A comparative study based on tensor factorization and clustering techniques for community mining in heterogeneous social network

In the real world, entities are often connected via multiple relations, forming multi-relational network. These complex networks need novel models for their representation and sophisticated tools for their analysis. Community detection is one of the primary tools for the structural and functional analysis of the networks at the macroscopic level. Already a lot of research work has been done on discovering communities in the networks with only single relation. However, the research work on discovering communities in multi-relational network (MRN) is still in its early stages. In this article, we have proposed a novel approach to extract the communities in a multi-relational network using DeepWalk network embedding technique and Consensus clustering. Empirical study is conducted on the real-world publicly available Twitter datasets. In our observations we found that our proposed model performs significantly better than some of the baseline approaches based on spectral clustering algorithm, modularity maximization, block clustering and non-negative matrix factorization.

The social network is a powerful data structure allowing the study of relationship information between entities. The existing methods only rely on analyzing homogeneous social network assuming only a single type of node and relation. Though, real world complex networks are not so. Usually it is a heterogeneous social network which assumes a network with different types of nodes and relation. A Multi Relational Network (MRN) is used to describe the nodes and links in the form of a directional semantic graph where each node is related with more than one relationship with others. The profile for each node can be generated based on the relation sequence of each node. To analyze the relation of node in the heterogeneous social network, role analysis is done in the profile creation. The evaluations are conducted on a real-world movie dataset with promising results.

Recognizing the latent community structure in the multi-relational networks has garnered inexorable attention by the researchers in the recent years. However, detecting overlapping communities in such complex networks is still an open research issue. There are two different types of overlapping possible in the network: crisp and fuzzy. In the network with crisp overlapping community structure, a node fully belongs to one or more communities at the same time. With fuzzy overlapping in the communities, a node can simultaneously belong to multiple clusters with different belonging factors. In this article, we attempt to discover fuzzy overlapping communities in multi-relational networks by combining non-negative matrix factorization, cluster ensemble approach and fuzzy c-means clustering. An extensive experimental study is performed on publicly available Twitter and YouTube datasets. The results obtained are promising and establish the efficacy of our scheme.

As tensors provide a natural representation for the higher-order relations, tensor factorization techniques such as Tucker decomposition and CANDECOMP/PARAFAC decomposition have been applied to many fields. Tucker decomposition has strong capacity of expression, but the time complexity is unpractical for the large-scale real problems. On the other hand, CANDECOMP/PARAFAC decomposition is linear in the feature dimensionality, but the assumption is so strong that it abandons some important information. Besides, both of TD and CP decompose a tensor into several factor matrices. However, the factor matrices are not natural for the representation of the higher-order relations. To overcome these problems, we propose a near linear tensor factorization approach, which decompose a tensor into factor tensors in order to model the higher-order relations, without loss of important information. In addition, to reduce the time complexity and the number of the parameters, we decompose each slice of the factor tensors into two smaller matrices. We conduct experiments on both synthetic datasets and real datasets. The experimental results on the synthetic datasets validate that our model has strong capacity of expression. The results on the real datasets show that our approach outperforms the state-of-the-art tensor factorization methods.

The multi-relational social network is a new social network, which is proposed in recent years and more complex than single relational social network. Therefore, the existing community discovery algorithm is lack and their results are crude. The paper proposes a new algorithm for discovering community in multi-relational social network based on modified common neighbors similarity. The core idea is the more common neighbors are shared between two nodes, the more similar the nodes are. Finally, we test our generalized algorithm on an artificial sparse network in four dimensions.

The low-rank tensor factorization (LRTF) technique has received increasing attention in many computer vision applications. Compared with the traditional matrix factorization technique, it can better preserve the intrinsic structure information and thus has a better low-dimensional subspace recovery performance. Basically, the desired low-rank tensor is recovered by minimizing the least square loss between the input data and its factorized representation. Since the least square loss is most optimal when the noise follows a Gaussian distribution, -norm-based methods are designed to deal with outliers. Unfortunately, they may lose their effectiveness when dealing with real data, which are often contaminated by complex noise. In this paper, we consider integrating the noise modeling technique into a generalized weighted LRTF (GWLRTF) procedure. This procedure treats the original issue as an LRTF problem and models the noise using a mixture of Gaussians (MoG), a procedure called MoG GWLRTF. To extend the applicability of the model, two typical tensor factorization operations, i.e., CANDECOMP/PARAFAC factorization and Tucker factorization, are incorporated into the LRTF procedure. Its parameters are updated under the expectation-maximization framework. Extensive experiments indicate the respective advantages of these two versions of MoG GWLRTF in various applications and also demonstrate their effectiveness compared with other competing methods.

