基于Kernel学习机的建模与分类的应用算法研究
摘要
研究从观测数据出发寻找规律，利用这些规律对未来数据进行预测，以实现为人类更好服务的目的，这是基于数据的机器学习的主要内容。然而基于数据的学习存在一个不适定的问题，因此一些理论上很优秀的学习方法在实际运用中往往差强人意。本文利用Kernel变换和正则化的思想在数据学习方面做了一系列前瞻性的研究。
1)对本文采用的基本理论进行了介绍。介绍了机器学习和Kernel学习机基本理论。介绍了Kernel算法的通用结构、Mercer定理及映射函数。介绍了统计学习理论和正则化网络的理论。回顾了Kernel相关算法的国内外进展情况。最后介绍了本文工作的基本框架结构、主要的创新性以及相关研究领域。
2)提出了一种新的具有先验类别信息的PKPCA算法，通过将样本类内差和类间差融入总体方差中，从而达到更好的分类目的。提出重构样本库的概念及构建算法，获得稀疏样本库，减少特征向量维数。可以证明KPCA和KFD是PKPCA参数取极限的两个特例。同时可以克服KFD只能求得(类别数—1)个特征向量的不足。最后，利用构造的函数类对第一个主元的分类能力进行仿真分析，以及对信用卡、天文、疾病等数据进行实验分析，表明本算法明显优于KPCA算法，获得了满意的分类效果。
3)对递推最小二乘进行非线性的Kernel变换，并采用正则化技术改写了目标函数，提出了一种RKRLS算法。获得了RKRLS模型的系数和误差表达式。在此基础上还提出了一种递推支持向量机算法。给出了DSV的概念，以及判断DSV的三个条件：ε不敏感性、ν敏感性和非奇异性条件。分别导出了RKRLS和RSVM算法在限定、增长和缩减记忆模式下的递推公式，均无需进行求逆计算。同时总结了算法具有小样本、可控的推广能力、鲁棒性和快速性等良好的工程特性。
4)提出了矢量基学习算法。通过分析样本矢量和解空间的夹角，推导了基矢量的判断准则。获得了辨识参数的增长和校正模式的递推公式。在此基础上更深入提出了矢量基学习网络，推导了网络基的自动生成规则。推导了网络节点增长的权值递推算法、网络基参数的校正算法以及网络权值的校正算法的递推公式。对糖酵解混沌振荡过程进行动态辨识建模，结果表明本算法具有较好的辨识效果和收敛性。
5)提出了MIMO矢量基学习网络的基本结构，网络可以实现建模和模
浙江大学博士学位论文
式分类的功能。利用梯度下降法对网络的权值进行训练，并且推导了BVS
的增长算法，以及网络训练的限制记忆递推公式。并进行了参数辨识和双重
螺旋分类的仿真研究，得到较好的辨识和分类效果。
6)对矢量基网络算法进行了更高层次的概括，提出了人类认知的矢量
基模型。本文利用这一认知模型对混沌序列进行了认知模拟，达到较好的认
知目的。仿真结果也说明，这种结构与人类的认知模式非常接近，可以对认
知科学的发展提供新的参考框架，同时人类的认知分析也对矢量基算法提供
了哲学层次的指导意义，促使算法在更高层次上得到更深入的发展。
7)将本文算法在橡胶工业的密炼过程得到实际的应用:在排除异常样
本点的情况下，利用5 VM的工业特性，进行排胶点的建模，获得好的应用
效果:利用动态的RKRLs和RsvM算法，通过对橡胶棍炼质量的门尼指标
进行建模和预测分析，表明算法具有较好的跟踪预测性能;利用矢量基学习
网络对密炼过程的门尼进行辨识建模和预报，获得了较好的效果，从而实现
了更好的门尼波动的控制。最终本文开发成功了“两栖智能密炼系统”，并
介绍了相应的软件操作和功能。
最后对本文的工作进行了总结，并从人类认知高度进行了展望。
Machine Learning is to find rules from data and to predict future data in order to better serve human being. While the question of learning from data is ill posed, so some excellent theories cannot satisfy the practical application properly. This thesis researches machine learning using Kernel function and Regularization Theory.
1) The basic theories used in this thesis were introduced, including Machine Learning, Kernel Machine, Statistical Learning Theory and Regularized Theory. The research situation about Kernel Machine was reviewed. At last, the basic structure, contributions and correlated fields were given.
