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Learning the Kernel Matrix with SemiDefinite Programming
, 2002
"... Kernelbased learning algorithms work by embedding the data into a Euclidean space, and then searching for linear relations among the embedded data points. The embedding is performed implicitly, by specifying the inner products between each pair of points in the embedding space. This information ..."
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Cited by 780 (22 self)
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is contained in the socalled kernel matrix, a symmetric and positive definite matrix that encodes the relative positions of all points. Specifying this matrix amounts to specifying the geometry of the embedding space and inducing a notion of similarity in the input spaceclassical model selection
Indexing by latent semantic analysis
 JOURNAL OF THE AMERICAN SOCIETY FOR INFORMATION SCIENCE
, 1990
"... A new method for automatic indexing and retrieval is described. The approach is to take advantage of implicit higherorder structure in the association of terms with documents (“semantic structure”) in order to improve the detection of relevant documents on the basis of terms found in queries. The p ..."
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Cited by 3723 (35 self)
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. The particular technique used is singularvalue decomposition, in which a large term by document matrix is decomposed into a set of ca. 100 orthogonal factors from which the original matrix can be approximated by linear combination. Documents are represented by ca. 100 item vectors of factor weights. Queries
An Extended Set of Fortran Basic Linear Algebra Subprograms
 ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE
, 1986
"... This paper describes an extension to the set of Basic Linear Algebra Subprograms. The extensions are targeted at matrixvector operations which should provide for efficient and portable implementations of algorithms for high performance computers. ..."
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Cited by 526 (72 self)
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This paper describes an extension to the set of Basic Linear Algebra Subprograms. The extensions are targeted at matrixvector operations which should provide for efficient and portable implementations of algorithms for high performance computers.
Gapped Blast and PsiBlast: a new generation of protein database search programs
 NUCLEIC ACIDS RESEARCH
, 1997
"... The BLAST programs are widely used tools for searching protein and DNA databases for sequence similarities. For protein comparisons, a variety of definitional, algorithmic and statistical refinements described here permits the execution time of the BLAST programs to be decreased substantially while ..."
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Cited by 8393 (85 self)
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for automatically combining statistically significant alignments produced by BLAST into a positionspecific score matrix, and searching the database using this matrix. The resulting PositionSpecific Iterated BLAST (PSIBLAST) program runs at approximately the same speed per iteration as gapped BLAST, but in many
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
Interior Point Methods in Semidefinite Programming with Applications to Combinatorial Optimization
 SIAM Journal on Optimization
, 1993
"... We study the semidefinite programming problem (SDP), i.e the problem of optimization of a linear function of a symmetric matrix subject to linear equality constraints and the additional condition that the matrix be positive semidefinite. First we review the classical cone duality as specialized to S ..."
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Cited by 557 (12 self)
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We study the semidefinite programming problem (SDP), i.e the problem of optimization of a linear function of a symmetric matrix subject to linear equality constraints and the additional condition that the matrix be positive semidefinite. First we review the classical cone duality as specialized
Closedform solution of absolute orientation using unit quaternions
 J. Opt. Soc. Am. A
, 1987
"... Finding the relationship between two coordinate systems using pairs of measurements of the coordinates of a number of points in both systems is a classic photogrammetric task. It finds applications in stereophotogrammetry and in robotics. I present here a closedform solution to the leastsquares pr ..."
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Cited by 973 (4 self)
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. These exact results are to be preferred to approximate methods based on measurements of a few selected points. The unit quaternion representing the best rotation is the eigenvector associated with the most positive eigenvalue of a symmetric 4 X 4 matrix. The elements of this matrix are combinations of sums
An affine invariant interest point detector
 In Proceedings of the 7th European Conference on Computer Vision
, 2002
"... Abstract. This paper presents a novel approach for detecting affine invariant interest points. Our method can deal with significant affine transformations including large scale changes. Such transformations introduce significant changes in the point location as well as in the scale and the shape of ..."
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Cited by 1455 (55 self)
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of the neighbourhood of an interest point. Our approach allows to solve for these problems simultaneously. It is based on three key ideas: 1) The second moment matrix computed in a point can be used to normalize a region in an affine invariant way (skew and stretch). 2) The scale of the local structure is indicated
Sequential data assimilation with a nonlinear quasigeostrophic model using Monte Carlo methods to forecast error statistics
 J. Geophys. Res
, 1994
"... . A new sequential data assimilation method is discussed. It is based on forecasting the error statistics using Monte Carlo methods, a better alternative than solving the traditional and computationally extremely demanding approximate error covariance equation used in the extended Kalman filter. The ..."
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Cited by 782 (22 self)
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covariance equation are avoided because storage and evolution of the error covariance matrix itself are not needed. The results are also better than what is provided by the extended Kalman filter since there is no closure problem and the quality of the forecast error statistics therefore improves. The method
On Spectral Clustering: Analysis and an algorithm
 ADVANCES IN NEURAL INFORMATION PROCESSING SYSTEMS
, 2001
"... Despite many empirical successes of spectral clustering methods  algorithms that cluster points using eigenvectors of matrices derived from the distances between the points  there are several unresolved issues. First, there is a wide variety of algorithms that use the eigenvectors in slightly ..."
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Cited by 1697 (13 self)
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in slightly different ways. Second, many of these algorithms have no proof that they will actually compute a reasonable clustering. In this paper, we present a simple spectral clustering algorithm that can be implemented using a few lines of Matlab. Using tools from matrix perturbation theory, we analyze
Results 1  10
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