The Distance Function Optimization for the Near Neighbors-Based Classifiers

Based on the analysis of conditions for a good distance function we found four rules that should be fulfilled. Then, we introduce two new distance functions, a metric and a pseudometric one. We have tested how they fit for distance-based classifiers, especially for the IINC classifier. We rank distance functions according to several criteria and tests. Rankings depend not only on criteria or nature of the statistical test, but also whether it takes into account different difficulties of tasks or whether it considers all tasks as equally difficult. We have found that the new distance functions introduced belong among the four or five best out of 23 distance functions. We have tested them on 24 different tasks, using the mean, the median, the Friedman aligned test, and the Quade test. Our results show that a suitable distance function can improve behavior of distance-based classification rules.