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33
ARPACK Users Guide: Solution of Large Scale Eigenvalue Problems by Implicitly Restarted Arnoldi Methods.
, 1997
"... this document is intended to provide a cursory overview of the Implicitly Restarted Arnoldi/Lanczos Method that this software is based upon. The goal is to provide some understanding of the underlying algorithm, expected behavior, additional references, and capabilities as well as limitations of the ..."
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Cited by 138 (14 self)
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this document is intended to provide a cursory overview of the Implicitly Restarted Arnoldi/Lanczos Method that this software is based upon. The goal is to provide some understanding of the underlying algorithm, expected behavior, additional references, and capabilities as well as limitations of the software. 1.7 Dependence on LAPACK and BLAS
MPIStarT: Delivering Network Performance to Numerical Applications
 In SC
, 1998
"... : We describe an MPI implementation for a cluster of SMPs interconnected by a highperformance interconnect. This work is a collaboration between a numerical applications programmer and a cluster interconnect architect. The collaboration started with the modest goal of satisfying the communication ..."
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Cited by 32 (1 self)
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: We describe an MPI implementation for a cluster of SMPs interconnected by a highperformance interconnect. This work is a collaboration between a numerical applications programmer and a cluster interconnect architect. The collaboration started with the modest goal of satisfying the communication needs of a specific numerical application, MITMatlab. However, by supporting the MPI standard MPIStarT readily extends support to a host of applications. MPIStarT is derived from MPICH by developing a custom implementation of the Channel Interface. Some changes in MPICH's ADI and Protocol Layers are also necessary for correct and optimal operation. MPIStarT relies on the host SMPs' shared memory mechanism for intraSMP communication. InterSMP communication is supported through StarTX. The StarTX NIU allows a cluster of PCIequipped host platforms to communicate over the Arctic Switch Fabric. Currently, StarTX is utilized by a cluster of SUN E5000 SMPs as well as a cluster of Intel Pen...
On the Use of Singular Value Decomposition for Text Retrieval
, 2000
"... Latent Semantic Indexing (LSI) uses the Singular Value Decomposition to reduce noisy dimensions and improve the performance of text retrieval systems. Preliminary results have shown modest improvements in retrieval accuracy and recall, but these have mainly explored small collections. In this paper ..."
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Cited by 30 (0 self)
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Latent Semantic Indexing (LSI) uses the Singular Value Decomposition to reduce noisy dimensions and improve the performance of text retrieval systems. Preliminary results have shown modest improvements in retrieval accuracy and recall, but these have mainly explored small collections. In this paper we investigate text retrieval on a large document collections (TREC) and focus on distribution of word norm (magnitude). Our results indicate inadequacy of word representations in LSI space on large collections. We emphasize the query expansion interpretation of LSI and propose a LSI term normalization that achieves better performance on larger collections (TREC and NPL).
1 Parallel Spectral Clustering in Distributed Systems
"... Spectral clustering algorithms have been shown to be more effective in finding clusters than some traditional algorithms such as kmeans. However, spectral clustering suffers from a scalability problem in both memory use and computational time when the size of a data set is large. To perform cluster ..."
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Cited by 25 (0 self)
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Spectral clustering algorithms have been shown to be more effective in finding clusters than some traditional algorithms such as kmeans. However, spectral clustering suffers from a scalability problem in both memory use and computational time when the size of a data set is large. To perform clustering on large data sets, we investigate two representative ways of approximating the dense similarity matrix. We compare one approach by sparsifying the matrix with another by the Nyström method. We then pick the strategy of sparsifying the matrix via retaining nearest neighbors and investigate its parallelization. We parallelize both memory use and computation on distributed computers. Through
Approximate inverse preconditioning in the parallel solution of sparse eigenproblems
"... A preconditioned scheme for solving sparse symmetric eigenproblems is proposed. The solution strategy relies upon the DACG algorithm, which is a Preconditioned Conjugate Gradient algorithm for minimizing the Rayleigh Quotient. A comparison with the well established ARPACK code, shows that when a sma ..."
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Cited by 19 (9 self)
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A preconditioned scheme for solving sparse symmetric eigenproblems is proposed. The solution strategy relies upon the DACG algorithm, which is a Preconditioned Conjugate Gradient algorithm for minimizing the Rayleigh Quotient. A comparison with the well established ARPACK code, shows that when a small number of the leftmost eigenpairs is to be computed, DACG is more efficient than ARPACK. Effective convergence acceleration of DACG is shown to be performed by a suitable approximate inverse preconditioner (AINV). The performance of such a preconditioner is shown to be safe, i.e. not highly dependent on a drop tolerance parameter. On sequential machines, AINV preconditioning proves a practicable alternative to the effective incomplete Cholesky factorization, and is more efficient than Block Jacobi. Due to its parallelizability, the AINV preconditioner is exploited for a parallel implementation of the DACG algorithm. Numerical tests account for the high degree of parallelization attainable on a Cray T3E machine and confirm the satisfactory scalability properties of the algorithm. A final comparison with PARPACK shows the (relative) higher efficiency of AINVDACG. KEY WORDS generalized eigenproblem, sparse approximate inverse, parallel algorithm 1.
