IBA-based framework for modeling similarity

Abstract

In this paper, we introduce a logic-driven framework for modeling similarity based on interpolative Boolean algebra (IBA). It consists of two main steps: data preprocessing and similarity measuring by means of IBA similarity measure and logical aggregation. The purpose of these steps is to detect dependencies and model interactions among attributes and/or similarities using an appropriate operator. The proposed framework is general, providing different approaches to multi-attribute object comparison: attribute-by-attribute comparison, object-level comparison and their combination. It is also a generic framework since various similarity measures can be easily derived. The proposed IBA-based similarity framework has a solid mathematical background, which ensures all necessary properties of similarity measure are satisfied. It is interpretable and close to human perception. The framework's applicability is illustrated by two numerical examples that confirm the need for a different level of aggregations. Furthermore, the example of similarity-based classification demonstrates the descriptive power and transparency of the framework on real financial data.