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261
Enhanced Word Clustering for Hierarchical Text Classification
, 2002
"... In this paper we propose a new informationtheoretic divisive algorithm for word clustering applied to text classification. In previous work, such "distributional clustering" of features has been found to achieve improvements over feature selection in terms of classification accuracy, especially at ..."
Abstract

Cited by 44 (2 self)
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In this paper we propose a new informationtheoretic divisive algorithm for word clustering applied to text classification. In previous work, such "distributional clustering" of features has been found to achieve improvements over feature selection in terms of classification accuracy, especially at lower number of features [2, 28]. However the existing clustering techniques 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, thus converging to a local minimum. 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 achieves higher classification accuracy especially at lower number of features. 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 20 Newsgroups data set and a 3level hierarchy of HTML documents collected from Dmoz Open Directory.
THE ACCURACY OF FLOATING POINT SUMMATION
, 1993
"... The usual recursive summation technique is just one of several ways of computing the sum of n floating point numbers. Five summation methods and their variations are analyzed here. The accuracy of the methods is compared using rounding error analysis and numerical experiments. Four ofthe methods are ..."
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Cited by 40 (0 self)
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The usual recursive summation technique is just one of several ways of computing the sum of n floating point numbers. Five summation methods and their variations are analyzed here. The accuracy of the methods is compared using rounding error analysis and numerical experiments. Four ofthe methods are shown to be special cases of a general class of methods, and an error analysis is given for this class. No one method is uniformly more accurate than the others, but some guidelines are givenon the choice of method in particular cases.
Classroom examples of robustness problems in geometric computations
 In Proc. 12th European Symposium on Algorithms, volume 3221 of Lecture Notes Comput. Sci
, 2004
"... ..."
The pitfalls of verifying floatingpoint computations
 ACM Transactions on programming languages and systems
"... Current critical systems often use a lot of floatingpoint computations, and thus the testing or static analysis of programs containing floatingpoint operators has become a priority. However, correctly defining the semantics of common implementations of floatingpoint is tricky, because semantics ma ..."
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Cited by 34 (2 self)
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Current critical systems often use a lot of floatingpoint computations, and thus the testing or static analysis of programs containing floatingpoint operators has become a priority. However, correctly defining the semantics of common implementations of floatingpoint is tricky, because semantics may change according to many factors beyond sourcecode level, such as choices made by compilers. We here give concrete examples of problems that can appear and solutions for implementing in analysis software. 1
Toward Correctly Rounded Transcendentals
 IEEE Transactions on Computers
, 1998
"... The Table Maker's Dilemma is the problem of always getting correctly rounded results when computing the elementary functions. After a brief presentation of this problem, we present new developments that have helped us to solve this problem for the doubleprecision exponential function in a small d ..."
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Cited by 32 (14 self)
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The Table Maker's Dilemma is the problem of always getting correctly rounded results when computing the elementary functions. After a brief presentation of this problem, we present new developments that have helped us to solve this problem for the doubleprecision exponential function in a small domain. These new results show that this problem can be solved, at least for the doubleprecision format, for the most usual functions. Index TermsFloatingpoint arithmetic, rounding, elementary functions, Table Maker's Dilemma.  ###p###  1INTRODUCTION HE IEEE754 standard for floatingpoint arithmetic [2], [11] requires that the results of the arithmetic operations should always be correctly rounded. That is, once a rounding mode is chosen among the four possible ones, the system must behave as if the result were first computed exactly, with infinite precision, then rounded. There is no similar requirement for the elementary...
Floating point verification in HOL Light: the exponential function
 UNIVERSITY OF CAMBRIDGE COMPUTER LABORATORY
, 1997
"... Since they often embody compact but mathematically sophisticated algorithms, operations for computing the common transcendental functions in floating point arithmetic seem good targets for formal verification using a mechanical theorem prover. We discuss some of the general issues that arise in veri ..."
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Cited by 31 (6 self)
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Since they often embody compact but mathematically sophisticated algorithms, operations for computing the common transcendental functions in floating point arithmetic seem good targets for formal verification using a mechanical theorem prover. We discuss some of the general issues that arise in verifications of this class, and then present a machinechecked verification of an algorithm for computing the exponential function in IEEE754 standard binary floating point arithmetic. We confirm (indeed strengthen) the main result of a previously published error analysis, though we uncover a minor error in the hand proof and are forced to confront several subtle issues that might easily be overlooked informally. The development described here includes, apart from the proof itself, a formalization of IEEE arithmetic, a mathematical semantics for the programming language in which the algorithm is expressed, and the body of pure mathematics needed. All this is developed logically from first prin...
