Detection of chain structures embedded in multidimensional symbolic data

The detection of meaningful geometrical structures in multidimensional data is of major interest in data analysis and data mining. In this paper, we will first present the notion of a locally monotonic chain structure based on the Cartesian system model (CSM) which is the mathematical model to manipulate symbolic data. The locally monotonic chain structures include not only monotonic chain structures but also various complex structures organized by several monotonic chains. Then, secondly, we will describe a method to detect the locally monotonic chain structures of objects embedded in multidimensional symbolic data. We will illustrate the usefulness of our method by using both several artificially generated data sets and a real data set.