Dissimilarity measures for histogram-valued data and divisive clustering of symbolic objects

Contemporary datasets are becoming increasingly larger and more complex, while techniques to analyse them are becoming more and more inadequate. Thus, new methods are needed to handle these new types of data. This study introduces methods to cluster histogram-valued data. However, histogram-valued data are difficult to handle computationally because observations typically have a different number and length of subintervals. Thus, a transformation for histogram data is proposed as a technique for handling them more easily computationally. From this technique, three new dissimilarity measures for histogram data are proposed. Then, how the monothetic clustering algorithm based on Chavent (1998, 2000) can be extended to histogram data is shown, and a polythetic clustering algorithm for symbolic objects is developed (based on all p variables). Validity criteria to aid in the selection of the optimal number of clusters are described and verified by some simulation studies. The new methodology is illustrated on a large dataset collected from the US Forestry Service. Index words: Symbolic data, Histogram-valued data, Dissimilarity measure, Monothetic algorithm, Polythetic algorithm, Validity Dissimilarity Measures for Histogram-valued Data and Divisive Clustering of Symbolic Objects