Sparse Similarity and Network Navigability for Markov Clustering Enhancement

Markov clustering (MCL) is an effective unsupervised pattern recognition algorithm for data clustering in high-dimensional feature space that simulates stochastic flows on a network of sample similarities to detect the structural organization of clusters in the data. However, it presents two main drawbacks: (1) its community detection performance in complex networks has been demonstrating results far from the state-of-the-art methods such as Infomap and Louvain, and (2) it has never been generalized to deal with data nonlinearity. In this work both aspects, although closely related, are taken as separated issues and addressed as such. Regarding the community detection, field under the network science ceiling, the crucial issue is to convert the unweighted network topology into a ‘smart enough’ pre-weighted connectivity that adequately steers the stochastic flow procedure behind Markov clustering. Here a conceptual innovation is introduced and discussed focusing on how to leverage network latent geometry notions in order to design similarity measures for pre-weighting the adjacency matrix used in Markov clustering community detection. The results demonstrate that the proposed strategy improves Markov clustering significantly, to the extent that it is often close to the performance of current state-of-the-art methods for community detection. These findings emerge considering both synthetic ‘realistic’ networks (with known ground-truth communities) and real networks (with community metadata), even when the real network connectivity is corrupted by noise artificially induced by missing or spurious links. Regarding the nonlinearity aspect, the development of algorithms for unsupervised pattern recognition by nonlinear clustering is a notable problem in data science. Minimum Curvilinearity (MC) is a principle that approximates nonlinear sample distances in the high-dimensional feature space by curvilinear distances, which are computed as transversal paths over their minimum spanning tree, and then stored in a kernel. Here, a nonlinear MCL algorithm termed MC-MCL is proposed, which is the first nonlinear kernel extension of MCL and exploits Minimum Curvilinearity to enhance the performance of MCL in real and synthetic high-dimensional data with underlying nonlinear patterns. Furthermore, improvements in the design of the so-called MC-kernel by applying base modifications to better approximate the data hidden geometry have been evaluated with positive outcomes. Thus, different nonlinear MCL versions are compared with baseline and state-of-art clustering methods, including DBSCAN, K-means, affinity propagation, density peaks, and deep-clustering. As result, the design of a suitable nonlinear kernel provides a valuable framework to estimate nonlinear distances when its kernel is applied in combination with MCL. Indeed, nonlinear-MCL variants overcome classical MCL and even state-of-art clustering algorithms in different nonlinear datasets. This dissertation discusses the enhancements and the generalized understanding of how network geometry plays a fundamental role in designing algorithms based on network navigability

Coupled node similarity learning for community detection in attributed networks

© 2018 by the authors. Attributed networks consist of not only a network structure but also node attributes. Most existing community detection algorithms only focus on network structures and ignore node attributes, which are also important. Although some algorithms using both node attributes and network structure information have been proposed in recent years, the complex hierarchical coupling relationships within and between attributes, nodes and network structure have not been considered. Such hierarchical couplings are driving factors in community formation. This paper introduces a novel coupled node similarity (CNS) to involve and learn attribute and structure couplings and compute the similarity within and between nodes with categorical attributes in a network. CNS learns and integrates the frequency-based intra-attribute coupled similarity within an attribute, the co-occurrence-based inter-attribute coupled similarity between attributes, and coupled attribute-to-structure similarity based on the homophily property. CNS is then used to generate the weights of edges and transfer a plain graph to a weighted graph. Clustering algorithms detect community structures that are topologically well-connected and semantically coherent on the weighted graphs. Extensive experiments verify the effectiveness of CNS-based community detection algorithms on several data sets by comparing with the state-of-the-art node similarity measures, whether they involve node attribute information and hierarchical interactions, and on various levels of network structure complexity

