摘要
作为粒计算的三个主要模型之一，粗糙集理论可以直接对数据进行分析和推理，从中发现隐含的知识，揭示潜在的规律。因此，是一种天然的数据挖掘方法。而作为数据挖掘的另一种经典方法，神经网络是一种模仿生物神经网络行为特征，进行分布式并行信息处理的智能计算模型。鉴于粗糙集和神经网络在信息处理方式、知识获取方式、抑制噪声能力、泛化测试能力等方面有很多互补之处，将两者集成的粒度神经网络模型作为智能集成系统的一个新的重要分支，已成为该领域的研究热点问题之一。
本文从两个方面研究了基于粗糙集的粒度神经网络模型。一种方式是使用粗糙集作为前置系统，利用属性约简算法对数据集进行粒度约简，以简化神经网络的结构，提高神经网络的训练速度和预测精度。另一种方式是利用粗糙集及其扩展模型来提取决策规则，根据提取的规则来定义粒度神经元及其连接权值，实现粗糙集和神经网络的无缝融合。此外，本文还研究了每一种粒度神经网络模型的极速学习算法，该算法通过数学变换实现了学习过程的一次性完成。本文的主要研究内容包括以下几个方面：
1.在保证分类能力不变的基础上，通过粗糙集理论中的属性约简算法对训练样本集进行粒度约简。根据约简后的训练集，优化粒度BP神经网络的结构，加快网络的训练速度，提高网络的泛化能力。针对传统BP算法训练速度慢、易陷入局部最小和过拟合等问题，本文提出了基于具有全局搜索能力的量子微粒群算法来自适应地确定粒度BP网络的隐层神经元个数、连接权值和阈值等参数。
2.利用粗糙集和AP聚类算法来优化粒度RBF神经网络结构，提出了一种新的粒度RBF神经网络模型。在该模型中，利用无需任何先验知识的AP聚类算法对约简后的数据集进行聚类，将聚类后得到的中心及其宽度传递给粒度RBF网络隐层中的RBF单元。然后，对每一个约简后的样本实例，计算隐层中RBF单元的输出，并利用传统RBF算法训练粒度RBF网络。
3.提出了一种改进的极速学习算法，用来优化单隐层粒度神经网络模型。该算法利用AP聚类自适应地确定极速学习算法中的隐层节点个数，并以聚类中心和宽度构造了新的激活函数（高斯函数）。利用该算法来优化粒度BP神经网络和粒度RBF神经网络，实现这两种粒度神经网络在统一框架下的自适应极速学习，以此建立了具有自适应极速学习能力的单隐层粒度神经网络模型。
4.根据属性约简和值约简后的数据集提取的决策规则，建立了一种新的粒度神经网络模型——粗规则粒度神经网络。在该模型中，规则匹配层取代了传统神经网络结构中的隐层，该层的每一个粒度神经元代表一条决策规则，并依据规则的前件和后件初始化输入连接权值和输出连接权值。最后，利用极速学习算法进一步调整输出连接权值，以提高网络的分类能力。
5.考虑到决策规则还应具有一定的容错能力，基于变精度粗糙集理论，提出了粒度双神经元网络及其学习算法。在该模型中，中间层神经元都为粒度双神经元结构，用来表示每条决策规则的上近似和下近似。最后，利用极速学习算法调整网络的连接权值，以提高网络的分类能力。此外，为提高粒度双神经元处理大规模数据集的能力，本文引入AP聚类对数据集进行粒化处理，提出了基于AP聚类的粒度双神经元网络优化方法。
全文的主要工作是提出了几种基于粗糙集的粒度神经网络模型及其学习算法，并通过实验验证了网络结构及其学习算法的有效性。
Rough sets theory, as one of the three main models of granular computing, canfind hidden knowledge and reveal potential law by analyzing and reasoning on thedata directly. Therefore, it's a kind of natural data mining method. As another classicmethod of data mining, neural networks is a mathematical model for distributed andparallel information processing by imitating the behavioral characteristics ofbiological neural networks. Rough sets and neural networks have manycomplementarities in information processing, knowledge acquisition, noisesuppression capability and generalization ability. So, granular neural networksintegrated advantages of rough sets and neural networks, as a new important branch ofintelligent integrated system, has become one of hot topics in the domain of intelligentinformation processing.
The dissertation researched two integrated modes of rough sets and the neuralnetworks. One was that rough sets was regarded as a front-end processor, using itsattribute reduction algorithm to compress the dimensions of information space, tosimplify the structure of the neural network, improve neural network training speedand prediction accuracy. Another was that rough sets was used to extract decisionrules to define the granular neurons, determine the structure of neural networks and itsconnection weights which achieves the seamless integration of rough sets theory andneural networks. In addition, this dissertation also studied the extreme learningalgorithm of each integrated mode, completed learning process through mathematicaltransform. The main works of this dissertation included the following aspects:
1. On basis of guaranteeing the classification ability unchanged, simplify thetraining data set through attribute reduction algorithm of rough sets theory. Then, thereduced training set was used to optimize the structure of BP neural networks,accelerate its training speed, and improve its generalization ability. In view of thetraditional BP algorithm has some inherent vice, such as slow training speed, localminimum and over fitting problem, this dissertation proposed a new method todetermine adaptively weights and thresholds of granular BP neural network throughquantum-behaved particle swarm algorithm which has global search ability.
2. This dissertation presented a new model of granular RBF neural networksbased on rough sets and AP clustering algorithm. In this model, AP clusteringalgorithm, which doesn't need any prior knowledge, was used to cluster the reducted data set. Then, the centers and their widths obtained by AP algorithm were transmitedto RBF units in the hidden layer of granular RBF network. After that, the outputs ofRBF units in the hidden layer were calculated, and granular RBF networks weretrained by the traditional RBF learning algorithm.
3. When granular BP networks and granular RBF networks had a single hiddenlayer structure, this dissertation proposed an adaptive extreme learning algorithm tooptimize the connection weights and thresholds value. In this algorithm, AP clusteringalgorithm was used to determine adaptively the numbers of the neurons in the hiddenlayer, and obtain clustering centers and their withds which were defined the Gaussfunctions to be regarded as the new activation functions of the hidden layer.
4. According to extracted decision rules through the algorithms of attributereduction and value reduction, this dissertation proposed a new granular neuralnetwork model, called rough rule granular neural networks. In this model, rulematching layer replaced the hidden layer of traditional neural networks. Each neuronof rule matching layer represented a decision rule. Input weights and output weightswere initialized according to front components and latter components of rules. Then,the output weights were adjusted further by extreme learning algorithm to improve theclassification ability of the networks.
5. Considering decision rules should have the ability of fault-tolerant, thisdissertation proposed granular double neural networks and its learning algorithmbased on variable precision rough set model and extreme learining algorithm.In thismodel, neurons of the middle layer and the output layer were all granular doubleneurons which included upper approximation neuron and lower approximation neuronto represent the upper approximation and lower approximation of each rule. Finally,the output weights were adjusted further by extreme learning algorithm to improve theclassification ability of the networks. In addition, in order to improve the capability ofgranular double neural networks when processing mass data set, this dissertationproposed an optimized method based on AP clustering algorithm.
The dissertation studied several granular neural networks models and theirlearing algorithms, and verified the effectiveness of these models by experiments.
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