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radial basis functions, recurrent networks, self-organizing systems, modular networks, temporal processing, neurodynamics, and VLSI implementation. It integrates computer experiments throughout to demonstrate how neural networks are designed and perform in practice. Chapter objectives, problems, worked examples, a bibliography, photographs, illustrations, and a thorough glossary all reinforce concepts throughout. New chapters delve into such areas as SVMs, and reinforcement learning/neurodynamic programming, plus readers will find an entire chapter of case studies to illustrate the real-life, practical applications of neural networks. A highly detailed bibliography is included for easy reference. It is the book for professional engineers and research scientists.

Heaton, J., Introduction to Neural Networks with Java, Heaton Research, St. Louis, MO, 2005.

Introduction to Neural Networks with Java introduces the Java programmer to the world of neural networks and artificial intelligence (AI). Neural-network architectures such as the feedforward backpropagation, Hopfield, and Kohonen networks are discussed. Additional AI topics, such as Genetic Algorithms and Simulated Annealing, are also introduced. Practical examples are given for each neural network. Examples include the Traveling Salesman problem, handwriting recognition, fuzzy logic, and learning mathematical functions. All Java source code can be downloaded online. In addition to showing the programmer how to construct these neural networks, the book discusses the Java Object Oriented Neural Engine (JOONE). JOONE is a free open source Java neural engine.

Principe, J. C., R. Mikkulainen, Advances in Self-Organizing Maps, Series: Lecture Notes in Computer Science, Vol. 5629, Springer, New York, 2009.

This book constitutes the refereed proceedings of the 7th International Workshop on Advances in Self-Organizing Maps, WSOM 2009, held in St. Augustine, Florida, in June 2009. The 41 revised full papers presented were carefully reviewed and selected from numerous submissions. The papers deal with topics in the use of SOM in many areas of social sciences, economics, computational biology, engineering, time-series analysis, data visualization, and theoretical computer science.

Zurada, J. M., Introduction to Artificial Neural Systems, West Publishing Co., St. Paul, MN, 1992.

The book is one of the traditional textbooks on ANNs. The text grew out of a teaching effort in artificial neural systems offered for both electrical engineering and computer science majors. The author emphasizes that the practical significance of neural computation becomes apparent for large or very large-scale problems.

8

ENSEMBLE LEARNING

Chapter Objectives

Explain the basic characteristics of ensemble learning methodologies.

Distinguish between the different implementations of combination schemes for different learners.

Compare bagging and boosting approaches.

Introduce AdaBoost algorithm and its advantages.

One of the primary goals of data mining is to predict an β€œunknown” value of a new sample from observed samples. Such a prediction is achieved by two sequential phases as shown in Figure 8.1: (a) training phaseβ€”producing a predictive model from training samples using one of the available supervised learning algorithms; and (b) testing phaseβ€”evaluating the generated predictive model using test samples that are not used in the training phase. Numerous applications of a data-mining process showed validity of the so-called β€œNo-Free-Lunch Theorem.” It states that there is no single learning algorithm that is the best and most accurate in all applications. Each algorithm determines a certain model that comes with a set of assumptions. Sometimes these assumptions hold, sometimes not; therefore, no single algorithm β€œwins” all the time.

Figure 8.1. Training phase and testing phase for a predictive model. (a) Training phase; (b) testing phase.

In order to improve the accuracy of a predictive model, the promising approach called the ensemble learning is introduced. The idea is to combine results from various predictive models generated using training samples. The key motivation behind the proposed approach is to reduce the error rate. An initial assumption is that it will become much more unlikely that the ensemble will misclassify a new sample compared with a single predictive model. When combinining multiple, independent, and diverse β€œdecisions makers,” each of which is at least more accurate than random guessing, correct decisions should be reinforced. The idea may be demonstrated by some simple decision processes where single-human performances are compared with human ensembles. For example, given the question β€œHow many jelly beans are in the jar?”, the group average will outperform individual estimates. Or, in the TV series β€œWho Wants to be a Millionaire?” where audience (ensemble) vote is a support for the candidate who is not sure of the answer.

This idea is proven theoretically by Hansen and company through the statement: If N classifiers make independent errors and they have the error probability e < 0.5, then it can be shown that the error of an ensemble E is monotonically decreasing the function of N. Clearly, performances quickly decrease for dependent classifiers.

8.1 ENSEMBLE-LEARNING METHODOLOGIES

The ensemble-learning methodology consists of two sequential phases: (a) the training phase, and (b) the testing phase. In the training phase, the ensemble method generates several different predictive models from training samples as presented in Figure 8.2a. For predicting an unknown value of a test sample, the ensemble method aggregates outputs of each predictive model (Fig. 8.2b). An integrated predictive model generated by an ensemble approach consists of several predictive models (Predictive model.1, Predictive model.2, … , Predictive model. n) and a combining rule as shown in Figure 8.2b. We will refer to such a predictive model as an ensemble. The field of ensemble learning is still relatively new, and several names are used as synonyms depending on which predictive task is performed, including combination of multiple classifiers, classifier fusion, mixture of experts, or consensus aggregation.

Figure 8.2. Training phase and testing phase for building an ensemble. (a) Training phase; (b) testing phase.

To perform better than a single predictive model, an ensemble should consist of predictive models that are independent of each other, that is, their errors are uncorrelated, and each of them has an accuracy rate of >0.5. The outcome of each predictive model is aggregated to determine the output value of a test sample. We may analyze all steps of ensemble prediction for a classification task. For example, we may analyze a classification task where the ensemble consists of 15 classifiers, each of which classifies test samples into one of two categorical

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