Results 1  10
of
33
A divisive informationtheoretic feature clustering algorithm for text classification
 Journal of Machine Learning Research
, 2003
"... High dimensionality of text can be a deterrent in applying complex learners such as Support Vector Machines to the task of text classification. Feature clustering is a powerful alternative to feature selection for reducing the dimensionality of text data. In this paper we propose a new informationth ..."
Abstract

Cited by 108 (16 self)
 Add to MetaCart
High dimensionality of text can be a deterrent in applying complex learners such as Support Vector Machines to the task of text classification. Feature clustering is a powerful alternative to feature selection for reducing the dimensionality of text data. In this paper we propose a new informationtheoretic divisive algorithm for feature/word clustering and apply it to text classification. Existing techniques for such “distributional clustering ” of words are agglomerative in nature and result in (i) suboptimal word clusters and (ii) high computational cost. In order to explicitly capture the optimality of word clusters in an information theoretic framework, we first derive a global criterion for feature clustering. We then present a fast, divisive algorithm that monotonically decreases this objective function value. We show that our algorithm minimizes the “withincluster JensenShannon divergence ” while simultaneously maximizing the “betweencluster JensenShannon divergence”. In comparison to the previously proposed agglomerative strategies our divisive algorithm is much faster and achieves comparable or higher classification accuracies. We further show that feature clustering is an effective technique for building smaller class models in hierarchical classification. We present detailed experimental results using Naive Bayes and Support Vector Machines on the 20Newsgroups data set and a 3level hierarchy of HTML documents collected from the Open Directory project (www.dmoz.org).
Accurate Singular Values of Bidiagonal Matrices
 SIAM J. SCI. STAT. COMPUT
, 1990
"... Computing the singular values of a bidiagonal matrix is the fin al phase of the standard algow rithm for the singular value decomposition of a general matrix. We present a new algorithm hich computes all the singular values of a bidiagonal matrix to high relative accuracy independent of their magni ..."
Abstract

Cited by 100 (17 self)
 Add to MetaCart
Computing the singular values of a bidiagonal matrix is the fin al phase of the standard algow rithm for the singular value decomposition of a general matrix. We present a new algorithm hich computes all the singular values of a bidiagonal matrix to high relative accuracy independent of their magnitudes. In contrast, the standard algorithm for bidiagonal matrices may compute small singular values with no relative accuracy at all. Numerical experiments show that the new algorithm is comparable in speed to the standard algorithm , and frequently faster.
Vector Microprocessors
 In Hot Chips VII
, 1998
"... Vector Microprocessors by Krste Asanovic Doctor of Philosophy in Computer Science University of California, Berkeley Professor John Wawrzynek, Chair Most previous research into vector architectures has concentrated on supercomputing applications and small enhancements to existing vector superc ..."
Abstract

Cited by 77 (7 self)
 Add to MetaCart
Vector Microprocessors by Krste Asanovic Doctor of Philosophy in Computer Science University of California, Berkeley Professor John Wawrzynek, Chair Most previous research into vector architectures has concentrated on supercomputing applications and small enhancements to existing vector supercomputer implementations. This thesis expands the body of vector research by examining designs appropriate for singlechip fullcustom vector microprocessor implementations targeting a much broader range of applications. I present the design, implementation, and evaluation of T0 (Torrent0): the first singlechip vector microprocessor. T0 is a compact but highly parallel processor that can sustain over 24 operations per cycle while issuing only a single 32bit instruction per cycle. T0 demonstrates that vector architectures are well suited to fullcustom VLSI implementation and that they perform well on many multimedia and humanmachine interface tasks. The remainder of the thesis contains ...
An Analysis Of Division Algorithms And Implementations
 IEEE Transactions on Computers
, 1995
"... Floatingpoint division is generally regarded as a low frequency, high latency operation in typical floatingpoint applications. However, the increasing emphasis on high performance graphics and the industrywide usage of performance benchmarks forces processor designers to pay close attention to al ..."
Abstract

Cited by 53 (8 self)
 Add to MetaCart
Floatingpoint division is generally regarded as a low frequency, high latency operation in typical floatingpoint applications. However, the increasing emphasis on high performance graphics and the industrywide usage of performance benchmarks forces processor designers to pay close attention to all aspects of floatingpoint computation. Many algorithms are suitable for implementing division in hardware. This paper presents four major classes of algorithms in a unified framework, namely digit recurrence, functional iteration, very high radix, and variable latency. Digit recurrence algorithms, the most common of which is SRT, use subtraction as the fundamental operator, and they converge to a quotient linearly. Division by functional iteration converges to a quotient quadratically using multiplication. Very high radix division algorithms are similar to digit recurrence algorithms, but they incorporate multiplication to reduce the latency. Variable latency division algorithms reduce the...
Error bounds from extra precise iterative refinement
 ACM Transactions on Mathematical Software
, 2006
"... We present the design and testing of an algorithm for iterative refinement of the solution of linear equations, where the residual is computed with extra precision. This algorithm was originally proposed in the 1960s [6, 22] as a means to compute very accurate solutions to all but the most illcondi ..."
Abstract