The conventional notion of community that favors a high ratio of internal edges to outbound edges becomes invalid when each vertex participates in multiple communities. Such a behavior is commonplace in social networks. The significant overlaps among communities make most existing community detection algorithms ineffective. The lack of effective and efficient tools resulted in very few empirical studies on large-scale detection and analyses of overlapping community structure in real social networks. We developed recently a scalable and accurate method called the Partial Community Merger Algorithm (PCMA) with linear complexity and demonstrated its effectiveness by analyzing two online social networks, Sina Weibo and Friendster, with 79.4 and 65.6 million vertices, respectively. Here, we report in-depth analyses of the 2.9 million communities detected by PCMA to uncover their complex overlapping structure. Each community usually overlaps with a significant number of other communities and has far more outbound edges than internal edges. Yet, the communities remain well separated from each other. Most vertices in a community are multi-membership vertices, and they can be at the core or the peripheral. Almost half of the entire network can be accounted for by an extremely dense network of communities, with the communities being the vertices and the overlaps being the edges. The empirical findings ask for rethinking the notion of community, especially the boundary of a community. Realizing that it is how the edges are organized that matters, the f-core is suggested as a suitable concept for overlapping community in social networks. The results shed new light on the understanding of overlapping community.

In the social computing environment, the complete information about an individual is usually distributed in heterogeneous social networks, which are presented as linked data. Synthetically recognizing and integrating these distributed and heterogeneous data for efficiently information searching is an important but challenging work. In this paper, a dynamic weight (DW)-based similarity calculation is proposed to recognize and integrate similar individuals from distributed data environments. First, each link of an individual is weighted by applying DW. Then, a semantic similarity metric is proposed to combine the DW into similarity calculation. Then, a searching system framework for a similarity-based individual is designed and tested in real-world data sets. Finally, massive experiments are conducted both in benchmark and real-world social community data sets. The results show that our approach can produce a good result in similar individual searching in social networks. In addition, it performs significantly better than the existing state-of-the-art approaches in similar individual searching.

With the increasing popularity of streaming tensor data such as videos and audios, tensor factorization and completion have attracted much attention recently in this area. Existing work usually assume that streaming tensors only grow in one mode. However, in many real-world scenarios, tensors may grow in multiple modes (or dimensions), i.e., multi-aspect streaming tensors. Standard streaming methods cannot directly handle this type of data elegantly. Moreover, due to inevitable system errors, data may be contaminated by outliers, which cause significant deviations from real data values and make such research particularly challenging. In this paper, we propose a novel method for Outlier-Robust Multi-Aspect Streaming Tensor Completion and Factorization (OR-MSTC), which is a technique capable of dealing with missing values and outliers in multi-aspect streaming tensor data. The key idea is to decompose the tensor structure into an underlying low-rank clean tensor and a structured-sparse error (outlier) tensor, along with a weighting tensor to mask missing data. We also develop an efficient algorithm to solve the non-convex and non-smooth optimization problem of OR-MSTC. Experimental results on various real-world datasets show the superiority of the proposed method over the baselines and its robustness against outliers.

Finding meaningful communities in social network has attracted the attentions of many researchers. The community structure of complex networks reveals both their organization and hidden relations among their constituents. Most of the researches in the field of community detection mainly focus on the topological structure of the network without performing any content analysis. Nowadays, real world social networks are containing a vast range of information including shared objects, comments, following information, etc. In recent years, a number of researches have proposed approaches which consider both the contents that are interchanged in the networks and the topological structures of the networks in order to find more meaningful communities. In this research, the effect of topic analysis in finding more meaningful communities in social networking sites in which the users express their feelings toward different objects (like movies) by the means of rating is demonstrated by performing extensive experiments.

