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2000 | Buch

Introduction Kapitel lesen Erstes Kapitel lesen

Fuzzy Classifier Design

verfasst von: Dr. Ludmila I. Kuncheva

Verlag: Physica-Verlag HD

Buchreihe : Studies in Fuzziness and Soft Computing

Enthalten in: Professional Book Archive

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Über dieses Buch

Fuzzy sets were first proposed by Lotfi Zadeh in his seminal paper [366] in 1965, and ever since have been a center of many discussions, fervently admired and condemned. Both proponents and opponents consider the argu­ ments pointless because none of them would step back from their territory. And stiH, discussions burst out from a single sparkle like a conference pa­ per or a message on some fuzzy-mail newsgroup. Here is an excerpt from an e-mail messagepostedin1993tofuzzy-mail@vexpert. dbai. twvien. ac. at. by somebody who signed "Dave". , . . . Why then the "logic" in "fuzzy logic"? I don't think anyone has successfully used fuzzy sets for logical inference, nor do I think anyone wiH. In my admittedly neophyte opinion, "fuzzy logic" is a misnomer, an oxymoron. (1 would be delighted to be proven wrong on that. ) . . . I carne to the fuzzy literature with an open mind (and open wal­ let), high hopes and keen interest. I am very much disiHusioned with "fuzzy" per se, but I did happen across some extremely interesting things along the way. " Dave, thanks for the nice quote! Enthusiastic on the surface, are not many of us suspicious deep down? In some books and journals the word fuzzy is religiously avoided: fuzzy set theory is viewed as a second-hand cheap trick whose aim is nothing else but to devalue good classical theories and open up the way to lazy ignorants and newcomers.

