Toward Generalized Clustering through an One-Dimensional Approach

After generalizing the concept of clusters to incorporate clusters that are linked to other clusters through some relatively narrow bridges, an approach for detecting patches of separation between these clusters is developed based on an agglomerative clustering, more specifically the single-linkage, applied to one-dimensional slices obtained from respective feature spaces. The potential of this method is illustrated with respect to the analyses of clusterless uniform and normal distributions of points, as well as a one-dimensional clustering model characterized by two intervals with high density of points separated by a less dense interstice. This partial clustering method is then considered as a means of feature selection and cluster identification, and two simple but potentially effective respective methods are described and illustrated with respect to some hypothetical situations.