Common principal components model for symbolic data

Abstract

This paper proposes a dimension reduction technique in the framework of symbolic data analysis (SDA). Recent advances in technology have increased the complexity of datasets, and today, their size is much larger than it was in the past decade. Most statistical methods do not have sufficient power to analyze these datasets. SDA was proposed by Diday at the end of the 1980s and is a new approach for analyzing huge and complex data.SDA examines “symbolic data”, which consist of concepts. A concept consists of not only values but also “higher-level units” such as an interval and a distribution. Their combination can also be represented as a kind of a concept. This implies that complex data can be formally handled in the framework of SDA. However, there are very few studies based on this simple idea. Therefore, practical methods should be developed to apply this idea to solve problems in the real world. In this study, we focus on the case in which a concept contains some subsets (the concept acts as a typical complex dataset) and develop a new method to analyze this dataset directly using SDA. In this paper, we propose a dimension reduction technique in the framework of SDA, especially for a group structure, and introduce a numerical example.