Preprocessing Perceptrons and Multivariate Decision Limits

Preprocessing Perceptrons and Multivariate Decision Limits

Patrik Eklund (Umeå University, Sweden) and Lena Kallin Westin (Umeå University, Sweden)
DOI: 10.4018/978-1-60566-218-3.ch005
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Abstract

Classification networks, consisting of preprocessing layers combined with well-known classification networks, are well suited for medical data analysis. Additionally, by adjusting network complexity to corresponding complexity of data, the parameters in the preprocessing network can, in comparison with networks of higher complexity, be more precisely understood and also effectively utilised as decision limits. Further, a multivariate approach to preprocessing is shown in many cases to increase correctness rates in classification tasks. Handling network complexity in this way thus leads to efficient parameter estimations as well as useful parameter interpretations.
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The Preprocessing Perceptron

A linear regression is given by the weighted sum

where xi are inputs and wi and γ are parameters of the linear function. A logistic regression performs a sigmoidal activation of the weighted sum, i.e.,

Note that a logistic regression function is precisely a (single-layer) perceptron in the terminology of neural networks (Duda et. al., 2001). The preprocessing perceptron consists similarly of a weighted sum but includes preprocessing functions for each input variable. Suitable preprocessing functions are sigmoids (sigmoidal functions)

(1) where α is the parameter representing the position of the inflexion point, i.e., the soft cut-off or decision limit, and β corresponds1 to the slope value at the inflexion point. Often the sigmoid is also used as an activation function in neural networks. In this case, α is usually set 0 and β is set to 1, i.e.,

(2)

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Table of Contents
Foreword
Riccardo Bellazzi
Preface
Petr Berka, Jan Rauch, Djamel Abdelkader Zighed
Acknowledgment
Petr Berka, Jan Rauch, Djamel Abdelkader Zighed
Chapter 1
Jana Zvárová, Arnošt Veselý
This chapter introduces the basic concepts of medical informatics: data, information, and knowledge. Data are classified into various types and... Sample PDF
Data, Information and Knowledge
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Chapter 2
Michel Simonet, Radja Messai, Gayo Diallo
Health data and knowledge had been structured through medical classifications and taxonomies long before ontologies had acquired their pivot status... Sample PDF
Ontologies in the Health Field
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Chapter 3
Alberto Freitas, Pavel Brazdil, Altamiro Costa-Pereira
This chapter introduces cost-sensitive learning and its importance in medicine. Health managers and clinicians often need models that try to... Sample PDF
Cost-Sensitive Learning in Medicine
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Chapter 4
Arnošt Veselý
This chapter deals with applications of artificial neural networks in classification and regression problems. Based on theoretical analysis it... Sample PDF
Classification and Prediction with Neural Networks
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Chapter 5
Patrik Eklund, Lena Kallin Westin
Classification networks, consisting of preprocessing layers combined with well-known classification networks, are well suited for medical data... Sample PDF
Preprocessing Perceptrons and Multivariate Decision Limits
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Chapter 6
Xiu Ying Wang, Dagan Feng
The rapid advance and innovation in medical imaging techniques offer significant improvement in healthcare services, as well as provide new... Sample PDF
Image Registration for Biomedical Information Integration
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Chapter 7
ECG Processing  (pages 137-160)
Lenka Lhotská, Václav Chudácek, Michal Huptych
This chapter describes methods for preprocessing, analysis, feature extraction, visualization, and classification of electrocardiogram (ECG)... Sample PDF
ECG Processing
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Chapter 8
EEG Data Mining Using PCA  (pages 161-180)
Lenka Lhotská, Vladimír Krajca, Jitka Mohylová, Svojmil Petránek, Václav Gerla
This chapter deals with the application of principal components analysis (PCA) to the field of data mining in electroencephalogram (EEG) processing.... Sample PDF
EEG Data Mining Using PCA
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Chapter 9
Darryl N. Davis, Thuy T.T. Nguyen
Risk prediction models are of great interest to clinicians. They offer an explicit and repeatable means to aide the selection, from a general... Sample PDF
Generating and Verifying Risk Prediction Models using Data Mining
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Chapter 10
Vangelis Karkaletsis, Konstantinos Stamatakis, Karampiperis, Karampiperis, Pythagoras Karampiperis, Pythagoras Karampiperis
The World Wide Web is an important channel of information exchange in many domains, including the medical one. The ever increasing amount of freely... Sample PDF
Management of Medical Website Quality Labels via Web Mining
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Chapter 11
Rainer Schmidt
In medicine, a lot of exceptions usually occur. In medical practice and in knowledge-based systems, it is necessary to consider them and to deal... Sample PDF
Two Case-Based Systems for Explaining Exceptions in Medicine
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Chapter 12
Bruno Crémilleux, Arnaud Soulet, Jiri Kléma, Céline Hébert, Olivier Gandrillon
The discovery of biologically interpretable knowledge from gene expression data is a crucial issue. Current gene data analysis is often based on... Sample PDF
Discovering Knowledge from Local Patterns in SAGE Data
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Chapter 13
Jirí Kléma, Filip Železný, Igor Trajkovski, Filip Karel, Bruno Crémilleux
This chapter points out the role of genomic background knowledge in gene expression data mining. The authors demonstrate its application in several... Sample PDF
Gene Expression Mining Guided by Background Knowledge
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Chapter 14
Pamela L. Thompson, Xin Zhang, Wenxin Jiang, Zbigniew W. Ras, Pawel Jastreboff
This chapter describes the process used to mine a database containing data, related to patient visits during Tinnitus Retraining Therapy. The... Sample PDF
Mining Tinnitus Database for Knowledge
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Chapter 15
Dinora A. Morales, Endika Bengoetxea, Pedro Larrañaga
Infertility is currently considered an important social problem that has been subject to special interest by medical doctors and biologists. Due to... Sample PDF
Gaussian-Stacking Multiclassifiers for Human Embryo Selection
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Chapter 16
Mining Tuberculosis Data  (pages 332-349)
Marisa A. Sánchez, Sonia Uremovich, Pablo Acrogliano
This chapter reviews the current policies of tuberculosis control programs for the diagnosis of tuberculosis. The international standard for... Sample PDF
Mining Tuberculosis Data
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Chapter 17
Mila Kwiatkowska, M. Stella Atkins, Les Matthews, Najib T. Ayas, C. Frank Ryan
This chapter describes how to integrate medical knowledge with purely inductive (data-driven) methods for the creation of clinical prediction rules.... Sample PDF
Knowledge-Based Induction of Clinical Prediction Rules
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Chapter 18
Petr Berka, Jan Rauch, Marie Tomecková
The aim of this chapter is to describe goals, current results, and further plans of long-time activity concerning application of data mining and... Sample PDF
Data Mining in Atherosclerosis Risk Factor Data
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About the Contributors