title: Genetic algorithms: fitness function for feature selection algorithm
body: <p>I have data set n x m where there are n observations and each observation consists of m values for m attributes. Each observation has also observed result assigned to it. m is big, too big for my task. I am trying to find a best and smallest subset of m attributes that still represents the whole dataset quite well, so that I could use only these attributes for teaching a neural network.</p>
  
  <p>I want to use genetic algorithm for this. The problem is the fittness function. It should tell how well the generated model (subset of attributes) still reflects the original data. And I don't know how to evaluate certain subset of attributes against the whole set.
  Of course I could use the neural network(that will later use this selected data anyway) for checking how good the subset is - the smaller the error, the better the subset. BUT, this takes a looot of time in my case and I do not want to use this solution. I am looking for some other way that would preferably operate only on the data set.</p>
  
  <p>What I thought about was: having subset S (found by genetic algorithm), trim data set so that it contains values only for subset S and check how many observations in this data ser are no longer distinguishable (have same values for same attributes) while having different result values. The bigger the number is, the worse subset it is. But this seems to me like a bit too computationally exhausting.</p>
  
  <p>Are there any other ways to evaluate how well a subset of attributes still represents the whole data set?</p>