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The Electronic Journal of Combinatorics, 2016 This is a survey of distance-regular graphs. We present an introduction to distance-regular graphs for the reader who is unfamiliar with the subject, and then give an overview of some developments in the area of distance-regular graphs since the monograph 'BCN' [Brouwer, A.E., Cohen, A.M., Neumaier, A., Distance-Regular Graphs, Springer-Verlag, Berlin,
Edwin R. van Dam +2 more
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Impact of regularization on Spectral Clustering [PDF]
, 2014 The performance of spectral clustering can be considerably improved via regularization, as demonstrated empirically in Amini et. al (2012). Here, we provide an attempt at quantifying this improvement through theoretical analysis.
Joseph, Antony, Yu, Bin
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The American Mathematical Monthly, 2011 A graph G=(V,E) is called a unit-distance graph in the plane if there is an injective embedding of V in the plane such that every pair of adjacent vertices are at unit distance apart. If additionally the corresponding edges are non-crossing and all vertices have the same degree r we talk of a regular matchstick graph.
Kurz, Sascha, Pinchasi, Rom
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Mathematics, 2023 NONNEGATIVE matrix factorization (NMF) is an effective technique for dimensionality reduction of high-dimensional data for tasks such as machine learning and data visualization.
Jie Li, Yaotang Li, Chaoqian Li
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Remote Sensing, 2022 Due to the great benefit of rich spectral information, hyperspectral images (HSIs) have been successfully applied in many fields. However, some problems of concern also limit their further applications, such as high dimension and expensive labeling.
Lei Pan +5 more
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Two distance-regular graphs [PDF]
Journal of Algebraic Combinatorics, 2011 We construct two families of distance-regular graphs, namely the subgraph of the dual polar graph of type B_3(q) induced on the vertices far from a fixed point, and the subgraph of the dual polar graph of type D_4(q) induced on the vertices far from a fixed edge. The latter is the extended bipartite double of the former.
Brouwer, Andries E. +1 more
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JONNEE: Joint Network Nodes and Edges Embedding
IEEE Access, 2021 Recently, graph embedding models significantly improved the quality of graph machine learning tasks, such as node classification and link prediction. In this work, we propose a model called JONNEE (JOint Network Nodes and Edges Embedding), which learns ...
Ilya Makarov +2 more
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Regular Partitions of Regular Graphs [PDF]
Canadian Mathematical Bulletin, 1978 In the study of the combinatorial structure of edge-graphs of convex polytopes one may ask whether a given graph possesses a partition consisting of certain kinds of subgraphs.In this paper we describe some special partitions of 3-valent and 4-valent graphs.
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Feature representation via graph-regularized entropy-weighted nonnegative matrix factorization [PDF]
AUT Journal of Mathematics and ComputingFeature extraction plays a crucial role in dimensionality reduction in machine learning applications. Nonnegative Matrix Factorization (NMF) has emerged as a powerful technique for dimensionality reduction; however, its equal treatment of all features ...
Hazhir Sohrabi +2 more
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Edge Regular Graph Products [PDF]
The Electronic Journal of Combinatorics, 2013 A regular nonempty graph $\Gamma$ is called edge regular, whenever there exists a nonegative integer $\lambda_{\Gamma}$, such that any two adjacent vertices of $\Gamma$ have precisely $\lambda_{\Gamma}$ common neighbours. An edge regular graph $\Gamma$ with at least one pair of vertices at distance 2 is called amply regular, whenever there exists a ...
Frelih, Boštjan, Miklavič, Štefko
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