Revisiting Resolution and Inter-Layer Coupling Factors in Modularity for Multilayer Networks

Modularity for multilayer networks, also called multislice modularity, is parametric to a resolution factor and an inter-layer coupling factor. The former is useful to express layer-specific relevance and the latter quantifies the strength of node linkage across the layers of a network. However, such parameters can be set arbitrarily, thus discarding any structure information at graph or community level. Other issues are related to the inability of properly modeling order relations over the layers, which is required for dynamic networks. In this paper we propose a new definition of modularity for multilayer networks that aims to overcome major issues of existing multislice modularity. We revise the role and semantics of the layer-specific resolution and inter-layer coupling terms, and define parameter-free unsupervised approaches for their computation, by using information from the within-layer and inter-layer structures of the communities. Moreover, our formulation of multilayer modularity is general enough to account for an available ordering of the layers and relating constraints on layer coupling. Experimental evaluation was conducted using three state-of-the-art methods for multilayer community detection and nine real-world multilayer networks. Results have shown the significance of our modularity, disclosing the effects of different combinations of the resolution and inter-layer coupling functions. This work can pave the way for the development of new optimization methods for discovering community structures in multilayer networks.Comment: Accepted at the IEEE/ACM Conf. on Advances in Social Network Analysis and Mining (ASONAM 2017

Approximate Matching in ACSM Dissimilarity Measure

AbstractThe paper introduces a new patch-based dissimilarity measure for image comparison employing an approximation strategy. It extends the Average Common Sub-matrix measure computing the exact dissimilarity among images. In the exact method, dissimilarity between two images is obtained by considering the average area of the biggest square sub-matrices in common between the images, by exact match of the extracted sub-matrices pixel by pixel. As an extension, the proposed dissimilarity measure computes an approximate match between the sub-matrices, which is obtained by omitting a controlled number of pixels at a given column offset inside the sub-matrices. The proposed dissimilarity measure is extensively compared with other well-known approximate methods for image comparison in the state-of-the-art. Experiments demonstrate the superiority of the proposed approximate measure in terms of execution time with respect to the exact method, and in terms of retrieval precision with respect to the other state-of-the-art methods