An optimally weighted fuzzy k-NN algorithm

The nearest neighbor rule is a non-parametric approach and has been widely used for pattern classification. The k-nearest neighbor (k-NN) rule assigns crisp memberships of samples to class labels; whereas the fuzzy k-NN neighbor rule replaces crisp memberships with fuzzy memberships. The membership assignment by the conventional fuzzy k-NN algorithm has a disadvantage in that it depends on the choice of some distance function, which is not based on any principle of optimality. To overcome this problem, we introduce in this paper a computational scheme for determining optimal weights to be combined with different fuzzy membership grades for classification by the fuzzy k-NN approach. We show how this optimally weighted fuzzy k-NN algorithm can be effectively applied for the classification of microarray-based cancer data.