Cited by 29 (6 self)
 Add to MetaCart
We present the design and testing of an algorithm for iterative refinement of the solution of linear equations, where the residual is computed with extra precision. This algorithm was originally proposed in the 1960s [6, 22] as a means to compute very accurate solutions to all but the most illconditioned linear systems of equations. However two obstacles have until now prevented its adoption in standard subroutine libraries like LAPACK: (1) There was no standard way to access the higher precision arithmetic needed to compute residuals, and (2) it was unclear how to compute a reliable error bound for the computed solution. The completion of the new BLAS Technical Forum Standard [5] has recently removed the first obstacle. To overcome the second obstacle, we show how a single application of iterative refinement can be used to compute an error bound in any norm at small cost, and use this to compute both an error bound in the usual infinity norm, and a componentwise relative error bound. We report extensive test results on over 6.2 million matrices of dimension 5, 10, 100, and 1000. As long as a normwise (resp. componentwise) condition number computed by the algorithm is less than 1/max{10, √ n}εw, the computed normwise (resp. componentwise) error bound is at most
The bidiagonal singular values decomposition and Hamiltonian mechanics
 SIAM J. Num. Anal
, 1991
"... We consider computing the singular value decomposition of a bidiagonal matrixB. This problem arises in the singular value decomposition of a general matrix, and in the eigenproblem for a symmetric positive de nite tridiagonal matrix. We show that if the entries of B are known with high relative accu ..."
Abstract

Cited by 25 (6 self)
 Add to MetaCart
We consider computing the singular value decomposition of a bidiagonal matrixB. This problem arises in the singular value decomposition of a general matrix, and in the eigenproblem for a symmetric positive de nite tridiagonal matrix. We show that if the entries of B are known with high relative accuracy, the singular values and singular vectors ofB will be determined to much higher accuracy than the standard perturbation theory suggests. We also show that the algorithm in [Demmel and Kahan] computes the singular vectors as well as the singular values to this accuracy. We also give a Hamiltonian interpretation of the algorithm and use di erential equation methods to prove many of the basic facts. The Hamiltonian approach suggests a way to use ows to predict the accumulation of error in other eigenvalue algorithms as well.
An adaptable and extensible geometry kernel
 In Proc. Workshop on Algorithm Engineering
, 2001
"... ii ..."
Computing the Generalized Singular Value Decomposition
 SIAM J. Sci. Comput
, 1991
"... We present a variation of Paige's algorithm for computing the generalized singular value decomposition (GSVD) of two matrices A and B. There are two innovations. The first is a new preprocessing step which reduces A and B to upper triangular forms satisfying certain rank conditions. The second is a ..."
Abstract

Cited by 19 (1 self)
 Add to MetaCart
We present a variation of Paige's algorithm for computing the generalized singular value decomposition (GSVD) of two matrices A and B. There are two innovations. The first is a new preprocessing step which reduces A and B to upper triangular forms satisfying certain rank conditions. The second is a new 2 \Theta 2 triangular GSVD algorithm, which constitutes the inner loop of Paige's algorithm. We present proofs of stability and high accuracy of the 2 \Theta 2 GSVD algorithm, and demonstrate it using examples on which all previous algorithms fail. 1 Introduction The purpose of this paper is to describe a variation of Paige's algorithm [28] for computing the following generalized singular value decomposition (GSVD) introduced by Van Loan [33], and Paige and Saunders [25]. This is also called the quotient singular value decomposition (QSVD) in [8]. Theorem 1.1 Let A 2 IR m\Thetan and B 2 IR p\Thetan have rank(A T ; B T ) = n. 1 Then there are orthogonal matrices U , V and Q su...
Formal verification of IA64 division algorithms
 Proceedings, Theorem Proving in Higher Order Logics (TPHOLs), LNCS 1869
, 2000
"... Abstract. The IA64 architecture defers floating point and integer division to software. To ensure correctness and maximum efficiency, Intel provides a number of recommended algorithms which can be called as subroutines or inlined by compilers and assembly language programmers. All these algorithms ..."
Abstract

Cited by 18 (4 self)
 Add to MetaCart
Abstract. The IA64 architecture defers floating point and integer division to software. To ensure correctness and maximum efficiency, Intel provides a number of recommended algorithms which can be called as subroutines or inlined by compilers and assembly language programmers. All these algorithms have been subjected to formal verification using the HOL Light theorem prover. As well as improving our level of confidence in the algorithms, the formal verification process has led to a better understanding of the underlying theory, allowing some significant efficiency improvements. 1