Top-Down Granulation Modeling Based on the Principle of Justifiable Granularity

Information granulation is an effective vehicle to explore data structure and has become a timely research topic. In this article, a top-down granulation model (T-GrM) adhering to the two fundamental requirements (coverage and specificity) in the principle of justifiable granularity is designed. Here, this principle is employed as a fundamental method for constructing information granules in each layer, and as an indicator to determine whether the obtained partitions need to be further divided in the next layer. For capturing the correlation among features and reflecting the data structure, an improved version of a T-GrM is offered by incorporating the principal component analysis. The proposed granulation models are evaluated on synthetic datasets, where the obtained experimental results offer some insights into the feasibility of the designed models and describe the effect of parameter values on the constructed information granules. The improved version of the T-GrM has the advantage of being transparent by generating information granules on several principal components, and thereby, the description of information granules is simpler and descriptive. As application examples, two real-world datasets are analyzed to exhibit the advantage of the constructed information granules.