Consideration on hierarchical cluster analysis based on connecting adjacent hyper-rectangles

This paper proposes a new clustering method based on connecting adjacent hyper-rectangles. The k-means clustering is one of the well-known clustering techniques. At first, many clustering methods must decide the number of clusters. Our method searches a set of hyper-rectangles that satisfies the properties (1) each hyper-rectangle covers some of the samples, and (2) each sample is covered by at least one of the hyper-rectangles. Then, a collection of connected hyper-rectangles is assumed to be a cluster. One of the characteristic features of our method is that it can work if there is no initial value on the number of clusters assumed. We apply the hierarchical clustering method to realize the clustering based on connecting adjacent hyper-rectangles. The effectiveness of the, proposed method is shown by applying a small artificial data and iris data.