Parallel Spectral Clustering
"... Abstract. Spectral clustering algorithm has been shown to be more effective in finding clusters than most traditional algorithms. However, spectral clustering suffers from a scalability problem in both memory use and computational time when a dataset size is large. To perform clustering on large dat ..."
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Cited by 16 (2 self)
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Abstract. Spectral clustering algorithm has been shown to be more effective in finding clusters than most traditional algorithms. However, spectral clustering suffers from a scalability problem in both memory use and computational time when a dataset size is large. To perform clustering on large datasets, we propose to parallelize both memory use and computation on distributed computers. Through an empirical study on a large document dataset of 193, 844 data instances and a large photo dataset of 637, 137, we demonstrate that our parallel algorithm can effectively alleviate the scalability problem. Key words: Parallel spectral clustering, distributed computing 1
A Parallel DavidsonType Algorithm for Several Eigenvalues
, 1998
"... this paper we propose a new parallelization of the Davidson algorithm adapted for many eigenvalues. In our parallelization we use a relationship between two consecutive subspaces which allows us to calculate eigenvalues in the subspace through an arrowhead matrix. Theoretical timing estimates for ..."
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Cited by 10 (8 self)
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this paper we propose a new parallelization of the Davidson algorithm adapted for many eigenvalues. In our parallelization we use a relationship between two consecutive subspaces which allows us to calculate eigenvalues in the subspace through an arrowhead matrix. Theoretical timing estimates for the parallel algorithm are developed and compared against our numerical results on the Paragon. Finally our algorithm is compared against another recent parallel algorithm for multiple eigenvalues, but based on Arnoldi: PARPACK. c 1998 Academic Press 1.
A Flexible OpenSource Toolbox for Scalable Complex Graph Analysis
, 2011
"... The Knowledge Discovery Toolbox (KDT) enables domain experts to perform complex analyses of huge datasets on supercomputers using a highlevel language without grappling with the difficulties of writing parallel code, calling parallel libraries, or becoming a graph expert. KDT provides a flexible Py ..."
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Cited by 9 (2 self)
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The Knowledge Discovery Toolbox (KDT) enables domain experts to perform complex analyses of huge datasets on supercomputers using a highlevel language without grappling with the difficulties of writing parallel code, calling parallel libraries, or becoming a graph expert. KDT provides a flexible Python interface to a small set of highlevel graph operations; composing a few of these operations is often sufficient for a specific analysis. Scalability and performance are delivered by linking to a stateoftheart backend compute engine that scales from laptops to large HPC clusters. KDT delivers very competitive performance from a generalpurpose, reusable library for graphs on the order of 10 billion edges and greater. We demonstrate speedup of 1 and 2 orders of magnitude over PBGL and Pegasus, respectively, on some tasks. Examples from simple use cases and key graphanalytic benchmarks illustrate the productivity and performance realized by KDT users. Semantic graph abstractions provide both flexibility and high performance for realworld use cases. Graphalgorithm researchers benefit from the ability to develop algorithms quickly using KDT’s graph and underlying matrix abstractions for distributed memory. KDT is available as opensource code to foster experimentation.
The Parallel Problems Server: A ClientServer Model for Interactive Large Scale Scientific Computation
 In Proceedings of VECPAR98
, 1998
"... . Applying fast scientific computing algorithms to large problems presents a difficult engineering problem. We describe a novel architecture for addressing this problem that uses a robust clientserver model for interactive largescale linear algebra computation. We discuss competing approaches and ..."
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Cited by 9 (4 self)
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. Applying fast scientific computing algorithms to large problems presents a difficult engineering problem. We describe a novel architecture for addressing this problem that uses a robust clientserver model for interactive largescale linear algebra computation. We discuss competing approaches and demonstrate the relative strengths of our approach. By way of example, we describe MITMatlab, a powerful transparent client interface to the linear algebra server. With MITMatlab, it is now straightforward to implement fullblown algorithms intended to work on very large problems while still using the powerful interactive and visualization tools that Matlab provides. We also examine the efficiency of our model by timing selected operations and comparing them to commonly used approaches. 1 Introduction We describe a novel architecture for a "linear algebra server" that operates on very large matrices. Matrices are created by the server and distributed across many machines or processors. Oper...
MATLAB p 2.0: Interactive supercomputing made practical
 M.Sc. thesis, Massachusetts Inst. Technol
, 2002
"... ..."