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A training algorithm for optimal margin classifiers
 PROCEEDINGS OF THE 5TH ANNUAL ACM WORKSHOP ON COMPUTATIONAL LEARNING THEORY
, 1992
"... A training algorithm that maximizes the margin between the training patterns and the decision boundary is presented. The technique is applicable to a wide variety of classifiaction functions, including Perceptrons, polynomials, and Radial Basis Functions. The effective number of parameters is adjust ..."
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Cited by 1332 (44 self)
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A training algorithm that maximizes the margin between the training patterns and the decision boundary is presented. The technique is applicable to a wide variety of classifiaction functions, including Perceptrons, polynomials, and Radial Basis Functions. The effective number of parameters is adjusted automatically to match the complexity of the problem. The solution is expressed as a linear combination of supporting patterns. These are the subset of training patterns that are closest to the decision boundary. Bounds on the generalization performance based on the leaveoneout method and the VCdimension are given. Experimental results on optical character recognition problems demonstrate the good generalization obtained when compared with other learning algorithms.
A New Evolutionary System for Evolving Artificial Neural Networks
 IEEE Transactions on Neural Networks
, 1996
"... This paper presents a new evolutionary system, i.e., EPNet, for evolving artificial neural networks (ANNs). The evolutionary algorithm used in EPNet is based on Fogel's evolutionary programming (EP) [1], [2], [3]. Unlike most previous studies on evolving ANNs, this paper puts its emphasis on ev ..."
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Cited by 159 (35 self)
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This paper presents a new evolutionary system, i.e., EPNet, for evolving artificial neural networks (ANNs). The evolutionary algorithm used in EPNet is based on Fogel's evolutionary programming (EP) [1], [2], [3]. Unlike most previous studies on evolving ANNs, this paper puts its emphasis on evolving ANN's behaviours. This is one of the primary reasons why EP is adopted. Five mutation operators proposed in EPNet reflect such an emphasis on evolving behaviours. Close behavioural links between parents and their offspring are maintained by various mutations, such as partial training and node splitting. EPNet evolves ANN's architectures and connection weights (including biases 1 ) simultaneously in order to reduce the noise in fitness evaluation. The parsimony of evolved ANNs is encouraged by preferring node/connection deletion to addition. EPNet has been tested on a number of benchmark problems in machine learning and ANNs, such as the parity problem, the medical diagnosis problems (bre...
A nonparametric approach to pricing and hedging derivative securities via learning networks
 Journal of Finance
, 1994
"... http://www.jstor.org/about/terms.html. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, no ..."
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Cited by 108 (4 self)
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http://www.jstor.org/about/terms.html. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, noncommercial use. Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at
Spatial Transformations in the Parietal Cortex Using Basis Functions
, 1997
"... Sensorimotor transformations are nonlinear mappings of sensory inputs to motor responses. We explore here the possibility that the responses of single neurons in the parietal cortex serve as basis functions for these transformations. Basis function decomposition is a general method for approximating ..."
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Cited by 69 (7 self)
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Sensorimotor transformations are nonlinear mappings of sensory inputs to motor responses. We explore here the possibility that the responses of single neurons in the parietal cortex serve as basis functions for these transformations. Basis function decomposition is a general method for approximating nonlinear functions that is computationally efficient and well suited for adaptive modification. In particular, the responses of single parietal neurons can be approximated by the product of a Gaussian function of retinal location and a sigmoid function of eye position, called a gain field. A large set of such functions forms a basis set that can be used to perform an arbitrary motor response through a direct projection. We compare this hypothesis with other approaches that are commonly used to model population codes, such as computational maps and vectorial representations. Neither of these alternatives can fully account for the responses of parietal neurons, and they are computationally less efficient for nonlinear transformations. Basis functions also have the advantage of not depending on any coordinate system or reference frame. As a consequence, the position of an object can be represented in multiple reference frames simultaneously, a property consistent with the behavior of hemineglect patients with lesions in the parietal cortex.
Regression Modeling in BackPropagation and Projection Pursuit Learning
, 1994
"... We studied and compared two types of connectionist learning methods for modelfree regression problems in this paper. One is the popular backpropagation learning (BPL) well known in the artificial neural networks literature; the other is the projection pursuit learning (PPL) emerged in recent years ..."
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Cited by 67 (1 self)
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We studied and compared two types of connectionist learning methods for modelfree regression problems in this paper. One is the popular backpropagation learning (BPL) well known in the artificial neural networks literature; the other is the projection pursuit learning (PPL) emerged in recent years in the statistical estimation literature. Both the BPL and the PPL are based on projections of the data in directions determined from interconnection weights. However, unlike the use of fixed nonlinear activations (usually sigmoidal) for the hidden neurons in BPL, the PPL systematically approximates the unknown nonlinear activations. Moreover, the BPL estimates all the weights simultaneously at each iteration, while the PPL estimates the weights cyclically (neuronbyneuron and layerbylayer) at each iteration. Although the BPL and the PPL have comparable training speed when based on a GaussNewton optimization algorithm, the PPL proves more parsimonious in that the PPL requires a fewer hi...
