Methods to Determine Node Centrality and Clustering in Graphs with Uncertain Structure

Much of the past work in network analysis has focused on analyzing discrete graphs, where binary edges represent the "presence" or "absence" of a relationship. Since traditional network measures (e.g., betweenness centrality) utilize a discrete link structure, complex systems must be transformed to this representation in order to investigate network properties. However, in many domains there may be uncertainty about the relationship structure and any uncertainty information would be lost in translation to a discrete representation. Uncertainty may arise in domains where there is moderating link information that cannot be easily observed, i.e., links become inactive over time but may not be dropped or observed links may not always corresponds to a valid relationship. In order to represent and reason with these types of uncertainty, we move beyond the discrete graph framework and develop social network measures based on a probabilistic graph representation. More specifically, we develop measures of path length, betweenness centrality, and clustering coefficient---one set based on sampling and one based on probabilistic paths. We evaluate our methods on three real-world networks from Enron, Facebook, and DBLP, showing that our proposed methods more accurately capture salient effects without being susceptible to local noise, and that the resulting analysis produces a better understanding of the graph structure and the uncertainty resulting from its change over time.Comment: Longer version of paper appearing in Fifth International AAAI Conference on Weblogs and Social Media. 9 pages, 4 Figure

Real-time analytics for complex structure data

University of Technology Sydney. Faculty of Engineering and Information Technology.The advancement of data acquisition and analysis technology has resulted in many real-world data being dynamic and containing rich content and structured information. More specifically, with the fast development of information technology, many current real-world data are always featured with dynamic changes, such as new instances, new nodes and edges, and modifications to the node content. Different from traditional data, which are represented as feature vectors, data with complex relationships are often represented as graphs to denote the content of the data entries and their structural relationships, where instances (nodes) are not only characterized by the content but are also subject to dependency relationships. Plus, real-time availability is one of outstanding features of today’s data. Real-time analytics is dynamic analysis and reporting based on data entered into a system before the actual time of use. Real-time analytics emphasizes on deriving immediate knowledge from dynamic data sources, such as data streams, and knowledge discovery and pattern mining are facing complex, dynamic data sources. However, how to combine structure information and node content information for accurate and real-time data mining is still a big challenge. Accordingly, this thesis focuses on real-time analytics for complex structure data. We explore instance correlation in complex structure data and utilises it to make mining tasks more accurate and applicable. To be specific, our objective is to combine node correlation with node content and utilize them for three different tasks, including (1) graph stream classification, (2) super-graph classification and clustering, and (3) streaming network node classification. Understanding the role of structured patterns for graph classification: the thesis introduces existing works on data mining from an complex structured perspective. Then we propose a graph factorization-based fine-grained representation model, where the main objective is to use linear combinations of a set of discriminative cliques to represent graphs for learning. The optimization-oriented factorization approach ensures minimum information loss for graph representation, and also avoids the expensive sub-graph isomorphism validation process. Based on this idea, we propose a novel framework for fast graph stream classification. A new structure data classification algorithm: The second method introduces a new super-graph classification and clustering problem. Due to the inherent complex structure representation, all existing graph classification methods cannot be applied to super-graph classification. In the thesis, we propose a weighted random walk kernel which calculates the similarity between two super-graphs by assessing (a) the similarity between super-nodes of the super-graphs, and (b) the common walks of the super-graphs. Our key contribution is: (1) a new super-node and super-graph structure to enrich existing graph representation for real-world applications; (2) a weighted random walk kernel considering node and structure similarities between graphs; (3) a mixed-similarity considering structured content inside super-nodes and structural dependency between super-nodes; and (4) an effective kernel-based super-graph classification method with sound theoretical basis. Empirical studies show that the proposed methods significantly outperform the state-of-the-art methods. Real-time analytics framework for dynamic complex structure data: For streaming networks, the essential challenge is to properly capture the dynamic evolution of the node content and node interactions in order to support node classification. While streaming networks are dynamically evolving, for a short temporal period, a subset of salient features are essentially tied to the network content and structures, and therefore can be used to characterize the network for classification. To achieve this goal, we propose to carry out streaming network feature selection (SNF) from the network, and use selected features as gauge to classify unlabeled nodes. A Laplacian based quality criterion is proposed to guide the node classification, where the Laplacian matrix is generated based on node labels and network topology structures. Node classification is achieved by finding the class label that results in the minimal gauging value with respect to the selected features. By frequently updating the features selected from the network, node classification can quickly adapt to the changes in the network for maximal performance gain. Experiments and comparisons on real-world networks demonstrate that SNOC is able to capture dynamics in the network structures and node content, and outperforms baseline approaches with significant performance gain

Internal combustion engine sensor network analysis using graph modeling

In recent years there has been a rapid development in technologies for smart monitoring applied to many different areas (e.g. building automation, photovoltaic systems, etc.). An intelligent monitoring system employs multiple sensors distributed within a network to extract useful information for decision-making. The management and the analysis of the raw data derived from the sensor network includes a number of specific challenges still unresolved, related to the different communication standards, the heterogeneous structure and the huge volume of data. In this paper we propose to apply a method based on complex network theory, to evaluate the performance of an Internal Combustion Engine. Data are gathered from the OBD sensor subset and from the emission analyzer. The method provides for the graph modeling of the sensor network, where the nodes are represented by the sensors and the edge are evaluated with non-linear statistical correlation functions applied to the time series pairs. The resulting functional graph is then analyzed with the topological metrics of the network, to define characteristic proprieties representing useful indicator for the maintenance and diagnosis

