Class-aware tensor factorization for multi-relational classification

Katsimpras, Georgios; Παλιούρας, Γεώργιος

doi:10.1016/j.ipm.2019.102068

Cited by 4 publications

(1 citation statement)

References 33 publications

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“…The work in [84,85,86,87,88,89,90,91,92] employs such tensor model to learn an inherent structure from multi-relational data. The following rank-L factorization was employed, known as the RESCAL decomposition [87], whereby each frontal slice of A is factorized as where U ∈ R N ×L is a factor matrix which maps the Ndimensional entity space to an L-dimensional latent component space, and R m ∈ R L×L models the interactions of latent components within the m-th relation type.…”

Section: Tensor Representation Of Multi-relational Graphsmentioning

confidence: 99%

Graph Signal Processing -- Part III: Machine Learning on Graphs, from Graph Topology to Applications

Stanković¹,

Mandic²,

Daković³

et al. 2020

Preprint

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Many modern data analytics applications on graphs operate on domains where graph topology is not known a priori, and hence its determination becomes part of the problem definition, rather than serving as prior knowledge which aids the problem solution. Part III of this monograph starts by addressing ways to learn graph topology, from the case where the physics of the problem already suggest a possible topology, through to most general cases where the graph topology is learned from the data. A particular emphasis is on graph topology definition based on the correlation and precision matrices of the observed data, combined with additional prior knowledge and structural conditions, such as the smoothness or sparsity of graph connections. For learning sparse graphs (with small number of edges), the least absolute shrinkage and selection operator, known as LASSO is employed, along with its graph specific variant, graphical LASSO. For completeness, both variants of LASSO are derived in an intuitive way, and explained. An in-depth elaboration of the graph topology learning paradigm is provided through several examples on physically well defined graphs, such as electric circuits, linear heat transfer, social and computer networks, and spring-mass systems. As many graph neural networks (GNN) and convolutional graph networks (GCN) are emerging, we have also reviewed the main trends in GNNs and GCNs, from the perspective of graph signal filtering. We have in particular studied the diffusion process over graphs and have shown that the trend of various improvements on GCNs can also be understood from the graph diffusion perspective. Given that the existing GCNs have been introduced largely in a heuristic manner, the definition of different diffusion processes can also serve as a basis for a new design of GCNs. Tensor representation of lattice-structured graphs is next considered, and it is shown that tensors (multidimensional data arrays) are a special class of graph signals, whereby the graph vertices reside on a high-dimensional regular lattice structure. This part of monograph concludes with two emerging applications in financial data processing and underground transportation networks modeling. By means of portfolio cuts of an asset graph, we show how domain knowledge can be meaningfully incorporated into investment analysis. In the underground traffic example, we demonstrate how graph theory can be used to identify the stations in the London underground network which have the greatest influence on the functionality of the traffic, and proceed, in an innovative way, to assess the impact of a station closure on service levels across the city. Contents 1 Introduction 2 2 Geometrically Defined Graph Topologies 3 3 Graph Topology Based on Signal Similarity 4 4 Learning of Graph Laplacian from Data 8 4.1 Imposing Sparsity on the Connection Metric 10 4.2 Smoothness Constrained Learning of Graph Laplacian .

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