Local-global nested graph kernels using nested complexity traces

IEEE Trans. Neural Netw. Learning Syst.

et al. 2023

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Network representations are powerful tools to modelling the dynamic time-varying financial complex systems consisting of multiple co-evolving financial time series, e.g., stock prices, etc. In this work, we develop a novel framework to compute the kernel-based similarity measure between dynamic time-varying financial networks. Specifically, we explore whether the proposed kernel can be employed to understand the structural evolution of the financial networks with time associated with standard kernel machines. For a set of time-varying financial networks with each vertex representing the individual time series of a different stock and each edge between a pair of time series representing the absolute value of their Pearson correlation, our start point is to compute the commute time matrix associated with the weighted adjacency matrix of the network structures, where each element of the matrix can be seen as the enhanced correlation value between pairwise stocks. For each network, we show how the commute time matrix allows us to identify a reliable set of dominant correlated time series as well as an associated dominant probability distribution of the stock belonging to this set. Furthermore, we represent each original network as a discrete dominant Shannon entropy time series computed from the dominant probability distribution. With the dominant entropy time series for each pair of financial networks to hand, we develop an Entropic Dynamic Time Warping Kernels through the classical dynamic time warping framework, for analyzing the financial time-varying networks. We show that the proposed kernel bridges the gap between graph kernels and the classical dynamic time warping framework for multiple financial time series analysis. Experiments on time-varying networks extracted through New York Stock Exchange (NYSE) database demonstrate that the proposed method can effectively detect abrupt changes in networks as time series structures and can be used to characterize different stages in time-varying financial network evolutions.

Section: B the Dynamic Time Warping Frameworkmentioning

confidence: 99%

Entropic Dynamic Time Warping Kernels for Co-Evolving Financial Time Series Analysis

IEEE Trans. Neural Netw. Learning Syst.

et al. 2023

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“…Given a set of graphs G, for each sample graph Gp ∈ G: (1) we compute the K-dimensional DB representation DB K p;v rooted at each vertex (e.g., vertex v 2 of Gp). We represent this as a K-dimensional vertex vector, where each element Hs(G K p;2 ) of DB K p;v represents the Shannon entropy of the K-layer expansion subgraph rooted at v 2 [32].…”

Section: Align Tomentioning

confidence: 99%

“…To construct reliable correspondence information for the graphs, in this work we employ a depth-based (DB) representation [32] as the initial vectorial vertex representations (i.e.R K ). This is because the DB representation of each vertex is computed by measuring the entropies on a family of k-layer expansion subgraphs rooted at the vertex, where the parameter k varies from 1 to K. It has been shown that such a Kdimensional DB representation can be viewed as a nested vertex representation that encapsulates a rich nested entropybased information content flow from each local vertex to the global graph structure, as a function of depth.…”

Section: Align Tomentioning

confidence: 99%

“…We sort the K-dimensional prototype representations in PR K according to their degree D R (µ K j ), and rearrange X K p and A K p accordingly. As we have stated in Section II-B, in this work we employ the K-dimensional DB representations [32] as the initialized vectorial vertex representations to compute the K-level correspondence matrix (C K p ) of each graph G p . Specifically, the DB representation can encapsulate rich nested structure information from each local vertex to the global graph structure through the K-layer expansion subgraphs rooted at the vertex.…”

Section: A Aligned Vertex Grid Structures Of Graphsmentioning

confidence: 99%

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Learning Graph Convolutional Networks based on Quantum Vertex Information Propagation

Jiao

IEEE Trans. Knowl. Data Eng.

et al. 2021

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This paper proposes a new Quantum Spatial Graph Convolutional Neural Network (QSGCNN) model that can directly learn a classification function for graphs of arbitrary sizes. Unlike state-of-the-art Graph Convolutional Neural Network (GCNN) models, the proposed QSGCNN model incorporates the process of identifying transitive aligned vertices between graphs and transforms arbitrary sized graphs into fixed-sized aligned vertex grid structures. In order to learn representative graph characteristics, a new quantum spatial graph convolution is proposed and employed to extract multi-scale vertex features, in terms of quantum information propagation between grid vertices of each graph. Since the quantum spatial convolution preserves the grid structures of the input vertices (i.e., the convolution layer does not alter the original spatial position of vertices), the proposed QSGCNN model allows to directly employ the traditional convolutional neural network architecture to further learn from the global graph topology, providing an end-to-end deep learning architecture that integrates the graph representation and learning in the quantum spatial graph convolution layer and the traditional convolutional layer for graph classifications. We indicate the effectiveness of the proposed QSGCNN model in relation to existing state-of-the-art methods. Experiments on benchmark graph classification datasets demonstrate the effectiveness of the proposed QSGCNN model.

“…The procedure of computing the correspondence matrix. Given a set of graphs, for each graph Gp: (1) we compute the K-dimensional depth-based (DB) representation DB K p;v rooted at each vertex (e.g., vertex 2) as the K-dimensional vectorial vertex representation, where each element Hs(G K p;2 ) represents the Shannon entropy of the K-layer expansion subgraph rooted at vertex v 2 of Gp[35]; (2) we identify a family of K-dimensional prototype representations PR K = {µ K 1 , . .…”

mentioning

confidence: 99%

Learning Backtrackless Aligned-Spatial Graph Convolutional Networks for Graph Classification

IEEE Trans. Pattern Anal. Mach. Intell.

Jiao

et al. 2022

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In this paper, we develop a novel Backtrackless Aligned-Spatial Graph Convolutional Network (BASGCN) model to learn effective features for graph classification. Our idea is to transform arbitrary-sized graphs into fixed-sized backtrackless aligned grid structures and define a new spatial graph convolution operation associated with the grid structures. We show that the proposed BASGCN model not only reduces the problems of information loss and imprecise information representation arising in existing spatially-based Graph Convolutional Network (GCN) models, but also bridges the theoretical gap between traditional Convolutional Neural Network (CNN) models and spatially-based GCN models. Furthermore, the proposed BASGCN model can both adaptively discriminate the importance between specified vertices during the convolution process and reduce the notorious tottering problem of existing spatially-based GCNs related to the Weisfeiler-Lehman algorithm, explaining the effectiveness of the proposed model. Experiments on standard graph datasets demonstrate the effectiveness of the proposed model.