《模式识别：算法方法》概述与决策算法详解

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《模式识别：算法方法》是一本由M.N. Murty和V.S. Devi合著的Springer出版的专业书籍，专注于向计算机科学领域的本科和研究生读者介绍模式识别的基本概念。本书的核心理念是提供清晰易懂的教学内容，而不是深入探讨数据预处理技术，它假定数据已经被适当的预处理成数值向量形式。作者们主要关注于利用这些数值数据来执行关键任务，如分类，通过大量的工作示例和章节末尾的练习题帮助读者掌握算法。书中强调的是算法层面的分析，而非仅仅停留在理论层面，适合那些希望进一步理解模式识别的科研人员作为参考资料。对于那些希望通过自我学习或短期课程深化对这一主题理解的学生来说，这本书是理想的选择。每个章节结束后，书还提供了“进一步阅读”部分和详细的参考文献列表，鼓励读者探索更广泛的学术资源。《Undergraduate Topics in Computer Science》系列以其新颖、简洁和现代的教学方法而闻名，由各自领域的权威专家撰写，并经过国际顾问团的审阅，确保了内容的高质量。该系列覆盖了计算和信息科学的各个核心领域，从基础知识到高级主题和应用，包含丰富的例子和习题，许多甚至还提供完整的解答，以便学生进行深入学习和实践。系列编辑Ian Mackie以及来自世界各地知名大学的顾问团成员，如Oxford的Samson Abramsky、Rio de Janeiro的Karin Breitman、Imperial College London的Chris Hankin等，共同确保了本系列书籍的学术质量和国际视野。这使得《模式识别：算法方法》不仅是一本实用的学习工具，也是一份连接理论与实践的桥梁，为计算机科学教育增添了深度和广度。

Introduction 5

Neural networks are modelled to mimic how the human brain learns. One type of

neural network, the perceptron, is used to f ind the linear decision bo undaries in high

dimensional spaces. Support vector machines (SVMs) are built based on this notion.

In Chapter 7, the role of neural networks and SVMs in classification is explored. It is

meaningful to use more than one classifier to arrive at the class label of a new pattern.

Such combinations of classifiers form the basis for Chapter 8.

Often, it is po ssible to have a large training data set which can be directly used

for classification. In such a context, clustering can be used to generate abstractions

of the data and these abstractions can be used for classification. For example, sets

of patterns corresponding to different classes can be clustered to form sub-classes.

Each such sub-class (cluster) can be represented by a single prototypical pattern;

these r epresentative patterns can be used to build the classifier instead of the entire

data set. In Chapter 9, a discussion on some of the popular clustering algorithms is

presented.

Discussion

Pattern recognition deals with classification and clustering of patterns. It is so

fundamental an idea that it finds a place in many a f ield. Pattern recognition can be

done statistically or syntactically—s tatistical pattern recognition is mo r e popular as it

can deal with noisy environments better.

Further Reading

Duda et al. (2000) have written an excellent book on pattern classification. The book

by Tan et al. (2007) on data mining is a good source for students. Russell and Norvig

(2003) have written a book on artificial intelligence which discusses learning and

pattern recognition techniques as a part of artificial intelligence. Neural network as

used for pattern classification is discussed by Bishop (2003).

Exercises

1. Consider the task of recognising the digits 0 to 9. Take a set of patterns

generated by the computer. What could be the features used for this problem?

Are the features semantic or syntactic? If the features chosen by you are only

syntactic, can you think of a set of features where some features are syntactic

and s ome are semantic?

8 Pattern Recognition

descriptions. Depending on the classification problem, distinguishing features of the

patterns are used. These features are called attributes. A pattern is the representation

of an object by the values taken by the attributes. In the classification problem, we

have a set of objects for which the values of the attributes are known. We have a set of

classes and each object belongs to one of these classes. The classes for the case where

the patterns are animals could be mammals, reptiles etc. In the case of the patterns

being balls, the classes could be football, cricket ball, table tennis ball etc. Given a

new pattern, the class of the pattern is to be determined. The choice of attributes and

representation of patterns is a very important step in pattern classification. A good

representation is one which makes use of discriminating attributes and also reduces

the computational burden in pattern classification.

2.1 Data Structures for Pattern Representation

2.1.1 Patterns as Vecto rs

An obvious representation of a pattern will be a vector. Each element of the vector

can represent one attribute of the pattern. The first element of the vector will contain

the value of the first attribute for the pattern being considered. For example, if we

are representing spherical objects, (30, 1) may represent a spherical object with 30

units of weight and 1 unit diameter. The class label can form part of the vector. If

spherical objects belong to class 1, the vector would be (30, 1, 1), where the first

element represents the weight of the object, the second element, the diameter of the

object and the third element represents the class of the object.

Example 1

Using the vector representation, a set of patterns, for exam ple can be represented as

1.0, 1.0, 1 ; 1.0, 2.0, 1

2.0, 1.0, 1 ; 2.0, 2.0, 1

4.0, 1.0, 2 ; 5.0, 1.0, 2

4.0, 2.0, 2 ; 5.0, 2.0, 2

1.0, 4.0, 2 ; 1.0, 5.0, 2

2.0, 4.0, 2 ; 2.0, 5.0, 2

4.0, 4.0, 1 ; 5.0, 5.0, 1

4.0, 5.0, 1 ; 5.0, 4.0, 1

where the first element is the first feature, the second element is the second feature and

the third element gives the class of the pattern. This can be represented graphically as

shown in Figure 2.1, where patterns of class 1 are represented using the symbol +,

patterns of class 2 are represented using X and the square represents a test pattern.

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