C++实现的神经网络与模糊逻辑探索

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"C++ Neural Networks and Fuzzy Logic" 是一本由 Valluru B. Rao 所著的书籍，由 MT Books, IDG Books Worldwide, Inc. 出版，ISBN 为 1558515526，出版日期为1995年6月1日。这本书专注于通过C++编程语言来阐述神经网络和模糊逻辑的概念，并提供了可作为实验基础的实例代码。在神经网络领域，模型的种类繁多，通常其理论解释是数学化的且复杂难懂。本书旨在通过C++编写的具体示例，帮助读者理解和探索神经网络的内部工作原理。作者强调实践是理解神经网络的关键，因为它们的学习过程充满趣味性。尽管书中主要用C++进行描述，但并未包含大量复杂的类库。除了一个用于回传算法的模拟器，书中提供的示例程序都是针对多种不同神经网络架构和范式的简单程序。这个回传模拟器设计得既广泛使用又易于操作，能处理大型输入数据集。书中的一个章节会使用这个模拟器解决金融预测问题，读者可以对提供的代码进行扩展和实验，有很大的灵活性。此外，书中还涵盖了多种不同的角度和方法，不仅限于神经网络，也包括模糊逻辑，这是一门研究不精确或不确定信息处理的学科。模糊逻辑与神经网络结合，可以增强系统在处理模糊或非结构化数据时的能力，适用于许多实际问题的解决方案，如决策支持、控制系统的优化等。书中通过实例和实践代码，不仅讲解了基本的神经网络架构，如感知机、多层前馈网络（含反向传播）、自组织映射（SOM）等，还可能涉及了递归网络、卷积网络以及模糊逻辑系统的设计和应用。读者可以通过这些实例学习如何在C++环境中构建和训练这些模型，同时了解如何将它们应用于实际问题的求解。《C++ Neural Networks and Fuzzy Logic》是一本面向实践者的书籍，旨在帮助读者通过编程实践深入理解神经网络和模糊逻辑，通过书中提供的代码，读者不仅可以学习到理论知识，还能提升解决实际问题的能力。无论你是初学者还是有一定经验的开发者，这本书都能提供有价值的洞见和实践经验。

C++ Neural Networks and Fuzzy Logic

by Valluru B. Rao

MTBooks, IDG Books Worldwide, Inc.

ISBN: 1558515526 Pub Date: 06/01/95

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Cash Register Game

A contestant in The Price is Right is sometimes asked to play the Cash Register Game. A few products are

described, their prices are unknown to the contestant, and the contestant has to declare how many units of

each item he or she would like to (pretend to) buy. If the total purchase does not exceed the amount specified,

the contestant wins a special prize. After the contestant announces how many items of a particular product he

or she wants, the price of that product is revealed, and it is rung up on the cash register. The contestant must

be careful, in this case, that the total does not exceed some nominal value, to earn the associated prize. We can

now cast the whole operation of this game, in terms of a neural network, called a Perceptron, as follows.

Consider each product on the shelf to be a neuron in the input layer, with its input being the unit price of that

product. The cash register is the single neuron in the output layer. The only connections in the network are

between each of the neurons (products displayed on the shelf) in the input layer and the output neuron (the

cash register). This arrangement is usually referred to as a neuron, the cash register in this case, being an

instar in neural network terminology. The contestant actually determines these connections, because when the

contestant says he or she wants, say five, of a specific product, the contestant is thereby assigning a weight of

5 to the connection between that product and the cash register. The total bill for the purchases by the

contestant is nothing but the weighted sum of the unit prices of the different products offered. For those items

the contestant does not choose to purchase, the implicit weight assigned is 0. The application of the dollar

limit to the bill is just the application of a threshold, except that the threshold value should not be exceeded for

the outcome from this network to favor the contestant, winning him or her a good prize. In a Perceptron, the

way the threshold works is that an output neuron is supposed to fire if its activation value exceeds the

threshold value.

Weights

The weights used on the connections between different layers have much significance in the working of the

neural network and the characterization of a network. The following actions are possible in a neural network:

1. Start with one set of weights and run the network. (NO TRAINING)

2. Start with one set of weights, run the network, and modify some or all the weights, and run the

network again with the new set of weights. Repeat this process until some predetermined goal is met.

(TRAINING)

Training

Since the output(s) may not be what is expected, the weights may need to be altered. Some rule then needs to

be used to determine how to alter the weights. There should also be a criterion to specify when the process of

successive modification of weights ceases. This process of changing the weights, or rather, updating the

weights, is called training. A network in which learning is employed is said to be subjected to training.

Training is an external process or regimen. Learning is the desired process that takes place internal to the

network.

