The minimum feature set problem

One approach to improving the generalization power of a neural net is to try to minimize the number of non-zero weights used. We examine two issues relevant to this approach, for single-layer nets. First we bound the VC dimension of the set of linearthreshold functions that have non-zero weights for at most s of n inputs. Second, we show that the problem of minimizing the number of non-zero input weights used (without misclassifying training examples) is both NP-hard and di cult to approximate.