顺序方法：模式识别与机器学习 [书评]

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《模式识别与机器学习中的顺序方法》一书是科学与工程数学领域中的一本重要著作。该书属于MATHEMATICS IN SCIENCE AND ENGINEERING系列的第52卷，由加州大学南加州分校的Richard Bellman编辑。本系列是由一系列专著和教材组成的，这些著作涵盖了各种科学和工程领域的数学研究内容。《模式识别与机器学习中的顺序方法》的作者是来自普渡大学电气工程学院的K.S.FU。该书于1968年由ACADEMIC PRESS出版，版权归其所有。本书的主题是关于模式识别和机器学习的顺序方法。模式识别是一种将输入数据与预定义的模式或模型进行匹配和分类的技术。机器学习则是使用算法和统计模型让计算机从数据中自动学习和改进性能的领域。这两个领域在当今的人工智能和数据科学中非常重要。顺序方法是在模式识别和机器学习中被广泛应用的一种方法。它与传统的批处理方法不同，批处理方法是将所有样本一次性输入模型进行处理，而顺序方法则是逐个样本地进行处理和学习。顺序方法具有许多优点，例如能够处理大规模数据、实时学习和适应变化等。本书的目标是介绍顺序方法在模式识别和机器学习中的原理、算法和应用。它包含了大量的数学推导和实例分析，为读者提供了理论和实践相结合的学习资源。本书的内容涵盖了顺序方法在不同领域中的应用，如语音识别、图像识别和信号处理等。此外，本书还介绍了基于顺序方法的一些常用技术，如隐马尔可夫模型、贝叶斯网络和强化学习等。《模式识别与机器学习中的顺序方法》是一本经典的著作，对于研究者、工程师和学生来说都具有重要的参考价值。它不仅介绍了顺序方法的基本原理，还提供了实际应用的案例和方法。本书的内容详细且易于理解，适合初学者入门和专业人士深入学习。此外，本书还提供了一些未来发展方向和研究课题，为读者拓展思路和研究领域提供了参考。综上所述，《模式识别与机器学习中的顺序方法》是一本在模式识别和机器学习领域具有重要意义的书籍。它详细介绍了顺序方法的原理、算法和应用，并提供了实际的案例和方法。该书是学术界和工业界从事模式识别和机器学习研究的人士的必备参考资料。它不仅对于理论研究具有指导意义，也对于实际应用具有实用性。

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CHAPTER

INTRODUCTION

Pattern

Recognition

The problem of pattern recognition is that of classifying or labeling

a group of objects on the basis of certain subjective requirements.

Those objects classified into the same pattern class usually have some

common properties. The classification requirements are subjective

since different types of classifications occur under different situations.

For example, in recognizing English characters, there are twenty-six

pattern classes. However, in distinguishing English characters. from

Chinese characters, there are only two pattern classes, i. e., English

and Chinese. Human beings perform the task of pattern recognition

in almost every level of the nervous system. Recently, engineers

faced the problem of designing machines for pattern recognition.

Preliminary results have been very encouraging. There have been

some successful attempts to design or to program machines to read

printed or typed characters, identify bank checks, classify electro-

cardiograms, recognize some spoken words, play checkers and chess,

and sort photographs. Other applications of pattern recognition

include handwritten characters or word recognition, general medical

diagnosis, system’s fault identification, seismic wave classification,

target detection, weather prediction, speech recognition, etc. The

simplest approach for pattern recognition is probably the approach

of “template-matching.” In this case, a set of templates or prototypes,

one for each pattern class, is stored in the machine. The input pattern

(with unknown classification) is compared with the template of each

class, and the classification is based on a preselected matching criterion

or similarity criterion. In other words,

the input pattern matches

the template of ith pattern class better than

matches any other

template, then the input is classified as from the ith pattern class.

Usually, for the simplicity of the machine, the templates are stored

INTRODUCTION

in their raw-data form. This approach has been used for some existing

printed-character recognizers and bank-check readers.

The disadvantages of the template-matching approach is that it

is sometimes difficult to select a good template from each pattern

class and to define a proper matching criterion. The difficulty is

especially remarkable when large variations and distortions are

expected in all the patterns belonging to one class. The recognition

handwritten characters is a good example in this case.

more sophisti-

cated approach is that instead of matching the input pattern with

the templates, the classification is based on a set of selected measure-

ments extracted from the input pattern. These selected measurements,

called “features,” are supposed to be invariant or less sensitive with

respect to the commonly encountered variations and distortions, and

to also contain less redundancies. Under this proposition, pattern

recognition can be considered as consisting of two subproblems. The

first subproblem

what measurements should be taken from the input

patterns. Usually, the decision of what to measure is rather subjective

and also dependent on the practical situations (for example, the avail-

ability of measurements, the cost of measurements, etc.). Unfortun-

ately, at present there is very little general theory for the selection

of feature measurements. However, there are some investigations

concerned with the selection of a subset and the ordering of features

in a given set of measurements. The criterion of feature selection or

ordering is often based on either the importance of the features in

characterizing the patterns or the contribution of the features to the

performance of recognition (i.e., the accuracy

recognition).

The second subproblem in pattern recognition is the problem of

classification (or making a decision on the class assignment to the

input patterns) based on the measurements taken from the selected

features. The device or machine which extracts the feature measure-

ments from input patterns is called a

feature extractor.

The device

or machine which performs the function of classification is called

clussijier.

simplified block diagram of a pattern recognition system

rXI

WSUreIWrltS

Fig.

1.1.

pattern recognition system.

1.2.

DETERMINISTIC CLASSIFICATION TECHNIQUES

shown in Fig.

I.l.+

Thus, in general terms, the template-matching

approach may be interpreted as

special case of the second approach-

“feature-extraction” approach, where the templates are stored in

terms of feature measurements and a special classification criterion

(matching)

used for the classifier.

7.2

Deterministic Classification Techniques

The concept of pattern classification may be expressed in terms

of the partition of feature space (or a mapping from feature space to

decision space). Suppose that

features are to be measured from

each input pattern. Each set of

features can be considered as a

vector

called a feature (measurement) vector, or a point in the

N-

dimensional feature space

In,.

The problem of classification is to

assign each possible vector or point in the feature space to a proper

pattern class. This can be interpreted as

partition

the feature

space into mutually exclusive regions, and each region will correspond

a particular pattern class. Mathematically, the problem of classi-

fication can be formulated in term of “discriminant functions”[

Let

)

,...,

be designated as the

possible pattern classes

to be recognized, and let

be the feature (measurement) vector where

represents the ith

feature measurement. Then the discriminant function

Di(X)

associated

with pattern class

...,

is such that if the input pattern

represented by the feature vector

is in class

denoted as

the value of

Di(X)

must be the largest. That is, for all

Di(X)

Dj(X),

i,j

...,

(

Thus, in the feature space

52,

the boundary of partition, called the

decision boundary, between regions associated with class

and

class

)

respectively, is expressed by the following equation

Dt(X)

Dj(X)

(1.3)

The division

two

parts is primarily

for

convenience rather than necessity.

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