Structure of social relations in the novel \emph{The Master and Margarita} by M. A. Bulgakov: A network analysis of verbal communications

A network analysis of the structure of social relationships in one of the most popular Russian novels of the Soviet era The Master and Margarita by M. Bulgakov has been carried out. The structure of the novel is complex (`a story within a story'); the real-world- and the other-world-characters are interacting. A complex and unusual structure of the character network is expected. Presumably, the network may be split in two subgraphs owing very different properties. This complex and unusual composition makes the novel especially attractive for a network analysis. In our study, only paired verbal communications between explicitly present and acting characters have been taken into account. Based on a character pair verbal communication matrix, a graph has been constructed, the vertices of which are the characters of the novel, while the edges correspond to the connections between them. Taking only dialog into account leads to the result, that the character network can be described by an ordinary, rather than a directed graph. Since the activity of the dialogs was out of our scope, the edges have been given no weights. The largest connected component of the graph consists of 76 characters. Centralities were computed to characterize the network. The assortativity coefficient of the network under consideration is negative -0.133, i.e., the network does not demonstrate the properties of a social network. The structure of the communities in the network was also analysed. In addition to the obvious large communities - the characters from the Yershalaim part of the novel and the characters of the Moscow part - the analysis also revealed a fine structure in the Moscow component. Using the analysis of centralities, a group of main characters has been detected. The central characters of the novel are Bezdomny, Woland, Levi Matthew, Koroviev, Azazello, Behemoth, Bosoi, Warenukha, Master, and Margarita.Comment: 21 pages, 2 figures, 4 tables, 39 reference

Community detection of political blogs network based on structure-attribute graph clustering model

Complex networks provide means to represent different kinds of networks with multiple features. Most biological, sensor and social networks can be represented as a graph depending on the pattern of connections among their elements. The goal of the graph clustering is to divide a large graph into many clusters based on various similarity criteria’s. Political blogs as standard social dataset network, in which it can be considered as blog-blog connection, where each node has political learning beside other attributes. The main objective of work is to introduce a graph clustering method in social network analysis. The proposed Structure-Attribute Similarity (SAS-Cluster) able to detect structures of community, based on nodes similarities. The method combines topological structure with multiple characteristics of nodes, to earn the ultimate similarity. The proposed method is evaluated using well-known evaluation measures, Density, and Entropy. Finally, the presented method was compared with the state-of-art comparative method, and the results show that the proposed method is superior to the comparative method according to the evaluations measures

空間的なテクスチャ解析によるコンプレックスネットワークに基づくテクスチャ解析の改善

This thesis proposes a new texture analysis model which enhanced from traditional complex network-based model for texture characterization via spatial texture analysis. The conceptual framework of the proposed model is to synergize between pattern recognition and graph theory research areas. The results of experiment show that the proposed model can capture robust textural information under various uncontrolled environments using standard texture databases. Texture analysis has played an important role in the last few decades. There are a growing number of techniques described in the literature, one of new area research is a complex network for texture characterization, which has developed in recent years. Inspired by the human brain system, the relation among structure texture elements on an image can be derived using the complex network model. Compared to the task of texture classification, development of the original complex network model is required in order to improve classification performance in environment variations. To fulfill this requirement, the enhancing complex network by spatial texture analysis (i.e., spatial distribution and spatial relation) has been achieved in this thesis. The proposed approach addresses the above requirement by investigating and modifying the original complex network model by extracting more discriminative information. A new graph connectivity measurement has been devised, including local spatial pattern mapping, which is denoted as a LSPM, to encode and describe local spatial arrangement of pixels. To the best of the author\u27s knowledge, as investigated in this thesis, the encoding spatial information which has been adapted within the original complex network model presented here were first proposed and reported by the author. The essence of this proposed graph connectivity measurement describes the spatial structure of local image texture cause it can effectively capture and detect micro-structures (e.g., edges, lines, spots) information which is critical being used to distinguish various pattern structures and invariant uncontrolled environments. Moreover, the graph-based representation has been investigated for improving the performance of texture classification. Spatial vector property has been comprised of deterministic graph modeling which decomposing the two component of the magnitude and the direction. Then, the proposed hybrid-based complex network comprises the enhancing graph-based representation, and the new graph connectivity measurement has been devised as an enhancing complex network-based model for texture characterization in this thesis. The experiments are evaluated by using four standard texture databases include Brodatz, UIUC, KTH-TIPS, and UMD. The experimental results are presented in terms of classification rate in this thesis to demonstrate that: firstly, the proposed graph connectivity measurement (LSPM) approach achieved on-average 86.25%, 77.25%, 89.38% and 94.06% respectively based on four databases. Secondly, the proposed graph-based spatial property approach achieved on-average 90.92%, 87.92%, 96.56% and 92.65%, respectively; finally, the hybrid-based complex network model achieved on-average 88.92%, 85.46%, 95.14% and 95.52% respectively. Accordingly, this thesis has advanced the original complex network-based model for texture characterization.九州工業大学博士学位論文 学位記番号：生工博甲第329号 学位授与年月日：平成30年9月21日1 Introduction|2 Literature Review|3 Complex Network Model and Spatial Information|4 Graph-based Representation in Texture Analysis|5 Hybrid-based Complex Network Model|6 Conclusions九州工業大学平成30年