Showing papers by "Richard C. Wilson published in 2018"

Network analysis using entropy component analysis

Abstract: Structural complexity measures have found widespread use in network analysis. For instance, entropy can be used to distinguish between different structures. Recently we have reported an approximate network von Neumann entropy measure, which can be conveniently expressed in terms of the degree configurations associated with the vertices that define the edges in both undirected and directed graphs. However, this analysis was posed at the global level, and did not consider in detail how the entropy is distributed across edges. The aim in this paper is to use our previous analysis to define a new characterization of network structure, which captures the distribution of entropy across the edges of a network. Since our entropy is defined in terms of vertex degree values defining an edge, we can histogram the edge entropy using a multi-dimensional array for both undirected and directed networks. Each edge in a network increments the contents of the appropriate bin in the histogram, indexed according to the degree pair in an undirected graph or the in/out-degree quadruple for a directed graph. We normalize the resulting histograms and vectorize them to give network feature vectors reflecting the distribution of entropy across the edges of the network. By performing principal component analysis (PCA) on the feature vectors for samples, we embed populations of graphs into a low-dimensional space. We explore a number of variants of this method, including using both fixed and adaptive binning over edge vertex degree combinations, using both entropy weighted and raw bin-contents, and using multi-linear principal component analysis (MPCA), aimed at extracting the tensorial structure of high-dimensional data, as an alternative to classical PCA for component analysis. We apply the resulting methods to the problem of graph classification, and compare the results obtained to those obtained using some alternative state-of-the-art methods on real-world data.

Thermodynamic Analysis of Time Evolving Networks

Abstract: The problem of how to represent networks, and from this representation, derive succinct characterizations of network structure and in particular how this structure evolves with time, is of central importance in complex network analysis. This paper tackles the problem by proposing a thermodynamic framework to represent the structure of time-varying complex networks. More importantly, such a framework provides a powerful tool for better understanding the network time evolution. Specifically, the method uses a recently-developed approximation of the network von Neumann entropy and interprets it as the thermodynamic entropy for networks. With an appropriately-defined internal energy in hand, the temperature between networks at consecutive time points can be readily derived, which is computed as the ratio of change of entropy and change in energy. It is critical to emphasize that one of the main advantages of the proposed method is that all these thermodynamic variables can be computed in terms of simple network statistics, such as network size and degree statistics. To demonstrate the usefulness of the thermodynamic framework, the paper uses real-world network data, which are extracted from time-evolving complex systems in the financial and biological domains. The experimental results successfully illustrate that critical events, including abrupt changes and distinct periods in the evolution of complex networks, can be effectively characterized.

Directed Graph Evolution from Euler-Lagrange Dynamics

Abstract: In this paper, we develop a variational principle from the von Neumann entropy for directed graph evolution. We minimise the change of entropy over time to investigate how directed networks evolve under the Euler-Lagrange equation. We commence from our recent work in which we show how to compute the approximate von Neumann entropy for a directed graph based on simple in and out degree statistics. To formulate our variational principle we commence by computing the directed graph entropy difference between different time epochs. This is controlled by the ratios of the in-degree and out-degrees at the two nodes forming a directed edge. It also reveals how the entropy change is related to correlations between the changes in-degree ratio and in-degree, and their initial values. We conduct synthetic experiments with three widely studied complex network models, namely Erdos-Renyi random graphs, Watts-Strogatz small-world networks, and Barabasi-Albert scale-free networks, to simulate the in-degree and out-degree distribution. Our model effectively captures the directed structural transitions in the dynamic network models. We also apply the method to the real-world financial networks. These networks reflect stock price correlations on the New York Stock Exchange(NYSE) and can be used to characterise stable and unstable trading periods. Our model not only effectively captures how the directed network structure evolves with time, but also allows us to detect periods of anomalous network behaviour.

A centrality measure for cycles and subgraphs II.

