A new modularity measure for Fuzzy Community detection problems based on overlap and grouping functions

One of the main challenges of fuzzy community detection problems is to be able to measure the quality of a fuzzy partition. In this paper, we present an alternative way of measuring the quality of a fuzzy community detection output based on n-dimensional grouping and overlap functions. Moreover, the proposed modularity measure generalizes the classical Girvan–Newman (GN) modularity for crisp community detection problems and also for crisp overlapping community detection problems. Therefore, it can be used to compare partitions of different nature (i.e. those composed of classical, overlapping and fuzzy communities). Particularly, as is usually done with the GN modularity, the proposed measure may be used to identify the optimal number of communities to be obtained by any network clustering algorithm in a given network. We illustrate this usage by adapting in this way a well-known algorithm for fuzzy community detection problems, extending it to also deal with overlapping community detection problems and produce a ranking of the overlapping nodes. Some computational experiments show the feasibility of the proposed approach to modularity measures through n-dimensional overlap and grouping functions.Supported by the Government of Spain (grant TIN2012-32482), the Government of Madrid (grant S2013/ICCE-2845)Peer reviewe

Big data para científicos sociales. Una introducción

Depto. de Sociología AplicadaFac. de Ciencias Políticas y SociologíaTRUEpu

Segmentación y clasificación en la toma de decisiones

Depto. de Estadística e Investigación OperativaFac. de Ciencias MatemáticasTRUEpu

On the semantics of bipolarity and fuzziness

Abstract This paper analyzes the relationship between fuzziness and bipolarity, notions which were devised to address different kinds of uncertainty: linguistic imprecision, in the former, and knowledge relevance and character or polarity, in the latter. Although different types of fuzziness and bipolarity have been defined, these relations are not always clear. This paper proposes the use of four-valued extensions to provide a formal method to rigorously define and compare the semantics and logical structure of diverse combinations of fuzziness and bipolarity types. As a result, this paper claims that these notions and their different types are independent and not semantically equivalent despite its possible formal equivalence

Comparative Assessment of the Image Divide and Link Algorithm in Different Color Spaces

In this paper, a comparative assessment of the Image Divide and Link Algorithm (ID&L) in different color spaces is presented. This, in order to show the significance of choosing a specific color space when the algorithm computes the dissimilarity measure between adjacent pixels. Specifically, the algorithm procedure is based on treating a digital image as a graph, assigning a weight to each edge based on the dissimilarity measure between adjacent pixels. Then, the algorithm constructs a spanning forest through a Kruskal scheme to order the edges successively while partitions are obtained. This process is driven until all the pixels of the image are segmented, that is, there are as many regions as pixels. The results of the algorithm which have been compared with those generated using different color spaces are shown.This research has been partially supported by the Government of Spain (grant TIN2015- -66471-P), the Government of Madrid (grant S2013/ICE-2845, CASI-CAM-CM), Complutense University (UCM research group 910149).Peer reviewe