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In this paper, we present a novel method for constructing a generative model to analyze the structure of labeled data. Given a time-series of sample graphs, we aim to learn a so-called “supergraph” that best describes the underlying average connectivity structure presenting in the data. In this time-series the vertex set is fixed and labeled and the set of possible connections between vertices change...
In this paper we present a method for constructing a generative prototype for a set of graphs by adopting a minimum description length approach. The method is posed in terms of learning a generative supergraph model from which the new samples can be obtained by an appropriate sampling mechanism. We commence by constructing a probability distribution for the occurrence of nodes and edges over the supergraph...
Structural complexity measures and embedding have both been extensively and separately employed for the problems of graph clustering and classification. In this paper we aim to explore whether entropy component analysis can be used as a means of combining these two fundamental approaches. Specifically we develop a novel method that embeds undirected graphs into a feature space based on the graph entropy...
In this paper, we aim to present a principled approach to the problem of depth-based complexity characterisation of graphs. Our idea is to decompose graphs into substructures of increasing size, and then to measure the complexity of these substructures using Shannon entropy or von-Neumann entropy. We commence by identifying the dominant vertex in a graph. From the dominant vertex, we construct subgraphs...
This talk focusses on work aimed at developing a principled probabilistic and information theoretic framework for learning generative models of relational structure. The aim is develop methods that can be used to learn models that can capture the variability present in graph-structures used to represent shapes or arrangements of shape-primitives in images. Here nodes represent the parts of shape-primitives...
In this paper we establish a formal link between network complexity in terms of Birkhoff-von Newmann decompositions and heat flow complexity (in terms of quantifying the heat flowing through the network at a given inverse temperature). Furthermore, we also define heat flow complexity in terms of thermodynamic depth, which results in a novel approach for characterizing networks and quantify their complexity...
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