Results 1  10
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25
Precomputing interactive dynamic deformable scenes
 ACM Trans. Graph
, 2003
"... dynamics by driving the scene with parameterized interactions representative of runtime usage. (b) Model reduction on observed dynamic deformations yields a lowrank approximation to the system’s parameterized impulse response functions. (c) Deformed state geometries are then sampled and used to pre ..."
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Cited by 71 (6 self)
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dynamics by driving the scene with parameterized interactions representative of runtime usage. (b) Model reduction on observed dynamic deformations yields a lowrank approximation to the system’s parameterized impulse response functions. (c) Deformed state geometries are then sampled and used to precompute and coparameterize a radiance transfer model for deformable objects. (d) The final simulation responds plausibly to interactions similar to those precomputed, includes complex collision and global illumination effects, and runs in real time. We present an approach for precomputing datadriven models of interactive physically based deformable scenes. The method permits realtime hardware synthesis of nonlinear deformation dynamics, including selfcontact and global illumination effects, and supports realtime user interaction. We use datadriven tabulation of the system’s deterministic state space dynamics, and model reduction to build efficient lowrank parameterizations of the deformed shapes. To support runtime interaction, we also tabulate impulse response functions for a palette of external excitations. Although our approach simulates particular systems under very particular interaction conditions, it has several advantages. First, parameterizing all possible scene deformations enables us to precompute novel reduced coparameterizations of global scene illumination for lowfrequency lighting conditions. Second, because the deformation dynamics are precomputed and parameterized as a whole, collisions are resolved within the scene during precomputation so that runtime selfcollision handling is implicit. Optionally, the datadriven models can be synthesized on programmable graphics hardware, leaving only the lowdimensional state space dynamics and appearance data models to be computed by the main CPU.
LowRank Approximations With Sparse Factors I: Basic Algorithms And Error Analysis
 SIAM J. MATRIX ANALYSIS APPLICATIONS
, 1999
"... We consider the problem of computing lowrank approximations of matrices. The novel aspects of our approach are that we require the lowrank approximations be written in a factorized form with sparse factors and the degree of sparsity of the factors can be traded off for reduced reconstruction error ..."
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Cited by 26 (1 self)
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We consider the problem of computing lowrank approximations of matrices. The novel aspects of our approach are that we require the lowrank approximations be written in a factorized form with sparse factors and the degree of sparsity of the factors can be traded off for reduced reconstruction error by certain user determined parameters. We give a detailed error analysis of our proposed algorithms and compare the computed sparse lowrank approximations with those obtained from singular value decomposition. We present numerical examples arising from some application areas to illustrate the efficiency and accuracy of our algorithms.
Dynamical lowrank approximation
 SIAM J. Matrix Anal. Appl
, 2006
"... Abstract. For the low rank approximation of timedependent data matrices and of solutions to matrix differential equations, an incrementbased computational approach is proposed and analyzed. In this method, the derivative is projected onto the tangent space of the manifold of rankr matrices at the ..."
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Cited by 18 (4 self)
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Abstract. For the low rank approximation of timedependent data matrices and of solutions to matrix differential equations, an incrementbased computational approach is proposed and analyzed. In this method, the derivative is projected onto the tangent space of the manifold of rankr matrices at the current approximation. With an appropriate decomposition of rankr matrices and their tangent matrices, this yields nonlinear differential equations that are wellsuited for numerical integration. The error analysis compares the result with the pointwise best approximation in the Frobenius norm. It is shown that the approach gives locally quasioptimal low rank approximations. Numerical experiments illustrate the theoretical results. Key words. Low rank approximation, timevarying matrices, continuous updating, smooth decomposition, matrix differential equations. AMS subject classifications. 65F30, 15A23 1. Introduction. Low
Computing Smallest Singular Triplets with Implicitly Restarted Lanczos Bidiagonalization
 APPL. NUMER. MATH
, 2004
"... A matrixfree algorithm, IRLANB, for the efficient computation of the smallest singular triplets of large and possibly sparse matrices is described. Key characteristics of the approach are its use of Lanczos bidiagonalization, implicit restarting, and harmonic Ritz values. The algorithm also uses a ..."
