Granular modeling and computing approaches for intelligent analysis of non-geometric data

Data analysis techniques have been traditionally conceived to cope with data described in terms of numeric vectors. The reason behind this fact is that numeric vectors have a well-defined and clear geometric interpretation, which facilitates the analysis from the mathematical viewpoint. However, the state-of-the-art research on current topics of fundamental importance, such as smart grids, networks of dynamical systems, biochemical and biophysical systems, intelligent trading systems, multimedia content-based retrieval systems, and social networks analysis, deal with structured and non-conventional information characterizing the data, providing richer and hence more complex patterns to be analyzed. As a consequence, representing patterns by complex (relational) structures and defining suitable, usually non-metric, dissimilarity measures is becoming a consolidated practice in related fields. However, as the data sources become more complex, the capability of judging over the data quality (or reliability) and related interpretability issues can be seriously compromised. For this purpose, automated methods able to synthesize relevant information, and at the same time rigorously describe the uncertainty in the available datasets, are very important: information granulation is the key aspect in the analysis of complex data. In this paper, we discuss our general viewpoint on the adoption of information granulation techniques in the general context of soft computing and pattern recognition, conceived as a fundamental approach towards the challenging problem of automatic modeling of complex systems. We focus on the specific setting of processing the so-called non-geometric data, which diverges significantly from what has been done so far in the related literature. We highlight the motivations, the founding concepts, and finally we provide the high-level conceptualization of the proposed data analysis framework.