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The Nature of Statistical Learning Theory
, 1999
"... Statistical learning theory was introduced in the late 1960’s. Until the 1990’s it was a purely theoretical analysis of the problem of function estimation from a given collection of data. In the middle of the 1990’s new types of learning algorithms (called support vector machines) based on the deve ..."
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Cited by 12991 (31 self)
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Statistical learning theory was introduced in the late 1960’s. Until the 1990’s it was a purely theoretical analysis of the problem of function estimation from a given collection of data. In the middle of the 1990’s new types of learning algorithms (called support vector machines) based on the developed theory were proposed. This made statistical learning theory not only a tool for the theoretical analysis but also a tool for creating practical algorithms for estimating multidimensional functions. This article presents a very general overview of statistical learning theory including both theoretical and algorithmic aspects of the theory. The goal of this overview is to demonstrate how the abstract learning theory established conditions for generalization which are more general than those discussed in classical statistical paradigms and how the understanding of these conditions inspired new algorithmic approaches to function estimation problems. A more
On finding dense subgraphs
 In ICALP ’09
, 2009
"... Abstract. Given an undirected graph G = (V, E), the density of a subgraph on vertex set S is defined as d(S) = E(S), where E(S) is the set of edges S in the subgraph induced by nodes in S. Finding subgraphs of maximum density is a very well studied problem. One can also generalize this notion t ..."
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Cited by 39 (2 self)
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Abstract. Given an undirected graph G = (V, E), the density of a subgraph on vertex set S is defined as d(S) = E(S), where E(S) is the set of edges S in the subgraph induced by nodes in S. Finding subgraphs of maximum density is a very well studied problem. One can also generalize this notion
Complexity of finding dense subgraphs
, 2002
"... The kf(k) dense subgraph problem((k; f(k))DSP) asks whether there is a kvertex subgraph of a given graph G which has at least f(k) edges. When f(k)=k(k − 1)=2, (k; f(k))DSP is equivalent to the wellknown kclique problem. The main purpose of this paper is to discuss the problem of nding slightl ..."
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The kf(k) dense subgraph problem((k; f(k))DSP) asks whether there is a kvertex subgraph of a given graph G which has at least f(k) edges. When f(k)=k(k − 1)=2, (k; f(k))DSP is equivalent to the wellknown kclique problem. The main purpose of this paper is to discuss the problem of nding
A local algorithm for finding dense subgraphs
 In Proc. 19th Annual ACMSIAM Symposium on Discrete Algorithms
, 2008
"... We present a local algorithm for finding dense subgraphs of bipartite graphs, according to the definition of density proposed by Kannan and Vinay. Our algorithm takes as input a bipartite graph with a specified starting vertex, and attempts to find a dense subgraph near that vertex. We prove that fo ..."
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Cited by 14 (3 self)
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We present a local algorithm for finding dense subgraphs of bipartite graphs, according to the definition of density proposed by Kannan and Vinay. Our algorithm takes as input a bipartite graph with a specified starting vertex, and attempts to find a dense subgraph near that vertex. We prove
Lovász ϑ function, SVMs and Finding Dense Subgraphs
"... In this paper we establish that the Lovász ϑ function on a graph can be restated as a kernel learning problem. We introduce the notion of SVM−ϑ graphs, on which Lovász ϑ function can be approximated well by a Support vector machine (SVM). We show that ErdösRényi random G(n, p) graphs are SVM−ϑ ..."
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In this paper we establish that the Lovász ϑ function on a graph can be restated as a kernel learning problem. We introduce the notion of SVM−ϑ graphs, on which Lovász ϑ function can be approximated well by a Support vector machine (SVM). We show that ErdösRényi random G(n, p) graphs are SVM−ϑ graphs for log4 n n ≤ p< 1. Even if we embed a large clique of size Θ np
Frequent Subgraph Discovery
, 2001
"... Over the years, frequent itemset discovery algorithms have been used to solve various interesting problems. As data mining techniques are being increasingly applied to nontraditional domains, existing approaches for finding frequent itemsets cannot be used as they cannot model the requirement of th ..."
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Cited by 407 (14 self)
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of these domains. An alternate way of modeling the objects in these data sets, is to use a graph to model the database objects. Within that model, the problem of finding frequent patterns becomes that of discovering subgraphs that occur frequently over the entire set of graphs. In this paper we present a
The Dense kSubgraph Problem
 Algorithmica
, 1999
"... This paper considers the problem of computing the dense kvertex subgraph of a given graph, namely, the subgraph with the most edges. An approximation algorithm is developed for the problem, with approximation ratio O(n ffi ), for some ffi ! 1=3. 1 Introduction We study the dense ksubgraph (D ..."
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Cited by 208 (12 self)
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(DkS) maximization problem, of computing the dense k vertex subgraph of a given graph. That is, on input a graph G and a parameter k, we are interested in finding a set of k vertices with maximum average degree in the subgraph induced by this set. As this problem is NPhard (say, by reduction from
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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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 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 number of possible algorithms for detecting community structure, as well as several other results, including a spectral measure of bipartite structure in networks and a new centrality measure that identifies those vertices that occupy central positions within the communities to which they belong. The algorithms and measures proposed are illustrated with applications to a variety of realworld complex networks.
Understanding packet delivery performance in dense wireless sensor networks
, 2003
"... Wireless sensor networks promise finegrain monitoring in a wide variety of environments. Many of these environments (e.g., indoor environments or habitats) can be harsh for wireless communication. From a networking perspective, the most basic aspect of wireless communication is the packet delivery ..."
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Cited by 657 (15 self)
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different environments:an indoor office building, a habitat with moderate foliage, and an open parking lot. Our findings have interesting implications for the design and evaluation of routing and mediumaccess protocols for sensor networks. Categories and Subject Descriptors C.2.1 [Network Architecture
A taxonomy and evaluation of dense twoframe stereo correspondence algorithms
 International Journal of Computer Vision
, 2002
"... Abstract. Stereo matching is one of the most active research areas in computer vision. While a large number of algorithms for stereo correspondence have been developed, relatively little work has been done on characterizing their performance. In this paper, we present a taxonomy of dense, twoframe ..."
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Cited by 1537 (23 self)
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Abstract. Stereo matching is one of the most active research areas in computer vision. While a large number of algorithms for stereo correspondence have been developed, relatively little work has been done on characterizing their performance. In this paper, we present a taxonomy of dense, two
Results 1  10
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