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Kronecker Graph
Kronecker graphs are a construction for generating graphs for modeling systems. The method constructs a sequence of graphs from a small base graph by iterating the Kronecker product. A variety of generalizations of Kronecker graphs exist. The Graph500 The Graph500 is a rating of supercomputer systems, focused on data-intensive loads. The project was announced on International Supercomputing Conference in June 2010. The first list was published at the ACM/IEEE Supercomputing Conference in Novem ... benchmark for supercomputers is based on the use of a stochastic version of Kronecker graphs. Stochastic kronecker graph is a kronecker graph with each component of the matrix made by real numbers between 0 and 1. The stochastic version of kronecker graph eliminates the staircase effect, which happens due to large multiplicity of kronecker graph. References Graph families {{combin-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Graph (discrete Mathematics)
In discrete mathematics, and more specifically in graph theory, a graph is a structure amounting to a Set (mathematics), set of objects in which some pairs of the objects are in some sense "related". The objects correspond to mathematical abstractions called ''Vertex (graph theory), vertices'' (also called ''nodes'' or ''points'') and each of the related pairs of vertices is called an ''edge'' (also called ''link'' or ''line''). Typically, a graph is depicted in diagrammatic form as a set of dots or circles for the vertices, joined by lines or curves for the edges. Graphs are one of the objects of study in discrete mathematics. The edges may be directed or undirected. For example, if the vertices represent people at a party, and there is an edge between two people if they shake hands, then this graph is undirected because any person ''A'' can shake hands with a person ''B'' only if ''B'' also shakes hands with ''A''. In contrast, if an edge from a person ''A'' to a person ''B'' m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tensor Product Of Graphs
In graph theory, the tensor product of graphs and is a graph such that * the vertex set of is the Cartesian product ; and * vertices and are adjacent in if and only if ** is adjacent to in , and ** is adjacent to in . The tensor product is also called the direct product, Kronecker product, categorical product, cardinal product, relational product, weak direct product, or conjunction. As an operation on binary relations, the tensor product was introduced by Alfred North Whitehead and Bertrand Russell in their Principia Mathematica (1912). It is also equivalent to the Kronecker product of the adjacency matrices of the graphs. The notation is also (and formerly normally was) used to represent another construction known as the Cartesian product of graphs, but nowadays more commonly refers to the tensor product. The cross symbol shows visually the two edges resulting from the tensor product of two edges. This product should not be confused with the strong product of grap ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Journal Of Machine Learning Research
The ''Journal of Machine Learning Research'' is a peer-reviewed open access scientific journal covering machine learning. It was established in 2000 and the first editor-in-chief was Leslie Kaelbling. The current editors-in-chief are Francis Bach (Inria) and David Blei (Columbia University). History The journal was established as an open-access alternative to the journal ''Machine Learning''. In 2001, forty editorial board members of ''Machine Learning'' resigned, saying that in the era of the Internet, it was detrimental for researchers to continue publishing their papers in expensive journals with pay-access archives. The open access model employed by the ''Journal of Machine Learning Research'' allows authors to publish articles for free and retain copyright, while archives are freely available online. Print editions of the journal were published by MIT Press until 2004 and by Microtome Publishing thereafter. From its inception, the journal received no revenue from the pr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Graph500
The Graph500 is a rating of supercomputer systems, focused on data-intensive loads. The project was announced on International Supercomputing Conference in June 2010. The first list was published at the ACM/IEEE Supercomputing Conference in November 2010. New versions of the list are published twice a year. The main performance metric used to rank the supercomputers is GTEPS (giga- traversed edges per second). Richard Murphy from Sandia National Laboratories, says that "The Graph500's goal is to promote awareness of complex data problems", instead of focusing on computer benchmarks like HPL (High Performance Linpack), which TOP500 is based on. Despite its name, there were several hundreds of systems in the rating, growing up to 174 in June 2014. The algorithm and implementation that won the championship is published in the paper titled "Extreme scale breadth-first search on supercomputers". There is also list Green Graph 500, which uses same performance metric, but sorts list ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