A MachineChecked Theory of Floating Point Arithmetic
, 1999
"... . Intel is applying formal verification to various pieces of mathematical software used in Merced, the first implementation of the new IA64 architecture. This paper discusses the development of a generic floating point library giving definitions of the fundamental terms and containing formal pr ..."
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Cited by 31 (5 self)
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. Intel is applying formal verification to various pieces of mathematical software used in Merced, the first implementation of the new IA64 architecture. This paper discusses the development of a generic floating point library giving definitions of the fundamental terms and containing formal proofs of important lemmas. We also briefly describe how this has been used in the verification effort so far. 1 Introduction IA64 is a new 64bit computer architecture jointly developed by HewlettPackard and Intel, and the forthcoming Merced chip from Intel will be its first silicon implementation. To avoid some of the limitations of traditional architectures, IA64 incorporates a unique combination of features, including an instruction format encoding parallelism explicitly, instruction predication, and speculative /advanced loads [4]. Nevertheless, it also offers full upwardscompatibility with IA32 (x86) code. 1 IA64 incorporates a number of floating point operations, the centerpi...
A Mechanically Checked Proof of the Correctness of the Kernel of the AMD5K86 FloatingPoint Division Algorithm
 IEEE Transactions on Computers
, 1996
"... We describe a mechanically checked proof of the correctness of the kernel of the floating point division algorithm used on the AMD5K 86 microprocessor. The kernel is a nonrestoring division algorithm that computes the floating point quotient of two double extended precision floating point numbers, ..."
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Cited by 30 (11 self)
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We describe a mechanically checked proof of the correctness of the kernel of the floating point division algorithm used on the AMD5K 86 microprocessor. The kernel is a nonrestoring division algorithm that computes the floating point quotient of two double extended precision floating point numbers, p and d (d 6= 0), with respect to a rounding mode, mode. The algorithm is defined in terms of floating point addition and multiplication. First, two NewtonRaphson iterations are used to compute a floating point approximation of the reciprocal of d. The result is used to compute four floating point quotient digits in the 24,,17 format (24 bits of precision and 17 bit exponents) which are then summed using appropriate rounding modes. We prove that if p and d are 64,,15 (possibly denormal) floating point numbers, d 6= 0 and mode specifies one of six rounding procedures and a desired precision 0 ! n 64, then the output of the algorithm is p=d rounded according to mode. We prove that every int...
Using model checking with symbolic execution to verify parallel numerical programs
 In: ISSTA (2006
"... We present a method to verify the correctness of parallel programs that perform complex numerical computations, including computations involving floatingpoint arithmetic. The method requires that a sequential version of the program be provided, to serve as the specification for the parallel one. Th ..."
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Cited by 28 (2 self)
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We present a method to verify the correctness of parallel programs that perform complex numerical computations, including computations involving floatingpoint arithmetic. The method requires that a sequential version of the program be provided, to serve as the specification for the parallel one. The key idea is to use model checking, together with symbolic computation, to establish the equivalence of the two programs. 1.
Robust Plane Sweep for Intersecting Segments
, 1997
"... In this paper, we reexamine in the framework of robust computation the BentleyOttmann algorithm for reporting intersecting pairs of segments in the plane. This algorithm has been reported as being very sensitive to numerical errors. Indeed, a simple analysis reveals that it involves predicates of d ..."
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Cited by 25 (2 self)
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In this paper, we reexamine in the framework of robust computation the BentleyOttmann algorithm for reporting intersecting pairs of segments in the plane. This algorithm has been reported as being very sensitive to numerical errors. Indeed, a simple analysis reveals that it involves predicates of degree 5, presumably never evaluated exactly in most implementation. Within the exactcomputation paradigm we introduce two models of computation aimed at replacing the conventional model of realnumber arithmetic. The first model (predicate arithmetic) assumes the exact evaluation of the signs of algebraic expressions of some degree, and the second model (exact arithmetic) assumes the exact computation of the value of...