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Cited by 13 (2 self)
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A matrixfree algorithm, IRLANB, for the efficient computation of the smallest singular triplets of large and possibly sparse matrices is described. Key characteristics of the approach are its use of Lanczos bidiagonalization, implicit restarting, and harmonic Ritz values. The algorithm also uses a deflation stategy that can be applied directly on Lanczos bidiagonalization. A refinenement postprocessing phase is applied on the converged singular vectors. The computational costs of the above techniques are kept small as they make direct use of the bidiagonal form obtained in the course of the Lanczos factorization. Several numerical experiments with the method are presented that illustrate its effectiveness and indicate that it performs well compared to existing codes.
Augmented implicitly restarted Lanczos bidiagonalization methods
 SIAM J. Sci. Comput
"... Abstract. New restarted Lanczos bidiagonalization methods for the computation of a few of the largest or smallest singular values of a large matrix are presented. Restarting is carried out by augmentation of Krylov subspaces that arise naturally in the standard Lanczos bidiagonalization method. The ..."
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Cited by 13 (6 self)
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Abstract. New restarted Lanczos bidiagonalization methods for the computation of a few of the largest or smallest singular values of a large matrix are presented. Restarting is carried out by augmentation of Krylov subspaces that arise naturally in the standard Lanczos bidiagonalization method. The augmenting vectors are associated with certain Ritz or harmonic Ritz vectors. Computed examples show the new methods to be competitive with available schemes. Key words. singular value computation, partial singular value decomposition, iterative method, largescale computation
Optical computing for fast light transport analysis
 SIGGRAPH Asia
, 2010
"... Figure 1: Our approach enables very efficient acquisition and analysis of light transport: to create the relighting results shown above, just forty low dynamic range photos were used to acquire 700Kpixel×100Kpixel transport matrices. Note the complex shadows cast by the hat (both sharp and soft), th ..."
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Cited by 12 (1 self)
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Figure 1: Our approach enables very efficient acquisition and analysis of light transport: to create the relighting results shown above, just forty low dynamic range photos were used to acquire 700Kpixel×100Kpixel transport matrices. Note the complex shadows cast by the hat (both sharp and soft), the complex highlights on the hair and the shadows it casts, and the many shadows, caustics and indirect lighting effects in the glass scene. We used an optical implementation of the Arnoldi algorithm to do both photo acquisition and lowrank matrix approximation; the entire process (photo capture, matrix reconstruction, relighting) took four minutes on a standard PC for each scene. We present a general framework for analyzing the transport matrix of a realworld scene at full resolution, without capturing many photos. The key idea is to use projectors and cameras to directly acquire eigenvectors and the Krylov subspace of the unknown transport matrix. To do this, we implement Krylov subspace methods partially in optics, by treating the scene as a “black box subroutine” that enables optical computation of arbitrary matrixvector products. We describe two methods—optical Arnoldi to acquire a lowrank approximation of the transport matrix for relighting; and optical GMRES to invert light transport. Our experiments suggest that good quality relighting and transport inversion are possible from a few dozen lowdynamic range photos, even for scenes with complex shadows, caustics, and other challenging lighting effects. 1
Restarted block Lanczos bidiagonalization methods, Numer. Algorithms
"... Abstract. The problem of computing a few of the largest or smallest singular values and associated singular vectors of a large matrix arises in many applications. This paper describes restarted block Lanczos bidiagonalization methods based on augmentation of Ritz vectors or harmonic Ritz vectors by ..."
