A method for calculating two-dimensional spatially extension distances and its clustering algorithm

Abstract

This paper presents a novel method for calculating the extension distance between a point and a two-dimensional convex set. The proposed method builds upon existing techniques by employing a line traversal approach. By traversing the convex set with a line originating from the point of interest, the extension distance is computed based on the intersection points between the line and the set along the two coordinate axes. The weights assigned to the intersection points play a crucial role in the distance calculation. By summing the extension distances in both directions, the overall extension distance of the point with respect to the set is obtained. Furthermore, a clustering algorithm is introduced, which incorporates the concept of an interaction factor commonly used in engineering experiments. The multidimensional data is projected onto feature planes created by combining pairs of features. The calculation method for extension distances between points and convex sets in two dimensions is applied to determine the distances between points and cluster classes (or cluster centers). The distances on each feature plane are then weighted, summed, and analyzed to establish the relationships between points and cluster classes, thereby achieving clustering. The feasibility of the proposed algorithm is validated through comparative experiments k-means algorithm on the iris dataset and the wine dataset. The experimental results confirm the effectiveness and viability of the proposed approach.