This chapter demonstrates intelligent data analysis, within the environment of uncertain reasoning, using the recently introduced CaRBS technique that has its mathematical rudiments in Dempster-Shafer theory. A series of classification and ranking analyses are undertaken on a bank rating application, looking at Moody’s bank financial strength rating (BFSR). The results presented involve the association of each bank to being low or high BFSR, with emphasis is on the graphical exposition of the results including the use of a series of simplex plots. Throughout the analysis there is discussion on how the present of ignorance in the results should be handled, whether it should be excluded (belief) or included (plausibility) in the evidence supporting the classification or ranking of the banks.
TopIntroduction
One direction of intelligent data analysis is within the environment that facilitates uncertain reasoning, which by its definition acknowledges the often imperfection of the considered data (Chen, 2001). Amongst the general methodologies associated with uncertain reasoning, is, Dempster-Shafer Theory (DST), introduced in Dempster (1967) and Shafer (1976). Indeed, an alternative term for DST, regularly employed, is evidential reasoning, which further epitomises the computational intelligence domain worked in (see for example, Srivastava and Liu, 2003; Smets, 1991).
The reasoning associated with DST has been contentiously argued as a generalisation of Bayesian probability calculus (Shafer and Srivastava, 1990), in contrast, Cobb and Shenoy (2003) suggest they have ‘roughly’ the same expressive power. Specific techniques that are based around DST include, in multi-criteria decision making DS/AHP (Beynon, 2002) and belief decision trees (Vannoorenberghe, 2004). Pertinent to this chapter’s analysis, inherent with DST based analyses is their close association with the ability to undertake such analysis in the presence of ignorance (Safranek et al., 1990).
A nascent DST based technique for object classification and ranking is CaRBS, which has the full title Classification and Ranking Belief Simplex, introduced in Beynon (2005a). It facilitates this analysis by constructing bodies of evidence (DST terminology), from characteristics describing the objects, which are then combined to offer the evidence used to classify or rank them. The CaRBS technique offers a visual representation of the contribution of characteristics to the classification and ranking of objects using simplex plots, including the concomitant levels of ambiguity and ignorance (Beynon, 2005b). While only recently introduced, it has been applied in the areas of; education (Jones and Beynon, 2007), finance (Beynon, 2005b) and medicine (Jones et al., 2006).
In this chapter, the two directions of analysis offered by the CaRBS technique, namely classification and ranking, are exposited. In the case of object classification, the objects are known to be classed to a given hypothesis or its complement. It follows, a quantifying objective function is described which places emphasis on the minimising of ambiguity in the objects’ classifications, but not the inherent ignorance associated with their individual classifications (Beynon, 2005b). In the case of the ranking of objects across the domain of the potential classifications, based on the objects’ characteristic values describing them, this is between the extremes of a given hypothesis and its complement. How the inherent ignorance is included depends on whether more formulaic belief or plausibility measures are employed (Beynon and Kitchener, 2005).
A sample bank rating problem is analysed using the CaRBS technique, with classification and ranking analyses performed on the associated data set. The relative simplicity of the CaRBS technique and visual presentation of the findings allows the reader the opportunity to succinctly view a form of DST based data analysis. This analysis includes an elucidation of the notions of ambiguity and ignorance in object classification, and belief or plausibility based ranking of objects. Moreover, the analysis, using CaRBS, is encompassing of the presence of ignorance in its facilitation of intelligent data analysis.
It is intended for this chapter to offer the reader a benchmark outline in the ability to intelligently analyse data, through classification and/or ranking, in an environment based on uncertain reasoning.