Least-squares community extraction in feature-rich networks using similarity data

Abstract

We explore a doubly-greedy approach to the issue of community detection in feature-rich networks. According to this approach, both the network and feature data are straightforwardly recovered from the underlying unknown non-overlapping communities, supplied with a center in the feature space and intensity weight(s) over the network each. Our least-squares additive criterion allows us to search for communities one-by-one and to find each community by adding entities one by one. A focus of this paper is that the feature-space data part is converted into a similarity matrix format. The similarity/link values can be used in either of two modes: (a) as measured in the same scale so that one may can meaningfully compare and sum similarity values across the entire similarity matrix (summability mode), and (b) similarity values in one column should not be compared with the values in other columns (nonsummability mode). The two input matrices and two modes lead us to developing four different Iterative Community Extraction from Similarity data (ICESi) algorithms, which determine the number of communities automatically. Our experiments at real-world and synthetic datasets show that these algorithms are valid and competitive.

An Effective Partitional Crisp Clustering Method Using Gradient Descent Approach

“…We applied the mechanism proposed in [66], which was later used in various papers, for instance [67][68][69], to generate our synthetic data. In this mechanism, first, we needed to determine the number of data points N, clusters K, and features V. Next, the clusters' cardinalities were determined randomly with two constraints: (a) no cluster should contain less than a pre-specified number of data points (we set this number to 30 in our experiments), and (b) the number of data points in all clusters should sum to N. Once the cluster cardinalities were determined, we generated each cluster from a multivariate normal distribution whose covariance matrix was diagonal with diagonal values derived uniformly at random from the range [0.05, 0.1]-they specify the cluster's spread.…”

“…The Min-Max method standardizes the data point xiv = x iv −x va x vb −x va such that xiv ∈ [0, 1]. Although it was empirically shown, for instance in [67], that the clustering result might differ depending on how the data were standardized, due to the intuitiveness of the output of the Min-Max technique, we chose it as the default for our experiments.…”