Automatically Determining the Number of Clusters in Unlabeled Data Sets

One of the major problems in cluster analysis is the determination of the number of clusters in unlabeled data, which is a basic input for most clustering algorithms. In this paper, we investigate a new method called Dark Block Extraction (DBE) for automatically estimating the number of clusters in unlabeled data sets, which is based on an existing algorithm for Visual Assessment of Cluster Tendency (VAT) of a data set, using several common image and signal processing techniques. Its basic steps include 1) generating a VAT image of an input dissimilarity matrix, 2) performing image segmentation on the VAT image to obtain a binary image, followed by directional morphological filtering, 3) applying a distance transform to the filtered binary image and projecting the pixel values onto the main diagonal axis of the image to form a projection signal, and 4) smoothing the projection signal, computing its first-order derivative, and then detecting major peaks and valleys in the resulting signal to decide the number of clusters. Our DBE method is nearly "automatic," depending on just one easy-to-set parameter. Several numerical and real-world examples are presented to illustrate the effectiveness of DBE.