Fuzzy k-NN classification with weights modified by most informative neighbors of nearest neighbors

In the conventional fuzzy k-NN classification rule, the vote cast by each nearest neighboring known (labelled) sample on the class membership grades of the unknown (unlabelled) sample is formed by weighting the nearest neighbor's class membership grades by the inverse of the nearest neighbor's distance to the unknown sample. This paper proposes a modification of the weight (distance) used for each nearest neighbor by employing the geometrical relation among the nearest neighbor, its most informative known neighbor of the same class and the unknown sample. It is also proposed that this modification be only (conditionally) applied when the feature vector of the unknown sample lies outside the convex hull of the feature vectors of the known samples of each class. Results on a large number of datasets from the UCI and KEEL repositories and synthetically generated datasets show that, in return for a modest increase in classification complexity over the original fuzzy k-NN rule, the proposed fuzzy k-NN rule offers a better classification accuracy than the accuracies of the original fuzzy k-NN rule and most other nearest neighbor type algorithms.