Improving k-Nearest Neighbor Rule: Using Geometrical Neighborhoods and Manifold-based metrics

Sample weighting and variations in neighborhood or data-dependent distance metric definitions are three principal directions considered for improving k-NN classification technique. Recently, manifold-based distance metrics attracted considerable interest and computationally less demanding approximations are developed. However, a careful comparison of these alternative approaches is missing. In this study, an extensive comparison is firstly performed for three alternative neighborhood definitions and four manifold-based distance measures. Then, a novel computationally less demanding feature line based method is proposed which exploits geometrical neighborhoods of test samples for feature line construction. Experimental results have shown that the improvements achieved by majority of the existing schemes are not considerable. It is also verified that the proposed scheme surpasses other computationally less demanding manifold-based schemes. keywords: nearest neighbor classifier; geometrical neighborhood definition; manifold-based metrics; interpolation inaccuracy; extrapolation inaccuracy