A comparison of different heterogeneous proximity functions and Euclidean distance

Proximity functions evaluate distances or similarities between objects. Unlike the Euclidean distance, heterogeneous proximity functions process variables differently according to their scale. The correct evaluation of nominal variables, whose values are unordered, is especially important. We compared five heterogeneous functions with the Euclidean distance to study whether functions sensitive to scale are better than a function assuming the same scale. In addition, we were interested of the relative performance of the five heterogeneous functions. The performance of the functions was measured with a nearest neighbor classifier that was applied to 12 medical data sets characterized with different scales. Unexpectedly, the performance of heterogeneous functions did not differ significantly from that of the Euclidean distance. As expected, significant differences between the Heterogeneous Value Difference Metric (HVDM) and the four value-matching-based heterogeneous functions favored HVDM. Additional research is needed to explain why heterogeneous functions did not outperform the Euclidean distance.