2) The thesis proposed a Priori Kernel Principal Component Analysis (PKPCA), which integrates between and within class variances into KPCA, and thus the classification performances can be enhanced. To get sparse sample library and reduce eigenvector dimension, a new concept of reconstructing sample library and its corresponding algorithm are introduced and presented, respectively. Further, both KPCA and Kernel Fisher Discriminant can be proved to be two special cases of PKPCA, and meanwhile PKPCA successfully avoids the disadvantage of KFD that can only get (class number -1) eigenvectors. Simulation results of two numerical function classes, as well as experiment results of a real world dataset involving credit card, chronometer and diseases, show that the proposed algorithm is valid and the classification performance is satisfied.
3) This thesis proposed a Regularized Kernel Recursive Least Square (RKRLS) algorithm. The coefficients and error of RKRLS model are gotten and the generalization ability is analyzed. Furthermore, this thesis proposed a Recursive Support Vector Machine algorithm. The norm of Dynamic Support Vector is put forward, and the three conditions including e -insensitive, v-sensitive and nonsingular conditions are proved. The recursive algorithms of restricted, increased, decreased mode are deduced without the calculation of the inversion. RKRLS and RSVM have four properties: small samples, controlled generalization ability, good robustness and rapidity, which are applicable to the
industry case.
4) This thesis proposed Vector Base Learning (VBL) algorithm. The method to construct BVL is designed through judging the angle of sample and solution space. The increasing-form algorithm and adjusting-form algorithm are deduced. Further more, a new Vector Base Learning (VBL) network is proposed which is based on the concept of Base Vector Set (BVS) and Network Base (NB). A method of automatically generating NBs is developed. The algorithms- of increasing network node, adjusting NB parameter and adjusting weights are presented. The dynamic glycolysis chaotic oscillation process is identified using VBL network, which shows that this algorithm has better convergence property than other algorithms.
5) This thesis proposed MIMO Vector Base Learning Network, which can be used to model and classify. The weights are trained with Gradient Descent Method. The increase algorithm of BVS, and restricted algorithm, was induced. At last parameter identification and double spirals were simulated,, and good identification result and classification performance were obtained.
6) This thesis proposed a Vector Base Cognition Model. The basic idea, structure and algorithm are introduced. A simulation is made using this cognitive model, which proved that Vector Base Cognition Model is valid. Three propositions are proposed based the Vector Base Network. Cognition of human being and Vector Base Cognition Model are compared, the corresponding connection is created.
7) The application for rubber mixing process is given: Abnormal modeling samples first removed, SVM is applied to build the discharge model to establish the rubber discharge condition, and long term practical production validated the discharge modeling method; Adopting dynamic RKRLS and RSVM, Mooney time serials is used to model and predict, which shows better prediction ability than RLS; Using V
1)对本文采用的基本理论进行了介绍。介绍了机器学习和Kernel学习机基本理论。介绍了Kernel算法的通用结构、Mercer定理及映射函数。介绍了统计学习理论和正则化网络的理论。回顾了Kernel相关算法的国内外进展情况。最后介绍了本文工作的基本框架结构、主要的创新性以及相关研究领域。
2)提出了一种新的具有先验类别信息的PKPCA算法，通过将样本类内差和类间差融入总体方差中，从而达到更好的分类目的。提出重构样本库的概念及构建算法，获得稀疏样本库，减少特征向量维数。可以证明KPCA和KFD是PKPCA参数取极限的两个特例。同时可以克服KFD只能求得(类别数—1)个特征向量的不足。最后，利用构造的函数类对第一个主元的分类能力进行仿真分析，以及对信用卡、天文、疾病等数据进行实验分析，表明本算法明显优于KPCA算法，获得了满意的分类效果。
3)对递推最小二乘进行非线性的Kernel变换，并采用正则化技术改写了目标函数，提出了一种RKRLS算法。获得了RKRLS模型的系数和误差表达式。在此基础上还提出了一种递推支持向量机算法。给出了DSV的概念，以及判断DSV的三个条件：ε不敏感性、ν敏感性和非奇异性条件。分别导出了RKRLS和RSVM算法在限定、增长和缩减记忆模式下的递推公式，均无需进行求逆计算。同时总结了算法具有小样本、可控的推广能力、鲁棒性和快速性等良好的工程特性。
4)提出了矢量基学习算法。通过分析样本矢量和解空间的夹角，推导了基矢量的判断准则。获得了辨识参数的增长和校正模式的递推公式。在此基础上更深入提出了矢量基学习网络，推导了网络基的自动生成规则。推导了网络节点增长的权值递推算法、网络基参数的校正算法以及网络权值的校正算法的递推公式。对糖酵解混沌振荡过程进行动态辨识建模，结果表明本算法具有较好的辨识效果和收敛性。
5)提出了MIMO矢量基学习网络的基本结构，网络可以实现建模和模
浙江大学博士学位论文
式分类的功能。利用梯度下降法对网络的权值进行训练，并且推导了BVS
的增长算法，以及网络训练的限制记忆递推公式。并进行了参数辨识和双重
螺旋分类的仿真研究，得到较好的辨识和分类效果。
6)对矢量基网络算法进行了更高层次的概括，提出了人类认知的矢量
基模型。本文利用这一认知模型对混沌序列进行了认知模拟，达到较好的认
知目的。仿真结果也说明，这种结构与人类的认知模式非常接近，可以对认