Tensors are becoming increasingly common in data mining, and consequently, tensor factorizations are becoming more important tools for data miners. When the data is binary, it is natural to ask if we can factorize it into binary factors while simultaneously making sure that the reconstructed tensor is still binary. Such factorizations, called Boolean tensor factorizations, can provide improved interpretability and find Boolean structure that is hard to express using normal factorizations. Unfortunately the algorithms for computing Boolean tensor factorizations do not usually scale well. In this paper we present a novel algorithm for finding Boolean CP and Tucker decompositions of large and sparse binary tensors. In our experimental evaluation we show that our algorithm can handle large tensors and accurately reconstructs the latent Boolean structure.

In the information retrieval field, effective and efficient extraction of topics from large-scale online text streams is challenging because it is a fully unsupervised learning task without prior knowledge. Most previous studies have focused on how to analyse text corpus to extract topics, rarely considering time dimensions. In the present study, we approached topic detection as a temporal optimization problem. Here, we propose a novel approach to incremental topic detection, called online topic detection using tensor factorization (OTD-TF), which is based on latent Dirichlet allocation (LDA). First, topics are obtained from the corpus in current time slices using LDA. Second, a topic tensor with a time dimension is constructed to identify the correlations between pairs of topics. Then, approximate topics are merged using TF. Finally, documents are reallocated to corresponding topic bins. By executing these steps continuously and incrementally, temporal topic detection can be achieved. In theoretical analyses and simulation experiments, OTD-TF outperformed other systems in terms of space and time complexity and achieved a high precision ratio. Our experimental evaluations also revealed interesting temporal patterns in topic emergence, development, extinction, burst and transience.

Fuzzy clustering is an invaluable data mining technique that allows each data point to belong to more than one cluster with some degree of membership. It is widely employed in exploratory data mining to discover overlapping communities in social networks, find structure in spectral data, and capture user interests in recommendation systems. Nowadays, the variety and volume of data are increasing at a tremendous rate. Data is power; the massive data, along with an effective technique, can unravel valuable information. The existing fuzzy clustering algorithms do not perform well on massive heterogeneous datasets. Processing an enormous amount of data is beyond the capacity of a single processor. The need of the hour is to develop fuzzy clustering techniques that can work on a distributed framework for Big Data processing and can handle heterogeneous data. In this research, we evaluate the performance of the recently proposed algorithm for the Fuzzy clustering of mixed-mode data FCMD-MD (D’Urso and Massari in Inf Sci 505:513–534, 2019) with different real-world datasets. We develop a distributed FCMD-MD, a fuzzy clustering algorithm for mixed-mode data in Apache SPARK. The experimental results show that the algorithm is scalable, performs well in a distributed environment, and clusters enormous heterogeneous data with high accuracy. We also compared the performance of distributed FCMD-MD and the distributed k-medoid algorithm.

The article is devoted to the topical issue of identifying information threats in virtual communities of social networks and mechanisms for counteracting such threats. The process of organization of monitoring and content analysis of virtual communities in social networks is studied. The technology of detecting information threats of virtual communities in social networks and methods of their assessment have been developed. An approach to finding pages of discussions on social networks based on the Louvain method is proposed. The technology of determining the degree of information threat of the virtual community in social networks and ways to counteract the information threats of the virtual community have been developed.

A hierarchical divisive algorithm is proposed for identifying communities in complex networks. To that effect, the definition of community in the weak sense of Radicchi [Proc. Natl. Acad. Sci. U.S.A. 101, 2658 (2004)] is extended into a criterion for a bipartition to be optimal: one seeks to maximize the minimum for both classes of the bipartition of the ratio of inner edges to cut edges. A mathematical program is used within a dichotomous search to do this in an optimal way for each bipartition. This includes an exact solution of the problem of detecting indivisible communities. The resulting hierarchical divisive algorithm is compared with exact modularity maximization on both artificial and real world data sets. For two problems of the former kind optimal solutions are found; for five problems of the latter kind the edge ratio algorithm always appears to be competitive. Moreover, it provides additional information in several cases, notably through the use of the dendrogram summarizing the resolution. Finally, both algorithms are compared on reduced versions of the data sets of Girvan and Newman [Proc. Natl. Acad. Sci. U.S.A. 99, 7821 (2002)] and of Lancichinetti [Phys. Rev. E 78, 046110 (2008)]. Results for these instances appear to be comparable.