摘要
随着数字技术与计算机的高速发展，人们需要处理的信息日渐呈现出高维和海量的特点。然而，随之而来的困扰是如何有效地分析和利用这些数据。这是模式识别、数据挖掘、软计算、机器学习等学科所共同面临的问题。在传统的模式分析中，许多分类方法的计算复杂度随着训练集样本个数的增加而快速增长。因此对于较大规模数据集的处理常常会陷入困境。基于核的模式分析方法是模式分析领域的一种新理论，首先以支持向量机的形式出现，是一种可以用来摆脱传统的计算和统计上困难的分类算法。此外，核方法提供了一个统一的框架，来思考和操作各种类型的数据，不管它们是向量、串或更复杂的对象，同时也能够进行多种类型的模式分析。由于工程应用中信息处理的需求，软计算方法得到大量的应用，其理论也在不断的发展，与其它方法的结合应用也在不断出现，使其在信息数据分析处理应用中显现出重要性。本文对核方法与软计算方法在模式分析中的应用进行了深入的研究，探讨了核方法与软计算方法在实际应用中出现的问题与局限性。并融合这些算法构建出更有效的模式分析新算法。全文共六章，主要研究工作为以下四个部分：
第一部分研究在核特征空间中的特征分析算法。核函数的使用提供了一种强有力的、符合原理的方法，在核特征空间中用人们熟知的线性算法分析非线性关系。本文结合核方法、主元分析和线性判别分析等机器学习方法，提出了一种特征分析的KPL方法。KPL方法既能够保持数据集的非线性关系又能够提取出数据集最有效分类的方向。
第二部分研究在核特征空间中的流形学习算法。首先，本文提出了的基于核局部线性嵌入方法，该方法能够自动选择最优的近邻个数，并能构造分布均匀的流形。克服了局部线性嵌入方法对其近邻个数太过敏感，以及要求流形上的分布比较均匀的难题。此外，等距特征映射算法是一种广泛使用的低维嵌入方法，本文将注意力集中在等距特征映射的一个关键问题：等距特征映射利用一个局部邻域信息来构建流形的全局嵌入，等距特征映射距离信息矩阵适当变化可描述成为一个Gram矩阵，因此等距特征映射和Mercer核之间的区别与联系在本文中呈现。
第三部分研究基于模糊理论的支持向量机，首先研究了模糊支持向量机理论，为了克服支持向量机对噪音的敏感问题，降低噪音对分类结果的不利影响，提出了一种新的基于直接构造分类方法的模糊多类分类支持向量机。该方法结合了模糊思想，并引入了模糊补偿的机制，重新构造并推导了相关的优化问题。实验表明，提出的这种方法在分类精度上有明显的改善。其次，本文将模糊集理论用于支持向量机核函数的构造中，提出了一种基于模糊核支持向量机。该方法用两样本的模糊隶属度点积来代替传统的点积运算，而样本的模糊隶属度值充分刻画了样本对于某类的隶属情况。利用模糊隶属度的点积描述了两样本隶属某类的紧密与相关程度。
第四部分研究核方法与软计算方法融合形成的优化算法。首先，利用支持向量机优化模糊推理系统，寻找模糊推理系统中关键的模糊规则，约简冗余规则。其次，核参数选择是基于核的学习算法的一种新型技术，对于基于核的模式分析起着至关重要的作用。本文通过几种软计算方法分别求出优化的支持向量机的参数。最后，本文提出了利用遗传算法与粗糙约简算法优化模糊神经网络。
The digital technologies and computer advances have led to high-dimensional and massive data collection. The following puzzle is how to analysis and utilize so much data. That is a common challenge for pattern analysis, data mining, soft computing and machine learning. In traditional pattern analysis, the computational complexity of many classifiers increases quickly as the number of training samples increases. So when applied to a large data set, those classifiers often become computational intractable. Kernel-based analysis is a powerful new theory of patterns analysis, first appears in the form of support vector machines, and overcomes the computational and statistical difficulties alluded to the traditional learning algorithms. Furthermore, the approach provides a unified framework to reason about and operate on data of all types, such as vectorial, strings, or more complex objects, which is enabling the analysis of a wide variety of patterns. Because of the need of information processing in abundant engineering applications, soft computing methods are used widely. The theory of soft computing developed rapidly, and some other relative theories appear constantly, which increases its importance in the application of data analysis and information processing. This doctoral dissertation investigates the use of kernel methods and soft computing methods in pattern analysis, reveals the practical problems in kernel methods and soft computing methods. These techniques are used to construct novel and effective pattern analysis methods. The dissertation consists of four parts with six chapters:
Part 1 is devoted to investigating features analysis algorithm in the kernel feature space. The use of kernel function provides a powerful and principled way of analyzing nonlinear relations using well-understood linear algorithms in an appropriate feature apace. This paper investigates kernel method, principal component analysis and linear discriminant analysis algorithms for proposed the KPL features analysis algorithm. The proposed KPL features analysis algorithm can keep good characteristic of nonlinear relationship of data and the optimal direction of classification.
Part 2 contributes to investigate manifold learning algorithm in the kernel feature space. Firstly, a nonlinear dimensionality reduction kernel method based locally linear embedding algorithm is proposed. The proposed algorithm can select the optimal number of nearest neighbors, construct uniform distribution manifold, and overcome the instability of pattern that is caused by the locally linear embedding impressionable the number of nearest neighbors and uniform distribution manifold. ISOMAP is one of widely-used low-dimensional embedding methods. In this paper, we pay our attention to a critical issue that the ISOMAP utilizes local neighborhood information matrices to construct a global embedding of the manifold, is described as Gram matrices, the relation between ISOMAP to Mercer kernel is displayed.
Part 3 is to study preconditioning fuzzy support vector machine methods. Firstly, a novel directly constructing fuzzy support vector machine method is presented in order to decreasing originally directly constructing methods sensitivity to noise data, and overcoming disadvantages of the noise data for classification results. The proposed methods integrate fuzzy thoughts, introduce fuzzy compensation, and reconstruct and deduce corresponding optimal problems. Experimental results indicate the proposed methods have higher precision than originally directly constructing methods. Secondly, this paper presents a novel support vector machine based on fuzzy kernel by applying fuzzy theories into SVM's kernel function. The proposed method replaces traditional inner product with the inner product of fuzzy membership value similarity measurement of two samples, where membership value of a sample sufficiently depicts a case of a sample pertaining to a class, and membership value similarity measurement describes two samples' tightness degree pertaining to a class.
Part 4 is devoted to investigating the fusion algorithms of kernel methods and soft computing methods. Kernel methods and soft computing methods are used to construct optimized algorithms. Firstly, support vector machine is used for optimizing the fuzzy inference system, SVM reduces the redundant rules and retain the key rules. Secondly, as a new technology, the choice of kernel parameters plays an important role on the kernel-based pattern analysis. Several soft computing algorithms are used to optimize parameter selection problem. Finally, genetic algorithm and rough set theory are used to optimize the adaptive neuro-fuzzy inference system's structure.
引文
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