Bounds for the Computational Power and Learning Complexity of Analog Neural Nets
 Proc. of the 25th ACM Symp. Theory of Computing
, 1993
"... . It is shown that high order feedforward neural nets of constant depth with piecewise polynomial activation functions and arbitrary real weights can be simulated for boolean inputs and outputs by neural nets of a somewhat larger size and depth with heaviside gates and weights from f\Gamma1; 0; 1g. ..."
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Cited by 60 (12 self)
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. It is shown that high order feedforward neural nets of constant depth with piecewise polynomial activation functions and arbitrary real weights can be simulated for boolean inputs and outputs by neural nets of a somewhat larger size and depth with heaviside gates and weights from f\Gamma1; 0; 1g. This provides the first known upper bound for the computational power of the former type of neural nets. It is also shown that in the case of first order nets with piecewise linear activation functions one can replace arbitrary real weights by rational numbers with polynomially many bits, without changing the boolean function that is computed by the neural net. In order to prove these results we introduce two new methods for reducing nonlinear problems about weights in multilayer neural nets to linear problems for a transformed set of parameters. These transformed parameters can be interpreted as weights in a somewhat larger neural net. As another application of our new proof technique we s...
Psychophysical support for a 2D view interpolation theory of object recognition
"... Does the human brain represent objects for recognition by storing a series of twodimensional snapshots, or are the object models, in some sense, threedimensional analogs of the objects they represent? One way to address this question is to explore the ability of the human visual system to generaliz ..."
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Cited by 57 (25 self)
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Does the human brain represent objects for recognition by storing a series of twodimensional snapshots, or are the object models, in some sense, threedimensional analogs of the objects they represent? One way to address this question is to explore the ability of the human visual system to generalize recognition from familiar to novel views of threedimensional objects. Three recently proposed theories of object recognition  viewpoint normalization or alignment of 3D models [Ullman, S. (1989) Cognition, 32, 193254], linear combination of 2D views [Ullman, S. & Basri, R. (1990)], and view approximation [Poggio, T. & Edelman, S. (1990) Nature, 343, 263266]  predict different patterns of generalization to novel views. We have exploited the conflicting predictions to test the three theories directly, in a psychophysical experiment involving computergenerated 3D objects. Our results suggest that the human visual system is better described as recognizing these objects by 2D view in...
Soft Computing: the Convergence of Emerging Reasoning Technologies
 Soft Computing
, 1997
"... The term Soft Computing (SC) represents the combination of emerging problemsolving technologies such as Fuzzy Logic (FL), Probabilistic Reasoning (PR), Neural Networks (NNs), and Genetic Algorithms (GAs). Each of these technologies provide us with complementary reasoning and searching methods to so ..."
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Cited by 54 (8 self)
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The term Soft Computing (SC) represents the combination of emerging problemsolving technologies such as Fuzzy Logic (FL), Probabilistic Reasoning (PR), Neural Networks (NNs), and Genetic Algorithms (GAs). Each of these technologies provide us with complementary reasoning and searching methods to solve complex, realworld problems. After a brief description of each of these technologies, we will analyze some of their most useful combinations, such as the use of FL to control GAs and NNs parameters; the application of GAs to evolve NNs (topologies or weights) or to tune FL controllers; and the implementation of FL controllers as NNs tuned by backpropagationtype algorithms.
Neural Networks for Optimal Approximation of Smooth and Analytic Functions
 Neural Computation
, 1996
"... . We prove that neural networks with a single hidden layer are capable of providing an optimal order of approximation for functions assumed to possess a given number of derivatives, if the activation function evaluated by each principal element satisfies certain technical conditions. Under these con ..."
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Cited by 43 (5 self)
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. We prove that neural networks with a single hidden layer are capable of providing an optimal order of approximation for functions assumed to possess a given number of derivatives, if the activation function evaluated by each principal element satisfies certain technical conditions. Under these conditions, it is also possible to construct networks that provide a geometric order of approximation for analytic target functions. The permissible activation functions include the squashing function (1 + e x ) 1 as well as a variety of radial basis functions. Our proofs are constructive. The weights and thresholds of our networks are chosen independently of the target function; we give explicit formulas for the coe#cients as simple, continuous, linear functionals of the target function. 1. Introduction. In recent years, there has been a great deal of research in the theory of approximation of real valued functions using artificial neural networks with one or more hidden layers, with each pr...
Class similarity and viewpoint invariance in the recognition of 3D objects
 Biological Cybernetics
, 1992
"... In human vision, the processes and the representations involved in identifying specific individuals are frequently assumed to be different from those used for basiclevel classification, because classification is largely viewpointinvariant, but identification is not. This assumption was tested in p ..."
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Cited by 39 (16 self)
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In human vision, the processes and the representations involved in identifying specific individuals are frequently assumed to be different from those used for basiclevel classification, because classification is largely viewpointinvariant, but identification is not. This assumption was tested in psychophysical experiments, in which objective similarity between stimuli (and, consequently, the level of their distinction) varied in a controlled fashion. Subjects were trained to discriminate between two classes of computer generated 3D objects, one resembling monkeys, and the other dogs. Both classes were defined by the same set of 56 parameters, which encoded sizes, shapes, and placement of the limbs, the ears, the snout, etc. Interpolation between parameter vectors of the class prototypes yielded shapes that changed smoothly between monkey and dog. Withinclass variation was induced in each trial by randomly perturbing all the parameters. After the subjects reached 90% correct performa...