Granular Vs. Point-Wise Metrics And Statistics To Accommodate Machine Learning Algorithms In Granular Feature Spaces

In this paper we propose two distinct ways of augmenting the existing clustering environment so that granular data (patterns) can be accommodated. The two approaches deal with either holistic or atomistic representations of metrics and descriptors when mining outcomes of granule-valued random variables. Granular computing is a paradigm oriented towards capturing and processing meaningful pieces of information, the so-called infor-mation granules. Epistemological foundations of granular computing are first addres-sed. While classical data mining is involved in the descriptive forming of information granules, we are primarily devoted to addressing a second level of abstraction: processing sets of granu-les, occurring as primary events (genuine outcomes of a set of granule-valued random variables), for abstrac-ting meta-granular knowledge. Next, we are concerned with formal foundations. Granular feature spaces are considered and their most relevant granular vs. point-wise metrics and descriptors are introduced, such as granular vs. point-wise dissimilarities, granular vs. point-wise centroid, granular vs. point-wise inertia, and so on. Finally, we apply such granular and point-wise descrip-tors and dissimilarities to Granular clus-tering, Dimensionality reduction and Multidimensional scaling carried out in terms of fuzzy granules.