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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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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.
Sascha Kurz, Rom Pinchasi
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Ars Mathematica Contemporanea, 2019 20 pages, 6 ...
Primoz Potocnik, Janos Vidali
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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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Nim-Regularity of Graphs [PDF]
The Electronic Journal of Combinatorics, 1999 Ehrenborg and Steingrímsson defined simplicial Nim, and defined Nim-regular complexes to be simplicial complexes for which simplicial Nim has a particular type of winning strategy. We completely characterize the Nim-regular graphs by the exclusion of two vertex-induced subgraphs, the graph on three vertices with one edge and the graph on five ...
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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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Journal of Combinatorial Theory, Series B, 1997 A covering projection from a graph \(G\) onto a graph \(H\) is a ``local isomorphism'': a mapping from the vertex set of \(G\) onto the vertex set of \(H\) such that, for every \(v\in V(G)\), the neighborhood of \(v\) is mapped bijectively onto the neighborhood (in \(H\)) of the image of \(v\).
Jan Kratochvíl +2 more
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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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