Recursive information granulation: aggregation and interpretation issues

This paper contributes to the conceptual and algorithmic framework of information granulation. We revisit the role of information granules that are relevant to several main classes of technical pursuits involving temporal and spatial granulation. A detailed algorithm of information granulation, regarded as an optimization problem reconciling two conflicting design criteria, namely, a specificity of information granules and their experimental relevance (coverage of numeric data), is provided in the paper. The resulting information granules are formalized in the language of set theory (interval analysis). The uniform treatment of data points and data intervals (sets) allows for a recursive application of the algorithm. We assess the quality of information granules through application of the fuzzy c-means (FCM) clustering algorithm. Numerical studies deal with two-dimensional (2D) synthetic data and experimental traffic data.