Inhaltsverzeichnis

Frontmatter
1. Introduction
Abstract
Fuzzy pattern recognition is sometimes identified with fuzzy clustering or with fuzzy if-then systems used as classifiers. In this book we adopt a broader view: fuzzy pattern recognition is about any pattern classification paradigm that involves fuzzy sets. To a certain extent fuzzy pattern recognition is dual to classical pattern recognition, as delineated in the early seventies by Duda and Hart [87], Fukunaga [100], Tou and Gonzalez [324], and thereby consists of three basic components: clustering, classifier design and feature selection [39] . Fuzzy clustering has been the most successful offspring of fuzzy pattern recognition so far. The fuzzy c-means algorithm devised by Bezdek [34] has admirable popularity in a great number of fields, both engineering and non-engineering. Fuzzy feature selection is virtually absent, or disguised as something else. This book is about the third component fuzzy classifier design.
Ludmila I. Kuncheva
2. Statistical pattern recognition
Abstract
Pattern recognition problems emerge constantly in our everyday life. The ring of the telephone triggers an on-line pattern recognition problem: who might this be? Hearing the voice on the line we are almost always able to tell who this is, no matter that the line might be noisy, or the person at the other end might have a cold. Humans easily identify faces, speakers, smells — tasks that are still a challenge for a computer. When we are able to instruct the computer how to label the objects into the prespecified groups, the problem becomes routine. Pattern recognition is about those problems that are still not algorithmically clear-cut. Examples of pattern recognition problems are: classification of crops and soil types from remote-sensing images; detection of clustered microcalcifications on mammograms; optical character recognition (OCR); classification of airmass for predicting a thunderstorm flood; discrimination between stars and galaxies in sky images; etc.
Ludmila I. Kuncheva
3. Statistical classifiers
Abstract
To design a Bayes-optimal classifier for a certain problem we need the prior probabilities (P(ω i )) and the class-conditional p.d.f’s (p(x∣ω i )) for all classes ω1,...,ω c .
Ludmila I. Kuncheva
4. Fuzzy sets
Abstract
In Bangor, North Wales, it is often drizzling or raining. At any time you will find in the streets people with umbrellas and without umbrellas, varying in number. For some of them it is raining, and yet for some others, it is not raining — both at the same time. So, ‘raining’ is a matter of judgement. We can assign a degree (of truth) to the statement “It is raining” , and funnily enough, both the proposition and its negation can hold true to a certain degree at the same time.
Ludmila I. Kuncheva
5. Fuzzy if-then classifiers
Abstract
A fuzzy if-then system has n inputs (x = [x 1, ... , x n ] T ϵ ℜ n ) and c outputs (y = [y1,...,y c ] T ϵ ℜ C ). Here are three popular acronyms for fuzzy (and also non-fuzzy) systems
  • SISO. Single input —single output systems (n = c = 1).
  • MISO. Multiple input —single output systems (n > 1, c = 1).
  • MIMO. Multiple input — multiple output systems (n > 1, c > 1).
Ludmila I. Kuncheva
6. Training of fuzzy if-then classifiers
Abstract
Assume we have a difficult pattern recognition problem which can easily be handled by a human but not by a machine. Assume also that the human recognition process is difficult to articulate or express in any functional or algorithmic form. Examples of such tasks are face recognition and speaker verification. In some problems we have some knowledge about the classes. An example is handwriting recognition where the theoretical shapes, connections, loops, etc. for each symbol are known, so the “ideal” prototype for each class is described by a set of rules. Nevertheless, handwriting recognition by a machine (and sometimes by a human) is still a challenge. Two natural approaches to designing a classifier are
  • Ask an expert how they solve the problem and try to encapsulate the knowledge in a fuzzy rule-base classifier.
  • Collect input-output data (i.e., a labeled data set) and extract the classifier parameters from the data.
Ludmila I. Kuncheva
7. Non if-then fuzzy models
Abstract
In Chapter 1 we adopted Definition 1 stating that a fuzzy classifier is any classifier which uses fuzzy sets either during its training or during its operation. So, fuzzy classifier modeling stretches beyond fuzzy if-then designs discussed in the previous two chapters. This chapter presents non-if-then fuzzy models. These models can be grouped in different ways (see [39, 81, 115, 118, 273, 320]) . However, the boundaries between these groups are not sharp because many of the classification schemes can be assigned to more than one group (see, e.g., [232] where the authors use multiple rule-based prototypes and call their method a knowledge-oriented fuzzy k-nearest neighbor classifier) .
Ludmila I. Kuncheva
8. Combinations of multiple classifiers using fuzzy sets
Abstract
Different classifiers can be built using the labeled data set Z. Instead of choosing for further use the classifier with the best accuracy, we can keep a set of them. Let D = {D1,..., DL} be a set of L classifiers designed on the data set Z. The idea is to combine their outputs hoping to increase the accuracy beyond that of the best classifier in the pool D. This is a theoretically justified hope as we show later but there is no guarantee that picking an arbitrary set of classifiers will render a successful team. Combining classifiers has been an important research topic coming under different names in the literature:
  • combination of multiple classifiers [172, 209, 282, 350, 352];
  • classifier fusion [62, 102, 115, 164] ;
  • mixture of experts [150, 151, 156, 256];
  • committees of neural networks [43, 79] ;
  • consensus aggregation [28, 29, 252];
  • voting pool of classifiers [24];
  • dynamic classifier selection [350];
  • composite classifier system [70];
  • classifier ensembles [79, 95];
  • divide-and-conquer classifiers [61];
  • pandemonium system of reflective agents [309];
  • change-glasses approach to classifier selection [189], etc.
Ludmila I. Kuncheva
9. Conclusions: What to choose?
Abstract
Fuzzy or non-fuzzy? This is always the question. Remember the motto on the first page of Chapter 4 (Fuzzy sets)? It continues as follows:
The people’s doctor Praying Mantis started stretching out his dry as grass hands to touch Buratino. ‘One of the two,’ he whispered, ‘the patient is either alive or dead’.
Ludmila I. Kuncheva
Backmatter
Metadaten
Titel
Fuzzy Classifier Design
verfasst von
Dr. Ludmila I. Kuncheva
Copyright-Jahr
2000
Verlag
Physica-Verlag HD
Electronic ISBN
978-3-7908-1850-5
Print ISBN
978-3-7908-2472-8
DOI
https://doi.org/10.1007/978-3-7908-1850-5