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A tutorial on support vector machines for pattern recognition
 Data Mining and Knowledge Discovery
, 1998
"... The tutorial starts with an overview of the concepts of VC dimension and structural risk minimization. We then describe linear Support Vector Machines (SVMs) for separable and nonseparable data, working through a nontrivial example in detail. We describe a mechanical analogy, and discuss when SV ..."
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Cited by 3390 (12 self)
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large (even infinite) VC dimension by computing the VC dimension for homogeneous polynomial and Gaussian radial basis function kernels. While very high VC dimension would normally bode ill for generalization performance, and while at present there exists no theory which shows that good generalization
Large margin methods for structured and interdependent output variables
 JOURNAL OF MACHINE LEARNING RESEARCH
, 2005
"... Learning general functional dependencies between arbitrary input and output spaces is one of the key challenges in computational intelligence. While recent progress in machine learning has mainly focused on designing flexible and powerful input representations, this paper addresses the complementary ..."
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Cited by 623 (12 self)
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Learning general functional dependencies between arbitrary input and output spaces is one of the key challenges in computational intelligence. While recent progress in machine learning has mainly focused on designing flexible and powerful input representations, this paper addresses
Interprocedural dataflow analysis via graph reachability
, 1994
"... The paper shows how a large class of interprocedural dataflowanalysis problems can be solved precisely in polynomial time by transforming them into a special kind of graphreachability problem. The only restrictions are that the set of dataflow facts must be a finite set, and that the dataflow fun ..."
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Cited by 451 (34 self)
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functions must distribute over the confluence operator (either union or intersection). This class of problems includes—but is not limited to—the classical separable problems (also known as “gen/kill ” or “bitvector” problems)—e.g., reaching definitions, available expressions, and live variables
Polynomial Time Approximation Schemes for Dense Instances of NPHard Problems
, 1995
"... We present a unified framework for designing polynomial time approximation schemes (PTASs) for "dense" instances of many NPhard optimization problems, including maximum cut, graph bisection, graph separation, minimum kway cut with and without specified terminals, and maximum 3satisfiabi ..."
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Cited by 188 (34 self)
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We present a unified framework for designing polynomial time approximation schemes (PTASs) for "dense" instances of many NPhard optimization problems, including maximum cut, graph bisection, graph separation, minimum kway cut with and without specified terminals, and maximum 3
Family of Ternary Arithmetic Polynomial Expansions based on . . .
, 2004
"... New classes of Linearly Independent Ternary Arithmetic (LITA) transforms being the bases of ternary arithmetic polynomial expansions are introduced here. Recursive equations defining the LITA transforms and the corresponding butterfly diagrams are shown. Various properties and relations between int ..."
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New classes of Linearly Independent Ternary Arithmetic (LITA) transforms being the bases of ternary arithmetic polynomial expansions are introduced here. Recursive equations defining the LITA transforms and the corresponding butterfly diagrams are shown. Various properties and relations between
Cartesian Genetic Programming
, 2000
"... This paper presents a new form of Genetic Programming called Cartesian Genetic Programming in which a program is represented as an indexed graph. The graph is encoded in the form of a linear string of integers. The inputs or terminal set and node outputs are numbered sequentially. The node funct ..."
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Cited by 230 (59 self)
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functions are also separately numbered. The genotype is just a list of node connections and functions. The genotype is then mapped to an indexed graph that can be executed as a program. Evolutionary algorithms are used to evolve the genotype in a symbolic regression problem (sixth order polynomial
Support vector machines: Training and applications
 A.I. MEMO 1602, MIT A. I. LAB
, 1997
"... The Support Vector Machine (SVM) is a new and very promising classification technique developed by Vapnik and his group at AT&T Bell Laboratories [3, 6, 8, 24]. This new learning algorithm can be seen as an alternative training technique for Polynomial, Radial Basis Function and MultiLayer Perc ..."
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Cited by 223 (3 self)
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The Support Vector Machine (SVM) is a new and very promising classification technique developed by Vapnik and his group at AT&T Bell Laboratories [3, 6, 8, 24]. This new learning algorithm can be seen as an alternative training technique for Polynomial, Radial Basis Function and Multi
POLYNOMIAL SELECTIONS AND SEPARATION BY POLYNOMIALS
, 807
"... ABSTRACT. K. Nikodem and the present author proved in [3] a theorem concerning separation by affine functions. Our purpose is to generalize that result for polynomials. As a consequence we obtain two theorems connected with separation of nconvex function from nconcave function by a polynomial of d ..."
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ABSTRACT. K. Nikodem and the present author proved in [3] a theorem concerning separation by affine functions. Our purpose is to generalize that result for polynomials. As a consequence we obtain two theorems connected with separation of nconvex function from nconcave function by a polynomial
Formula Complexity of Ternary Majorities
"... Abstract. It is known that any selfdual Boolean function can be decomposed into compositions of 3bit majority functions. In this paper, we define a notion of a ternary majority formula, which is a ternary tree composed of nodes labeled by 3bit majority functions and leaves labeled by literals. We ..."
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. We study their complexity in terms of formula size. In particular, we prove upper and lower bounds for ternary majority formula size of several Boolean functions. To devise a general method to prove the ternary majority formula size lower bounds, we give an upper bound for the largest separation
Results 1  10
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