The importance of having ef cient and effective methods for data mining and kn- ledge discovery (DM&KD), to which the present book is devoted, grows every day and numerous such methods have been developed in recent decades. There exists a great variety of different settings for the main problem studied by data mining and knowledge discovery, and it seems that a very popular one is formulated in terms of binary attributes. In this setting, states of nature of the application area under consideration are described by Boolean vectors de ned on some attributes. That is, by data points de ned in the Boolean space of the attributes. It is postulated that there exists a partition of this space into two classes, which should be inferred as patterns on the attributes when only several data points are known, the so-called positive and negative training examples. The main problem in DM&KD is de ned as nding rules for recognizing (cl- sifying) new data points of unknown class, i. e. , deciding which of them are positive and which are negative. In other words, to infer the binary value of one more attribute, called the goal or class attribute. To solve this problem, some methods have been suggested which construct a Boolean function separating the two given sets of positive and negative training data points.
Author(s): Evangelos Triantaphyllou
Series: Springer Optimization and Its Applications 43
Edition: 1
Publisher: Springer US
Year: 2010
Language: English
Pages: 350
Tags: Operations Research, Mathematical Programming; Mathematical Logic and Formal Languages; Operations Research/Decision Theory
Front Matter....Pages i-xxxiii
Front Matter....Pages 1-1
Introduction....Pages 3-20
Inferring a Boolean Function from Positive and Negative Examples....Pages 21-56
A Revised Branch-and-Bound Approach for Inferring a Boolean Function from Examples....Pages 57-72
Some Fast Heuristics for Inferring a Boolean Function from Examples....Pages 73-100
An Approach to Guided Learning of Boolean Functions....Pages 101-123
An Incremental Learning Algorithm for Inferring Boolean Functions....Pages 125-145
A Duality Relationship Between Boolean Functions in CNF and DNF Derivable from the Same Training Examples....Pages 147-150
The Rejectability Graph of Two Sets of Examples....Pages 151-170
Front Matter....Pages 171-171
The Reliability Issue in Data Mining: The Case of Computer-Aided Breast Cancer Diagnosis....Pages 173-190
Data Mining and Knowledge Discovery by Means of Monotone Boolean Functions....Pages 191-227
Some Application Issues of Monotone Boolean Functions....Pages 229-239
Mining of Association Rules....Pages 241-255
Data Mining of Text Documents....Pages 257-276
First Case Study: Predicting Muscle Fatigue from EMG Signals....Pages 277-287
Second Case Study: Inference of Diagnostic Rules for Breast Cancer....Pages 289-296
A Fuzzy Logic Approach to Attribute Formalization: Analysis of Lobulation for Breast Cancer Diagnosis....Pages 297-308
Conclusions....Pages 309-315
Back Matter....Pages 317-350
