Results 1  10
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1,978,064
A Note on the Ranks of SetInclusion Matrices
 Elect. J. Combin
, 2001
"... A recurrence relation is derived for the rank (over most fields) of the setinclusion matrices on a finite ground set. Given a finite set X of say v elements, let W = W t;k (v) be the (0,1)matrix of inclusions for tsubsets versus ksubsets of X : W T;K = 1 if T is contained in K, and 0 otherwise. ..."
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Cited by 2 (0 self)
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A recurrence relation is derived for the rank (over most fields) of the setinclusion matrices on a finite ground set. Given a finite set X of say v elements, let W = W t;k (v) be the (0,1)matrix of inclusions for tsubsets versus ksubsets of X : W T;K = 1 if T is contained in K, and 0 otherwise
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
Rank Aggregation Methods for the Web
, 2010
"... We consider the problem of combining ranking results from various sources. In the context of the Web, the main applications include building metasearch engines, combining ranking functions, selecting documents based on multiple criteria, and improving search precision through word associations. Wed ..."
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Cited by 473 (6 self)
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. Wedevelop a set of techniques for the rank aggregation problem and compare their performance to that of wellknown methods. A primary goal of our work is to design rank aggregation techniques that can effectively combat "spam," a serious problem in Web searches. Experiments show that our methods
TopicSensitive PageRank
, 2002
"... In the original PageRank algorithm for improving the ranking of searchquery results, a single PageRank vector is computed, using the link structure of the Web, to capture the relative "importance" of Web pages, independent of any particular search query. To yield more accurate search resu ..."
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Cited by 535 (10 self)
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results, we propose computing a set of PageRank vectors, biased using a set of representative topics, to capture more accurately the notion of importance with respect to a particular topic. By using these (precomputed) biased PageRank vectors to generate queryspecific importance scores for pages at query
Learning to rank using gradient descent
 In ICML
, 2005
"... We investigate using gradient descent methods for learning ranking functions; we propose a simple probabilistic cost function, and we introduce RankNet, an implementation of these ideas using a neural network to model the underlying ranking function. We present test results on toy data and on data f ..."
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Cited by 510 (17 self)
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We investigate using gradient descent methods for learning ranking functions; we propose a simple probabilistic cost function, and we introduce RankNet, an implementation of these ideas using a neural network to model the underlying ranking function. We present test results on toy data and on data
Good ErrorCorrecting Codes based on Very Sparse Matrices
, 1999
"... We study two families of errorcorrecting codes defined in terms of very sparse matrices. "MN" (MacKayNeal) codes are recently invented, and "Gallager codes" were first investigated in 1962, but appear to have been largely forgotten, in spite of their excellent properties. The ..."
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Cited by 741 (23 self)
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We study two families of errorcorrecting codes defined in terms of very sparse matrices. "MN" (MacKayNeal) codes are recently invented, and "Gallager codes" were first investigated in 1962, but appear to have been largely forgotten, in spite of their excellent properties
A Singular Value Thresholding Algorithm for Matrix Completion
, 2008
"... This paper introduces a novel algorithm to approximate the matrix with minimum nuclear norm among all matrices obeying a set of convex constraints. This problem may be understood as the convex relaxation of a rank minimization problem, and arises in many important applications as in the task of reco ..."
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Cited by 539 (20 self)
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This paper introduces a novel algorithm to approximate the matrix with minimum nuclear norm among all matrices obeying a set of convex constraints. This problem may be understood as the convex relaxation of a rank minimization problem, and arises in many important applications as in the task
Exact Matrix Completion via Convex Optimization
, 2008
"... We consider a problem of considerable practical interest: the recovery of a data matrix from a sampling of its entries. Suppose that we observe m entries selected uniformly at random from a matrix M. Can we complete the matrix and recover the entries that we have not seen? We show that one can perfe ..."
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Cited by 860 (27 self)
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perfectly recover most lowrank matrices from what appears to be an incomplete set of entries. We prove that if the number m of sampled entries obeys m ≥ C n 1.2 r log n for some positive numerical constant C, then with very high probability, most n × n matrices of rank r can be perfectly recovered
Classification in the KLONE knowledge representation system
 COGNITIVE SCIENCE
, 1985
"... KLONE lets one define and use a class of descriptive terms called Concepts, where each Concept denotes a set of objects A subsumption relation between Concepts is defined which is related to set inclusion by way of a semantics for Concepts. This subsumption relation defines a partial order on Conce ..."
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Cited by 676 (8 self)
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KLONE lets one define and use a class of descriptive terms called Concepts, where each Concept denotes a set of objects A subsumption relation between Concepts is defined which is related to set inclusion by way of a semantics for Concepts. This subsumption relation defines a partial order
Spacetime codes for high data rate wireless communication: Performance criterion and code construction
 IEEE TRANS. INFORM. THEORY
, 1998
"... We consider the design of channel codes for improving the data rate and/or the reliability of communications over fading channels using multiple transmit antennas. Data is encoded by a channel code and the encoded data is split into n streams that are simultaneously transmitted using n transmit ant ..."
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Cited by 1762 (28 self)
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antennas. The received signal at each receive antenna is a linear superposition of the n transmitted signals perturbed by noise. We derive performance criteria for designing such codes under the assumption that the fading is slow and frequency nonselective. Performance is shown to be determined by matrices
Results 1  10
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1,978,064