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133,466
Around matrixtree theorem
, 2006
"... Abstract. Generalizing the classical matrixtree theorem we provide a formula counting subgraphs of a given graph with a fixed 2core. We use this generalization to obtain an analog of the matrixtree theorem for the root system Dn (the classical theorem corresponds to the Ancase). Several byproduc ..."
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Cited by 5 (0 self)
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Abstract. Generalizing the classical matrixtree theorem we provide a formula counting subgraphs of a given graph with a fixed 2core. We use this generalization to obtain an analog of the matrixtree theorem for the root system Dn (the classical theorem corresponds to the Ancase). Several
Community detection in graphs
, 2009
"... The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of vertices in clusters, with many edges joining vertices of th ..."
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Cited by 801 (1 self)
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The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of vertices in clusters, with many edges joining vertices
SMOTE: Synthetic Minority Oversampling Technique
 Journal of Artificial Intelligence Research
, 2002
"... An approach to the construction of classifiers from imbalanced datasets is described. A dataset is imbalanced if the classification categories are not approximately equally represented. Often realworld data sets are predominately composed of ``normal'' examples with only a small percentag ..."
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Cited by 614 (28 self)
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good means of increasing the sensitivity of a classifier to the minority class. This paper shows that a combination of our method of oversampling the minority (abnormal) class and undersampling the majority (normal) class can achieve better classifier performance (in ROC space) than only under
GrassmannBerezin calculus and theorems of the matrixtree type
 Adv. Appl. Math
, 2004
"... We prove two generalizations of the matrixtree theorem. The first one, a result essentially due to Moon for which we provide a new proof, extends the “all minors ” matrixtree theorem to the “massive ” case where no condition on row or column sums is imposed. The second generalization, which is new ..."
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Cited by 22 (0 self)
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We prove two generalizations of the matrixtree theorem. The first one, a result essentially due to Moon for which we provide a new proof, extends the “all minors ” matrixtree theorem to the “massive ” case where no condition on row or column sums is imposed. The second generalization, which
SemiSupervised Learning Literature Survey
, 2006
"... We review the literature on semisupervised learning, which is an area in machine learning and more generally, artificial intelligence. There has been a whole
spectrum of interesting ideas on how to learn from both labeled and unlabeled data, i.e. semisupervised learning. This document is a chapter ..."
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Cited by 757 (8 self)
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chapter excerpt from the author’s
doctoral thesis (Zhu, 2005). However the author plans to update the online version frequently to incorporate the latest development in the field. Please obtain the latest
version at http://www.cs.wisc.edu/~jerryzhu/pub/ssl_survey.pdf
Finding community structure in networks using the eigenvectors of matrices
, 2006
"... We consider the problem of detecting communities or modules in networks, groups of vertices with a higherthanaverage density of edges connecting them. Previous work indicates that a robust approach to this problem is the maximization of the benefit function known as “modularity ” over possible div ..."
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Cited by 500 (0 self)
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divisions of a network. Here we show that this maximization process can be written in terms of the eigenspectrum of a matrix we call the modularity matrix, which plays a role in community detection similar to that played by the graph Laplacian in graph partitioning calculations. This result leads us to a
Efficient similarity search in sequence databases
, 1994
"... We propose an indexing method for time sequences for processing similarity queries. We use the Discrete Fourier Transform (DFT) to map time sequences to the frequency domain, the crucial observation being that, for most sequences of practical interest, only the first few frequencies are strong. Anot ..."
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Cited by 505 (21 self)
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. Another important observation is Parseval's theorem, which specifies that the Fourier transform preserves the Euclidean distance in the time or frequency domain. Having thus mapped sequences to a lowerdimensionality space by using only the first few Fourier coe cients, we use Rtrees to index
Results 1  10
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133,466