C++ Neural Networks and Fuzzy Logic:Preface

Cash Register Game 16

Feedback

If you wish to train a network so it can recognize or identify some predetermined patterns, or evaluate some

function values for given arguments, it would be important to have information fed back from the output

neurons to neurons in some layer before that, to enable further processing and adjustment of weights on the

connections. Such feedback can be to the input layer or a layer between the input layer and the output layer,

sometimes labeled the hidden layer. What is fed back is usually the error in the output, modified appropriately

according to some useful paradigm. The process of feedback continues through the subsequent cycles of

operation of the neural network and ceases when the training is completed.

Supervised or Unsupervised Learning

A network can be subject to supervised or unsupervised learning. The learning would be supervised if external

criteria are used and matched by the network output, and if not, the learning is unsupervised. This is one broad

way to divide different neural network approaches. Unsupervised approaches are also termed self−organizing.

There is more interaction between neurons, typically with feedback and intralayer connections between

neurons promoting self−organization.

Supervised networks are a little more straightforward to conceptualize than unsupervised networks. You apply

the inputs to the supervised network along with an expected response, much like the Pavlovian conditioned

stimulus and response regimen. You mold the network with stimulus−response pairs. A stock market

forecaster may present economic data (the stimulus) along with metrics of stock market performance (the

response) to the neural network to the present and attempt to predict the future once training is complete.

You provide unsupervised networks with only stimulus. You may, for example, want an unsupervised

network to correctly classify parts from a conveyor belt into part numbers, providing an image of each part to

do the classification (the stimulus). The unsupervised network in this case would act like a look−up memory

that is indexed by its contents, or a Content−Addressable−Memory (CAM).

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C++ Neural Networks and Fuzzy Logic:Preface

Feedback 17

C++ Neural Networks and Fuzzy Logic

by Valluru B. Rao

MTBooks, IDG Books Worldwide, Inc.

ISBN: 1558515526 Pub Date: 06/01/95

Previous Table of Contents Next

Noise

Noise is perturbation, or a deviation from the actual. A data set used to train a neural network may have

inherent noise in it, or an image may have random speckles in it, for example. The response of the neural

network to noise is an important factor in determining its suitability to a given application. In the process of

training, you may apply a metric to your neural network to see how well the network has learned your training

data. In cases where the metric stabilizes to some meaningful value, whether the value is acceptable to you or

not, you say that the network converges. You may wish to introduce noise intentionally in training to find out

if the network can learn in the presence of noise, and if the network can converge on noisy data.

Memory

Once you train a network on a set of data, suppose you continue training the network with new data. Will the

network forget the intended training on the original set or will it remember? This is another angle that is

approached by some researchers who are interested in preserving a network’s long−term memory (LTM) as

well as its short−term memory (STM). Long−term memory is memory associated with learning that persists

for the long term. Short−term memory is memory associated with a neural network that decays in some time

interval.

Capsule of History

You marvel at the capabilities of the human brain and find its ways of processing information unknown to a

large extent. You find it awesome that very complex situations are discerned at a far greater speed than what a

computer can do.

Warren McCulloch and Walter Pitts formulated in 1943 a model for a nerve cell, a neuron, during their

attempt to build a theory of self−organizing systems. Later, Frank Rosenblatt constructed a Perceptron, an

arrangement of processing elements representing the nerve cells into a network. His network could recognize

simple shapes. It was the advent of different models for different applications.

Those working in the field of artificial intelligence (AI) tried to hypothesize that you can model thought

processes using some symbols and some rules with which you can transform the symbols.

A limitation to the symbolic approach is related to how knowledge is representable. A piece of information is

localized, that is, available at one location, perhaps. It is not distributed over many locations. You can easily

see that distributed knowledge leads to a faster and greater inferential process. Information is less prone to be

damaged or lost when it is distributed than when it is localized. Distributed information processing can be

fault tolerant to some degree, because there are multiple sources of knowledge to apply to a given problem.

Even if one source is cut off or destroyed, other sources may still permit solution to a problem. Further, with

subsequent learning, a solution may be remapped into a new organization of distributed processing elements

that exclude a faulty processing element.

C++ Neural Networks and Fuzzy Logic:Preface

Noise 18

In neural networks, information may impact the activity of more than one neuron. Knowledge is distributed

and lends itself easily to parallel computation. Indeed there are many research activities in the field of

hardware design of neural network processing engines that exploit the parallelism of the neural network

paradigm. Carver Mead, a pioneer in the field, has suggested analog VLSI (very large scale integration)

circuit implementations of neural networks.

