Multidimensional Joint Scale and Cluster Analysis

This paper proposes a joint scaling and clustering method for dissimilarity (or similarity) data. Dissimilarity (or similarity) data is obtained as showing dissimilarity (or similarity) relationship among objects that are target data. Multidimensional scaling (MDS) is a typical method of scaling from the dissimilarity (or similarity) data in order to summarize the relationship of objects in lower dimensional space and obtain a classification structure of the objects in the lower dimensional space. However, the classification structure is obtained by the distance of objects in the lower dimensional space, and the classification is not based on the original dissimilarity that is given as the data. To solve this problem, this paper proposes a multidimensional scaling that includes the classification structure of objects based on the original dissimilarity data of the objects. We obtain a result of MDS for clusters as the result of clustering of objects based on the original dissimilarity data. This is beneficial if the number of objects is large such as a big data since the number of clusters is much smaller than the number of objects.