A density and connectivity based decision rule for pattern classification

• Surrounding Influence Region (SIR) decision rule is proposed for pattern classification.
• SIR decision rule is a parameter-free approach.
• Gabriel Graph is used to define the proximity, connectivity and density relations among the data points.
• A unique neighborhood is constructed for each sample point.
• SIR decision rule is superior to the k-NN and GGN decision rules in artificial and real data sets.

In this paper we propose a novel neighborhood classifier, Surrounding Influence Region (SIR) decision rule. Traditional Nearest Neighbor (NN) classifier is a distance-based method, and it classifies a sample using a predefined number of neighbors. In this study neighbors of a sample are determined using not only the distance, but also the connectivity and density information. One of the well-known proximity graphs, Gabriel Graph, is used for this purpose. The neighborhood is unique for each sample. SIR decision rule is a parameter-free approach. Our experiments with artificial and real data sets show that the performance of the SIR decision rule is superior to the k-NN and Gabriel Graph neighbor (GGN) classifiers in most of the data sets.