Local dominance unveils clusters in networks

Clusters or communities can provide a coarse-grained description of complex systems at multiple scales, but their detection remains challenging in practice. Community detection methods often define communities as dense subgraphs, or subgraphs with few connections in-between, via concepts such as the cut, conductance, or modularity. Here we consider another perspective built on the notion of local dominance, where low-degree nodes are assigned to the basin of influence of high-degree nodes, and design an efficient algorithm based on local information. Local dominance gives rises to community centers, and uncovers local hierarchies in the network. Community centers have a larger degree than their neighbors and are sufficiently distant from other centers. The strength of our framework is demonstrated on synthesized and empirical networks with ground-truth community labels. The notion of local dominance and the associated asymmetric relations between nodes are not restricted to community detection, and can be utilised in clustering problems, as we illustrate on networks derived from vector data

HIGH PERFORMANCE DECENTRALISED COMMUNITY DETECTION ALGORITHMS FOR BIG DATA FROM SMART COMMUNICATION APPLICATIONS

Many systems in the world can be represented as models of complex networks and subsequently be analysed fruitfully. One fundamental property of the real-world networks is that they usually exhibit inhomogeneity in which the network tends to organise according to an underlying modular structure, commonly referred to as community structure or clustering. Analysing such communities in large networks can help people better understand the structural makeup of the networks. For example, it can be used in mobile ad-hoc and sensor networks to improve the energy consumption and communication tasks. Thus, community detection in networks has become an important research area within many application fields such as computer science, physical sciences, mathematics and biology. Driven by the recent emergence of big data, clustering of real-world networks using traditional methods and algorithms is almost impossible to be processed in a single machine. The existing methods are limited by their computational requirements and most of them cannot be directly parallelised. Furthermore, in many cases the data set is very big and does not fit into the main memory of a single machine, therefore needs to be distributed among several machines. The main topic of this thesis is about network community detection within these big data networks. More specifically, in this thesis, a novel approach, namely Decentralized Iterative Community Clustering Approach (DICCA) for clustering large and undirected networks is introduced. An important property of this approach is its ability to cluster the entire network without the global knowledge of the network topology. Moreover, an extension of the DICCA called Parallel Decentralized Iterative Community Clustering approach (PDICCA) is proposed for efficiently processing data distributed across several machines. PDICCA is based on MapReduce computing platform to work efficiently in distributed and parallel fashion. In addition, the real-world networks are usually noisy and imperfect with missing and false edges. These imperfections are often difficult to eliminate and highly affect the quality and accuracy of conventional methods used to find the community structure in the network. However, in real-world networks, node attribute information is also available in addition to topology information. Considering more than one source of information for community detection could produce meaningful clusters and improve the robustness of the network. Therefore, a pre-processing approach that considers attribute information, shared neighbours and connectivity information aspects of the network for community detection is presented in this thesis as part of my research. Finally, a set of real-world mobile phone usage data obtained from Cambridge Laboratories (Device Analyzer) has been analysed as an exploratory step for viability to apply the algorithms developed in this thesis. All the proposed approaches have been evaluated and verified for feasibility using real-world large data set. The evaluation results of these experimentations prove very promising for the type of large data networks considered

Beyond similarity: A network approach for identifying and delimiting biogeographical regions

Biogeographical regions (geographically distinct assemblages of species and communities) constitute a cornerstone for ecology, biogeography, evolution and conservation biology. Species turnover measures are often used to quantify biodiversity patterns, but algorithms based on similarity and clustering are highly sensitive to common biases and intricacies of species distribution data. Here we apply a community detection approach from network theory that incorporates complex, higher order presence-absence patterns. We demonstrate the performance of the method by applying it to all amphibian species in the world (c. 6,100 species), all vascular plant species of the USA (c. 17,600), and a hypothetical dataset containing a zone of biotic transition. In comparison with current methods, our approach tackles the challenges posed by transition zones and succeeds in identifying a larger number of commonly recognised biogeographical regions. This method constitutes an important advance towards objective, data derived identification and delimitation of the world's biogeographical regions.Comment: 5 figures and 1 supporting figur