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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              [ comp.ai is moderated. To submit, just post and be patient, or if ]       [ that fails mail your article to |
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