Minimising Entropy Changes in Dynamic Network Evolution

Abstract

Abstract. In this paper, we propose a novel method to adaptively select the most informative and least redundant feature subset, which has strong discriminating power with respect to the target label. Unlike most traditional methods using vectorial features, our proposed approach is based on graph-based features and thus incorporates the relationships between feature samples into the feature selection process. To efficiently encapsulate the main characteristics of the graphbased features, we probe each graph structure using the steady state random walk and compute a probability distribution of the walk visiting the vertices. Furthermore, we propose a new information theoretic criterion to measure the joint relevance of different pairwise feature combinations with respect to the target feature, through the Jensen-Shannon divergence measure between the probability distributions from the random walk on different graphs. By solving a quadratic programming problem, we use the new measure to automatically locate the subset of the most informative features, that have both low redundancy and strong discriminating power. Unlike most existing state-of-the-art feature selection methods, the proposed information theoretic feature selection method can accommodate both continuous and discrete target features. Experiments on the problem of P2P lending platforms in China demonstrate the effectiveness of the proposed method.

Directed and undirected network evolution from Euler–Lagrange dynamics

“…von Neumann entropy is the extension of the Shannon entropy defined over the re-scaled eigenvalues of the normalised Laplacian matrix. A quadratic approximation of the von Neumann entropy gives a simple expression for the entropy associated with the degree combinations of nodes forming edges (Wang et al, 2017a). In accordance with intuition, those edges that connect high degree vertices have the lowest entropy, while those connecting low degree vertices have the highest entropy (Aytekin et al, 2016;Wang et al, 2017b).…”

“…During the crisis, the persistent connected component exhibits a more homogeneous structure as shown in Fig.8. Compared to the first order model (Wang et al, 2017a), our new second order network prediction gives structures that more closely resemble the original network structure. After the crisis, the network preserves most of its existing community structure and begins to reconnect again.…”

Time-Varying Gene Expression Network Analysis Reveals Conserved Transition States in Hematopoietic Differentiation between Human and Mouse

“…The energy reflects the connections within the network of a vertex define the way in which any abstract resource (information, influence, or importance) circulates in its neighboring vertexes. We report the results here in the hope of stimulating further investigation of network energy [ 38 , 39 , 40 , 41 , 42 ].…”

Open system quantum thermodynamics of time-varying graphs

“…Additionally, the authors show how to compute thermodynamic variables in terms of node degree statistics. Similarly, in [32] the authors investigate the variation of entropy in time evolving networks and show how global modifications of network structure are determined by correlations in the changes in joint degree statistics for those pairs of nodes connected by edges.…”