   Analysis in the combined I/O space is worth investigation.   
      
   Nonlinear NN techniques (Sensitivity coefficients, Optimal Brain   
   Damage, ...) that have been discussed in former postings and the FAQ   
   (See ftp://ftp.sas.com/pub/neural/importance.html#linmod_wgt) can be   
   searched using groups.google.com. These can lead to further searches   
   for free software.   
      
   Hope this helps.   
      
   Greg   
      
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