Symbolic Data Analysis: A Paradigm for Complex Data Mining?

Introduction

Standard data mining techniques take “attribute-value” tables as input. These tables’ cells are known as micro data by statisticians. But current technologies allow storing vast quantities of information from different sources in nature, with hierarchical data or with any other complexity in a data type such as images, multimedia data, and geographical data.

This information has missing values, nulls, internal variation, taxonomies, and rules. We need a new type of data analysis that allows us represent the complexity of reality, maintaining the internal variation and structure (Diday, 2010).

In Data Analysis Process or Data Mining, it is necessary to know the nature of null values - the cases are by absence value, null value or default value -, being also possible and valid to have some imprecision, due to differential semantic in a concept, diverse sources, linguistic imprecision, element resumed in Database, human errors, etc. (Chavent, 1997). So, we need a conceptual support to manipulate these types of situations. As we are going to see below, Symbolic Data Analysis (SDA) is a new issue based on a strong conceptual model called Symbolic Object (SO). The objective of SDA is to extend classical data analysis to symbolic tables in order to find SOs as concepts’ representation.

A “SO” is defined by its “intent” which contains a way to find its “extent”. For instance, the description of inhabitants in a region and the way of allocating an individual to this region is called “intent”, the set of individuals, which satisfies this intent, is called “extent” (Diday 2003). For this type of analysis, different experts are needed, each one giving their concepts.

Basically, Diday (2002) distinguishes between two types of concept:

• 1.

  The concepts of the real world: That kind of concept is defined by an “intent” and an “extent” which exists, have existed or will exist in the real world.

• 2.

  The concepts of our mind (among the so called “mental objects” by J.P. Changeux (1983)) which frame in our mind concepts of our imagination or of the real world by their properties and a “way of finding their extent” (by using the senses), and not the extent itself as (undoubtedly!), there is no room in our mind for all the possible extents (Diday, 2003).

A “SO” models a concept, in the same way our mind does, by using a description “d” (representing its properties) and a mapping “a” able to compute its extent, for instance, the description of what we call a “car” and a way of recognizing that a given entity of in the real world is a car. Hence, whereas a concept is defined by intent and extent, it is modeled by intent and a way of finding its extent is by “SOs” like those in our mind. It should be noticed that it is quite impossible to obtain all the characteristic properties of a concept and its complete extent. Therefore, a SO is just an approximation of a concept and the problems of quality, robustness and reliability of this approximation arise (Diday, 2003).

The purpose of this article is to present the fundamental concepts of the symbolic data analysis paradigm and symbolic object concept. Theoretical aspects and examples allow us to understand the SDA paradigm as a tool for mining complex data.

The topic is presented as follows: foundations of SDA and SO; Semantics applied to the SO Concept and Principles of SDA (in the section SDA and SO Formal definitions); Future Trends; Conclusions; References and Key Terms.

Foundations Of Sda And So

Diday presented the first article on 1988, in the Proceedings of the First Conference of the International Federation of Classification Societies (IFCS) (Bock & Diday 2000). Then, much work has been done up to the publication of Bock, Diday (2000) and the Proceedings of IFCS’2000 (Bock & Diday 2000). Diday has directed an important quantity of PhD Thesis, with relevant theoretical aspects for SO. Some of the most representatives works are: Brito P. (1991), De Carvalho F. (1992), Auriol E. (1995), Périnel E. (1996), Stéphan V. (1996), Ziani D. (1996), Chavent M. (1997), Polaillon G. (1998), Hillali Y. (1998), Mfoummoune E. (1998), Vautrain F. (2000), Rodriguez Rojas O. (2000), De Reynies M. (2001), Vrac M. (2002), Mehdi M. (2003) and Pak K. (2003).