Abstract

This paper presents a newly modified K-Mean technique for clustering data that are not situated around a single point center. When the clusters are elongated, the traditional K-Mean technique cannot yield meaningful results. In modifying the K-Mean technique to allow a center to be a line segment, elongated clusters can be extracted for analysis. The distance function is modified to measure the distance between a point and a set (line segment). The modified technique can be easily extended to multidimensional data where the center is shaped as a hyperplane, and the clusters of data that are situated around the hyperplane can be easily extracted and modeled into a regression model. The technique is applied to economic data of Chile, where the clusters are shown to be of irregular shapes, and where it is common to find regression model representing data sets.