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Cited by 7 (4 self)
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Abstract. The problem of computing a few of the largest or smallest singular values and associated singular vectors of a large matrix arises in many applications. This paper describes restarted block Lanczos bidiagonalization methods based on augmentation of Ritz vectors or harmonic Ritz vectors by block Krylov subspaces. Key words. partial singular value decomposition, restarted iterative method, implicit shifts, augmentation. AMS subject classifications. 65F15, 15A18
Markov methods for hierarchical coarsegraining of large protein dynamics
 In LNBI
, 2006
"... Abstract. Elastic network models (ENMs), and in particular the Gaussian Network Model (GNM), have been widely used in recent years to gain insights into the machinery of proteins. The extension of ENMs to supramolecular assemblies/complexes presents computational challenges, however, due to the diff ..."
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Cited by 6 (2 self)
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Abstract. Elastic network models (ENMs), and in particular the Gaussian Network Model (GNM), have been widely used in recent years to gain insights into the machinery of proteins. The extension of ENMs to supramolecular assemblies/complexes presents computational challenges, however, due to the difficulty of retaining atomic details in mode decomposition of large systems dynamics. Here, we present a novel approach to address this problem. Based on a Markovian description of communication/interaction stochastics, we map the fullatom GNM representation into a hierarchy of lower resolution networks, perform the analysis in the reduced space(s) and reconstruct the detailed models dynamics with minimal loss of data. The approach (hGNM) applied to chaperonin GroELGroES demonstrates that the shape and frequency dispersion of the dominant 25 modes of motion predicted by a fullresidue (8015 nodes) GNM analysis are almost identically reproduced by reducing the complex into a network of 35 soft nodes. 1
Structured Low Rank Approximation
 LINEAR ALGEBRA APPL
, 2002
"... This paper concerns the construction of a structured low rank matrix that is nearest to a given matrix. The notion of structured low rank approximation arises in various applications, ranging from signal enhancement to protein folding to computer algebra, where the empirical data collected in a matr ..."
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Cited by 6 (1 self)
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This paper concerns the construction of a structured low rank matrix that is nearest to a given matrix. The notion of structured low rank approximation arises in various applications, ranging from signal enhancement to protein folding to computer algebra, where the empirical data collected in a matrix do not maintain either the specified structure or the desirable rank as is expected in the original system. The task to retrieve useful information while maintaining the underlying physical feasibility often necessitates the search for a good structured lower rank approximation of the data matrix. This paper addresses some of the theoretical and numerical issues involved in the problem. Two procedures for constructing the nearest structured low rank matrix are proposed. The procedures are flexible enough that they can be applied to any lower rank, any linear structure, and any matrix norm in the measurement of nearness. The techniques can also be easily implemented by utilizing available optimization packages. The special case of symmetric Toeplitz structure using the Frobenius matrix norm is used to exemplify the ideas throughout the discussion. The concept, rather than the implementation details, is the main emphasis of the paper.
Correlating summarization of multisource news with kway graph biclustering
 ACM SIGKDD Explorations
"... With the emergence of enormous amount of online news, it is desirable to construct text mining methods that can extract, compare and highlight similarities of them. In this paper, we explore the research issue and methodology of correlated summarization for a pair of news articles. The algorithm ali ..."
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Cited by 5 (0 self)
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With the emergence of enormous amount of online news, it is desirable to construct text mining methods that can extract, compare and highlight similarities of them. In this paper, we explore the research issue and methodology of correlated summarization for a pair of news articles. The algorithm aligns the (sub)topics of the two news articles and summarizes their correlation by sentence extraction. A pair of news articles are modelled with a weighted bipartite graph. A mutual reinforcement principle is applied to identify a dense subgraph of the weighted bipartite graph. Sentences corresponding to the subgraph are correlated well in textual content and convey the dominant shared topic of the pair of news articles. As a further enhancement for lengthy articles, a kway biclustering algorithm can first be used to partition the bipartite graph into several clusters, each containing sentences from the two news reports. These clusters correspond to shared subtopics, and the above mutual reinforcement principle can then be applied to extract topic sentences within each subtopic group.