知科学的发展提供新的参考框架，同时人类的认知分析也对矢量基算法提供
了哲学层次的指导意义，促使算法在更高层次上得到更深入的发展。
7)将本文算法在橡胶工业的密炼过程得到实际的应用:在排除异常样
本点的情况下，利用5 VM的工业特性，进行排胶点的建模，获得好的应用
效果:利用动态的RKRLs和RsvM算法，通过对橡胶棍炼质量的门尼指标
进行建模和预测分析，表明算法具有较好的跟踪预测性能;利用矢量基学习
网络对密炼过程的门尼进行辨识建模和预报，获得了较好的效果，从而实现
了更好的门尼波动的控制。最终本文开发成功了“两栖智能密炼系统”，并
介绍了相应的软件操作和功能。
最后对本文的工作进行了总结，并从人类认知高度进行了展望。
Machine Learning is to find rules from data and to predict future data in order to better serve human being. While the question of learning from data is ill posed, so some excellent theories cannot satisfy the practical application properly. This thesis researches machine learning using Kernel function and Regularization Theory.
1) The basic theories used in this thesis were introduced, including Machine Learning, Kernel Machine, Statistical Learning Theory and Regularized Theory. The research situation about Kernel Machine was reviewed. At last, the basic structure, contributions and correlated fields were given.
2) The thesis proposed a Priori Kernel Principal Component Analysis (PKPCA), which integrates between and within class variances into KPCA, and thus the classification performances can be enhanced. To get sparse sample library and reduce eigenvector dimension, a new concept of reconstructing sample library and its corresponding algorithm are introduced and presented, respectively. Further, both KPCA and Kernel Fisher Discriminant can be proved to be two special cases of PKPCA, and meanwhile PKPCA successfully avoids the disadvantage of KFD that can only get (class number -1) eigenvectors. Simulation results of two numerical function classes, as well as experiment results of a real world dataset involving credit card, chronometer and diseases, show that the proposed algorithm is valid and the classification performance is satisfied.
3) This thesis proposed a Regularized Kernel Recursive Least Square (RKRLS) algorithm. The coefficients and error of RKRLS model are gotten and the generalization ability is analyzed. Furthermore, this thesis proposed a Recursive Support Vector Machine algorithm. The norm of Dynamic Support Vector is put forward, and the three conditions including e -insensitive, v-sensitive and nonsingular conditions are proved. The recursive algorithms of restricted, increased, decreased mode are deduced without the calculation of the inversion. RKRLS and RSVM have four properties: small samples, controlled generalization ability, good robustness and rapidity, which are applicable to the
industry case.
4) This thesis proposed Vector Base Learning (VBL) algorithm. The method to construct BVL is designed through judging the angle of sample and solution space. The increasing-form algorithm and adjusting-form algorithm are deduced. Further more, a new Vector Base Learning (VBL) network is proposed which is based on the concept of Base Vector Set (BVS) and Network Base (NB). A method of automatically generating NBs is developed. The algorithms- of increasing network node, adjusting NB parameter and adjusting weights are presented. The dynamic glycolysis chaotic oscillation process is identified using VBL network, which shows that this algorithm has better convergence property than other algorithms.
5) This thesis proposed MIMO Vector Base Learning Network, which can be used to model and classify. The weights are trained with Gradient Descent Method. The increase algorithm of BVS, and restricted algorithm, was induced. At last parameter identification and double spirals were simulated,, and good identification result and classification performance were obtained.
6) This thesis proposed a Vector Base Cognition Model. The basic idea, structure and algorithm are introduced. A simulation is made using this cognitive model, which proved that Vector Base Cognition Model is valid. Three propositions are proposed based the Vector Base Network. Cognition of human being and Vector Base Cognition Model are compared, the corresponding connection is created.
7) The application for rubber mixing process is given: Abnormal modeling samples first removed, SVM is applied to build the discharge model to establish the rubber discharge condition, and long term practical production validated the discharge modeling method; Adopting dynamic RKRLS and RSVM, Mooney time serials is used to model and predict, which shows better prediction ability than RLS; Using V
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