On a Multidimensional Cluster Scaling

This paper proposes a multidimensional cluster scaling (MDCS) which obtains scaling of multidimensional clus- ters (or groups). Conventional multidimensional scaling is well known as a method to obtain the scaling of multidi- mensional objects. However, there is no method to obtain the scaling of the clusters. The merit of this scaling method is its applicability for the analysis of large amounts of data such as big data. Since the purpose of the scaling method is to obtain the latent structure of a given data in a lower dimensional space in order to summarize the data features and the visualization of the data structure, for large amounts of data, a loss of the data information through the reduction of the dimensions has been a main problem with the use of the scaling method. The proposed method can solve this problem by the use of clusters of objects. Several numerical examples show the better performance of the proposed method.