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18
Evolving Artificial Neural Networks
, 1999
"... This paper: 1) reviews different combinations between ANN's and evolutionary algorithms (EA's), including using EA's to evolve ANN connection weights, architectures, learning rules, and input features; 2) discusses different search operators which have been used in various EA's; and 3) points out po ..."
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Cited by 410 (6 self)
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This paper: 1) reviews different combinations between ANN's and evolutionary algorithms (EA's), including using EA's to evolve ANN connection weights, architectures, learning rules, and input features; 2) discusses different search operators which have been used in various EA's; and 3) points out possible future research directions. It is shown, through a considerably large literature review, that combinations between ANN's and EA's can lead to significantly better intelligent systems than relying on ANN's or EA's alone
A Review of Evolutionary Artificial Neural Networks
, 1993
"... Research on potential interactions between connectionist learning systems, i.e., artificial neural networks (ANNs), and evolutionary search procedures, like genetic algorithms (GAs), has attracted a lot of attention recently. Evolutionary ANNs (EANNs) can be considered as the combination of ANNs and ..."
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Cited by 154 (23 self)
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Research on potential interactions between connectionist learning systems, i.e., artificial neural networks (ANNs), and evolutionary search procedures, like genetic algorithms (GAs), has attracted a lot of attention recently. Evolutionary ANNs (EANNs) can be considered as the combination of ANNs and evolutionary search procedures. This paper first distinguishes among three kinds of evolution in EANNs, i.e., the evolution of connection weights, of architectures and of learning rules. Then it reviews each kind of evolution in detail and analyses critical issues related to different evolutions. The review shows that although a lot of work has been done on the evolution of connection weights and of architectures, few attempts have been made to understand the evolution of learning rules. Interactions among different evolutions are seldom mentioned in current research. However, the evolution of learning rules and its interactions with other kinds of evolution play a vital role in EANNs. As t...
Feature Selection via Mathematical Programming
, 1997
"... The problem of discriminating between two finite point sets in ndimensional feature space by a separating plane that utilizes as few of the features as possible, is formulated as a mathematical program with a parametric objective function and linear constraints. The step function that appears in th ..."
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Cited by 60 (22 self)
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The problem of discriminating between two finite point sets in ndimensional feature space by a separating plane that utilizes as few of the features as possible, is formulated as a mathematical program with a parametric objective function and linear constraints. The step function that appears in the objective function can be approximated by a sigmoid or by a concave exponential on the nonnegative real line, or it can be treated exactly by considering the equivalent linear program with equilibrium constraints (LPEC). Computational tests of these three approaches on publicly available realworld databases have been carried out and compared with an adaptation of the optimal brain damage (OBD) method for reducing neural network complexity. One feature selection algorithm via concave minimization (FSV) reduced crossvalidation error on a cancer prognosis database by 35.4% while reducing problem features from 32 to 4. Feature selection is an important problem in machine learning [18, 15, 1...
Multicategory Classification by Support Vector Machines
 Computational Optimizations and Applications
, 1999
"... We examine the problem of how to discriminate between objects of three or more classes. Specifically, we investigate how twoclass discrimination methods can be extended to the multiclass case. We show how the linear programming (LP) approaches based on the work of Mangasarian and quadratic programm ..."
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Cited by 56 (0 self)
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We examine the problem of how to discriminate between objects of three or more classes. Specifically, we investigate how twoclass discrimination methods can be extended to the multiclass case. We show how the linear programming (LP) approaches based on the work of Mangasarian and quadratic programming (QP) approaches based on Vapnik's Support Vector Machines (SVM) can be combined to yield two new approaches to the multiclass problem. In LP multiclass discrimination, a single linear program is used to construct a piecewise linear classification function. In our proposed multiclass SVM method, a single quadratic program is used to construct a piecewise nonlinear classification function. Each piece of this function can take the form of a polynomial, radial basis function, or even a neural network. For the k > 2 class problems, the SVM method as originally proposed required the construction of a twoclass SVM to separate each class from the remaining classes. Similarily, k twoclass linear programs can be used for the multiclass problem. We performed an empirical study of the original LP method, the proposed k LP method, the proposed single QP method and the original k QP methods. We discuss the advantages and disadvantages of each approach. 1 1
Neural networks for classification: a survey
 and Cybernetics  Part C: Applications and Reviews
, 2000
"... Abstractâ€”Classification is one of the most active research and application areas of neural networks. The literature is vast and growing. This paper summarizes the some of the most important developments in neural network classification research. Specifically, the issues of posterior probability esti ..."
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Cited by 48 (0 self)
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Abstractâ€”Classification is one of the most active research and application areas of neural networks. The literature is vast and growing. This paper summarizes the some of the most important developments in neural network classification research. Specifically, the issues of posterior probability estimation, the link between neural and conventional classifiers, learning and generalization tradeoff in classification, the feature variable selection, as well as the effect of misclassification costs are examined. Our purpose is to provide a synthesis of the published research in this area and stimulate further research interests and efforts in the identified topics. Index Termsâ€”Bayesian classifier, classification, ensemble methods, feature variable selection, learning and generalization, misclassification costs, neural networks. I.
Mathematical Programming in Data Mining
 Data Mining and Knowledge Discovery
, 1996
"... Mathematical programming approaches to three fundamental problems will be described: feature selection, clustering and robust representation. The feature selection problem considered is that of discriminating between two sets while recognizing irrelevant and redundant features and suppressing them. ..."