Abstract: In a recent work we introduced a measure of importance for groups of vertices in a complex network. This centrality for groups is always between 0 and 1 and induces the eigenvector centrality over vertices. Furthermore, its value over any group is the fraction of all network flows intercepted by this group. Here we provide the rigorous mathematical constructions underpinning these results via a semi-commutative extension of a number theoretic sieve. We then established further relations between the eigenvector centrality and the centrality proposed here, showing that the latter is a proper extension of the former to groups of nodes. We finish by comparing the centrality proposed here with the notion of group-centrality introduced by Everett and Borgatti on two real-world networks: the Wolfe’s dataset and the protein-protein interaction network of the yeast Saccharomyces cerevisiae. In this latter case, we demonstrate that the centrality is able to distinguish protein complexes

A Centrality Measure for Cycles and Subgraphs II

Abstract: In a recent work we introduced a measure of importance for groups of vertices in a complex network. This centrality for groups is always between 0 and 1 and induces the eigenvector centrality over vertices. Furthermore, its value over any group is the fraction of all network flows intercepted by this group. Here we provide the rigorous mathematical constructions underpinning these results via a semi-commutative extension of a number theoretic sieve. We then established further relations between the eigenvector centrality and the centrality proposed here, showing that the latter is a proper extension of the former to groups of nodes. We finish by comparing the centrality proposed here with the notion of group-centrality introduced by Everett and Borgatti on two real-world networks: the Wolfe's dataset and the protein-protein interaction network of the yeast \textit{Saccharomyces cerevisiae}. In this latter case, we demonstrate that the centrality is able to distinguish protein complexes.

Plenoptic Imaging for Seeing Through Turbulence

Abstract: Atmospheric distortion is one of the main barriers to imaging over long distances. Changes in the local refractive index perturb light rays as they pass through, causing distortion in the images captured in a camera. This problem can be overcome to some extent by using a plenoptic imaging system (one which contains an array of microlenses in the optical path). In this paper, we propose a model of image distortion in the microlens images and propose a computational method for correcting the distortion. This algorithm estimates the distortion field in the microlenses. We then propose a second algorithm to infer a consistent final image from the multiple images of each pixel in the microlens array. These algorithms detect the distortion caused by changes in atmospheric refractive index and allow the reconstruction of a stable image even under turbulent imaging conditions. Finally we present some reconstruction results and examine whether there is any increase in performance from the camera system. We demonstrate that the system can detect and track distortions caused by turbulence and reconstruct an improved final image.

Structural, Syntactic, and Statistical Pattern Recognition. Joint IAPR International Workshop, S+SSPR 2018, Beijing, China, August 17–19, 2018, Proceedings

Abstract: With the fast development of smartphones and social media image sharing, automatic image annotation has become a research area of great interest. It enables indexing, extracting and searching in large collections of images in an easier and faster way. In this paper, we propose a model for the annotation extension of images using a semantic hierarchy. This latter is built from vocabulary keyword annotations combining a mixture of Bernoulli distributions with mixtures of Gaussians.

Categorization of RNA Molecules Using Graph Methods

Abstract: RNA molecules are a group of biologically active molecules which have a similar structure to DNA. Graph-based methods for classification have shown promise on other biological compounds such as protein. In this paper, we investigate the use of graph representations of RNA, graph-feature based methods and their role in classifying RNA into particular categories. We describe a number of possible graph representations of RNA structure and how useful information can be encoded in the graph. We show how graph-kernel and graph-feature methods can be used to provide descriptors for the molecules. Finally, on a moderately-sized database of 419 RNA structures, we explore how these methods can be used to classify RNA into high-level categories provided by the biological context or function of the molecules. We find that graph descriptors give state-of-the-art performance on sequence classification, but that the graph elements of the description do not add useful information above the base-sequence.

Quantum Edge Entropy for Alzheimer’s Disease Analysis

Abstract: In this paper, we explore how to the decompose the global statistical mechanical entropy of a network into components associated with its edges. Commencing from a statistical mechanical picture in which the normalised Laplacian matrix plays the role of Hamiltonian operator, thermodynamic entropy can be calculated from partition function associated with different energy level occupation distributions arising from Bose-Einstein statistics and Fermi-Dirac statistics. Using the spectral decomposition of the Laplacian, we show how to project the edge-entropy components so that the detailed distribution of entropy across the edges of a network can be achieved. We apply the resulting method to fMRI activation networks to evaluate the qualitative and quantitative characterisations. The entropic measurement turns out to be an effective tool to identify the differences in structure of Alzheimer’s disease by selecting the most salient anatomical brain regions.