Neural Network Construction

There are three aspects to the construction of a neural network:

1. Structure—the architecture and topology of the neural network

2. Encoding—the method of changing weights

3. Recall—the method and capacity to retrieve information

Let’s cover the first one—structure. This relates to how many layers the network should contain, and what

their functions are, such as for input, for output, or for feature extraction. Structure also encompasses how

interconnections are made between neurons in the network, and what their functions are.

The second aspect is encoding. Encoding refers to the paradigm used for the determination of and changing of

weights on the connections between neurons. In the case of the multilayer feed−forward neural network, you

initially can define weights by randomization. Subsequently, in the process of training, you can use the

backpropagation algorithm, which is a means of updating weights starting from the output backwards. When

you have finished training the multilayer feed−forward neural network, you are finished with encoding since

weights do not change after training is completed.

Finally, recall is also an important aspect of a neural network. Recall refers to getting an expected output for a

given input. If the same input as before is presented to the network, the same corresponding output as before

should result. The type of recall can characterize the network as being autoassociative or heteroassociative.

Autoassociation is the phenomenon of associating an input vector with itself as the output, whereas

heteroassociation is that of recalling a related vector given an input vector. You have a fuzzy remembrance of

a phone number. Luckily, you stored it in an autoassociative neural network. When you apply the fuzzy

remembrance, you retrieve the actual phone number. This is a use of autoassociation. Now if you want the

individual’s name associated with a given phone number, that would require heteroassociation. Recall is

closely related to the concepts of STM and LTM introduced earlier.

The three aspects to the construction of a neural network mentioned above essentially distinguish between

different neural networks and are part of their design process.

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C++ Neural Networks and Fuzzy Logic:Preface

Neural Network Construction 19

C++ Neural Networks and Fuzzy Logic

by Valluru B. Rao

MTBooks, IDG Books Worldwide, Inc.

ISBN: 1558515526 Pub Date: 06/01/95

Previous Table of Contents Next

Sample Applications

One application for a neural network is pattern classification, or pattern matching. The patterns can be

represented by binary digits in the discrete cases, or real numbers representing analog signals in continuous

cases. Pattern classification is a form of establishing an autoassociation or heteroassociation. Recall that

associating different patterns is building the type of association called heteroassociation. If you input a

corrupted or modified pattern A to the neural network, and receive the true pattern A, this is termed

autoassociation. What use does this provide? Remember the example given at the beginning of this chapter. In

the human brain example, say you want to recall a face in a crowd and you have a hazy remembrance (input).

What you want is the actual image. Autoassociation, then, is useful in recognizing or retrieving patterns with

possibly incomplete information as input. What about heteroassociation? Here you associate A with B. Given

A, you get B and sometimes vice versa. You could store the face of a person and retrieve it with the person’s

name, for example. It’s quite common in real circumstances to do the opposite, and sometimes not so well.

You recall the face of a person, but can’t place the name.

Qualifying for a Mortgage

Another sample application, which is in fact in the works by a U.S. government agency, is to devise a neural

network to produce a quick response credit rating of an individual trying to qualify for a mortgage. The

problem to date with the application process for a mortgage has been the staggering amount of paperwork and

filing details required for each application. Once information is gathered, the response time for knowing

whether or not your mortgage is approved has typically taken several weeks. All of this will change. The

proposed neural network system will allow the complete application and approval process to take three hours,

with approval coming in five minutes of entering all of the information required. You enter in the applicant’s

employment history, salary information, credit information, and other factors and apply these to a trained

neural network. The neural network, based on prior training on thousands of case histories, looks for patterns

in the applicant’s profile and then produces a yes or no rating of worthiness to carry a particular mortgage.

Let’s now continue our discussion of factors that distinguish neural network models from each other.

Cooperation and Competition

We will now discuss cooperation and competition. Again we start with an example feed forward neural

network. If the network consists of a single input layer and an output layer consisting of a single neuron, then

the set of weights for the connections between the input layer neurons and the output neuron are given in a

weight vector. For three inputs and one output, this could be W = {w

, w

}. When the output layer has

more than one neuron, the output is not just one value but is also a vector. In such a situation each neuron in

one layer is connected to each neuron in the next layer, with weights assigned to these interconnections. Then

the weights can all be given together in a two−dimensional weight matrix, which is also sometimes called a

correlation matrix. When there are in−between layers such as a hidden layer or a so−called Kohonen layer or

a Grossberg layer, the interconnections are made between each neuron in one layer and every neuron in the

next layer, and there will be a corresponding correlation matrix. Cooperation or competition or both can be

imparted between network neurons in the same layer, through the choice of the right sign of weights for the

C++ Neural Networks and Fuzzy Logic:Preface

Sample Applications 20

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