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Cited by 26 (3 self)
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Mathematical programming approaches to three fundamental problems will be described: feature selection, clustering and robust representation. The feature selection problem considered is that of discriminating between two sets while recognizing irrelevant and redundant features and suppressing them. This creates a lean model that often generalizes better to new unseen data. Computational results on real data confirm improved generalization of leaner models. Clustering is exemplified by the unsupervised learning of patterns and clusters that may exist in a given database and is a useful tool for knowledge discovery in databases (KDD). A mathematical programming formulation of this problem is proposed that is theoretically justifiable and computationally implementable in a finite number of steps. A resulting kMedian Algorithm is utilized to discover very useful survival curves for breast cancer patients from a medical database. Robust representation is concerned with minimizing trained m...
Geometry in Learning
 In Geometry at Work
, 1997
"... One of the fundamental problems in learning is identifying members of two different classes. For example, to diagnose cancer, one must learn to discriminate between benign and malignant tumors. Through examination of tumors with previously determined diagnosis, one learns some function for distingui ..."
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Cited by 19 (6 self)
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One of the fundamental problems in learning is identifying members of two different classes. For example, to diagnose cancer, one must learn to discriminate between benign and malignant tumors. Through examination of tumors with previously determined diagnosis, one learns some function for distinguishing the benign and malignant tumors. Then the acquired knowledge is used to diagnose new tumors. The perceptron is a simple biologically inspired model for this twoclass learning problem. The perceptron is trained or constructed using examples from the two classes. Then the perceptron is used to classify new examples. We describe geometrically what a perceptron is capable of learning. Using duality, we develop a framework for investigating different methods of training a perceptron. Depending on how we define the "best" perceptron, different minimization problems are developed for training the perceptron. The effectiveness of these methods is evaluated empirically on four practical applic...
A Preliminary Study on Designing Artificial Neural Networks Using CoEvolution
 in Proceedings of the IEEE Singapore International Conference on Intelligent Control and Instrumentation
, 1995
"... The design of optimal artificial neural networks (ANNs) is a key issue in the study of ANNs from the point of view of both theory and applications. There are strong biological and engineering evidences to support that the information processing capability of an ANN is determined by its architecture. ..."
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Cited by 17 (8 self)
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The design of optimal artificial neural networks (ANNs) is a key issue in the study of ANNs from the point of view of both theory and applications. There are strong biological and engineering evidences to support that the information processing capability of an ANN is determined by its architecture. However, no systematic method for designing ANNs exists although there are many attempts in attacking this problem. This paper adopts an evolutionary approach to ANN design. The indirect encoding scheme of ANN architectures is used. That is, a genetic algorithm is used to evolve a set of grammar rules which generate an ANN architecture. A novel method of coevolving a set of rules is proposed in this paper. In our coevolutionary system, each individual in a population represents a rule. The whole population is the complete set of grammar rules which are used to generate an architecture. Preliminary experiments have been carried out to evolve ANN architectures for the parity problem with var...
Feature Minimization within Decision Trees
 Computational Optimization and Applications
, 1996
"... Decision trees for classification can be constructed using mathematical programming. Within decision tree algorithms, the feature minimization problem is to construct accurate decisions using as few features or attributes within each decision as possible. Feature minimization is an important aspe ..."
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Cited by 14 (2 self)
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Decision trees for classification can be constructed using mathematical programming. Within decision tree algorithms, the feature minimization problem is to construct accurate decisions using as few features or attributes within each decision as possible. Feature minimization is an important aspect of data mining since it helps identify what attributes are important and helps produce accurate and interpretable decision trees. In feature minimization with bounded accuracy, we minimize the number of features using a given misclassification error tolerance. This problem can be formulated as a parametric bilinear program and is shown to be NPcomplete. A parametric FrankWolfe method is used to solve the bilinear subproblems. The resulting minimization algorithm produces more compact, accurate, and interpretable trees. This procedure can be applied to many di#erent error functions. Formulations and results for two error functions are given. One method, FM RLPP, dramatically reduced the number of features of one dataset from 147 to 2 while maintaining an 83.6% testing accuracy. Computational results compare favorably with the standard univariate decision tree method, C4.5, as well as with linear programming methods of tree construction. Key Words: Data mining, machine learning, feature minimization, decision trees, bilinear programming. # Knowledge Discovery and Data Mining Group, Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, NY 12180. Email bredee@rpi.edu, bennek@rpi.edu. Telephone (518) 2766899. FAX (518) 2764824. This material is based on research supported by National Science Foundation Grant 949427. 1
Evolving Artificial Neural Networks for Medical Applications
 in Proc. of 1995 AustraliaKorea Joint Workshop on Evolutionary Computation
, 1995
"... Artificial neural network (ANN) architecture design has been one of the most tedious and difficult tasks in ANN applications due to the lack of satisfactory and systematic methods of designing a near optimal architecture. Evolutionary algorithms have been shown to be very effective in evolving novel ..."
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Cited by 9 (8 self)
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Artificial neural network (ANN) architecture design has been one of the most tedious and difficult tasks in ANN applications due to the lack of satisfactory and systematic methods of designing a near optimal architecture. Evolutionary algorithms have been shown to be very effective in evolving novel ANN architectures for various problems. This paper proposes a new method for evolving ANN architectures and weights at the same time. The new method has been applied to four realworld data sets in the medical domain and achieved very good results. The traditional trialanderror approach to designing ANNs has been replaced by an automatic evolutionary system which can find a near optimal architecture and connection weights for a problem. 1 Introduction Artificial neural networks (ANNs) have been used widely in many application areas in recent years. Most applications use feedforward ANNs and the backpropagation (BP) training algorithm. There are numerous variants of the classical BP alg...