Mesoscopic analysis of networks: Applications to exploratory analysis and data clustering

Abstract

We investigate the adaptation and performance of modularity-based algorithms, designed in the scope of complex networks, to analyze the mesoscopic structure of correlation matrices. Using a multi-resolution analysis we are able to describe the structure of the data in terms of clusters at different topological levels. We demonstrate the applicability of our findings in two different scenarios: to analyze the neural connectivity of the nematode Caenorhabditis elegans, and to automatically classify a typical benchmark of unsupervised clustering, the Iris data set, with considerable success.

Structural Patterns in Complex Systems Using Multidendrograms

“…For positive values of r, we have access to the substructures underneath those at r = 0, and for negative values of r we have access to the superstructures. A detailed analysis can be found in [25,26]. The screening of the full mesoscale, i.e., the range of values of r for which we detect different modular configurations from individual nodes to the whole network, provides a good representation of the internal structural patterns of the network.…”

A novel cosine distance for detecting communities in complex networks

“…Our algorithm results 277 communities with the optimal modularity as high as Q max = 0.951 which is greater than Q max = 0.927 by BCID algorithm and Q max = 0.720 by a fast fine-tuning algorithm presented in Ref. [33]. The optimal degree and cosine distance threshold are k r = 1 and d r = 0.67.…”

“…The coordinates of nodes v 1 , v 3 , v 4 , v33 , v 34 in Friendship network areTable 1shows part of cosine distances of nodes. The degree threshold of this network can be set as 1, 2, 3, 4, 5, 6, 9, 10, 12, 16 and 17.…”

Stochastic block model and exploratory analysis in signed networks

“…Biased results will be obtained if an inappropriate method is chosen. Even if we know something beforehand, it is still difficult for a method that is exclusively designed for a certain type of mesoscopic structure to uncover the aforementioned miscellaneous structures that may simultaneously coexist in a network or may even overlap with each other [8,[16][17][18][19][20].…”

“…However, we frequently encounter the signed networks, which have both positive and negative edges, in biology [19,32], computer science [33], and last but definitely not least, social science [34][35][36][37]. The negative connections usually represent hostility, conflict, opposition, disagreement, and distrust between individuals or organizations, as well as the anticorrelation among objectives, whose coupled relation with positive links has been empirically shown to play a crucial role in the function and evolution of the whole network [32,37].…”