流形正则化多核模型的监督与半监督分类研究与应用

发布时间：2019-05-15 12:26

【摘要】：数据分类作为机器学习最基础的学习任务之一,随着网络化信息化的发展,所需分类的数据复杂程度越来越高。多核学习因描述数据特征能力强,是复杂数据集分类的有效方法理论。从分类角度看,数据集分为输入数据部分,是数据的空间或属性信息,和相对应的输出数据部分,是数据的类别标号信息。输入数据样本,来自自然世界或工程,其往往存在固有的制约或约束关系,这种关系本质上可以用数学流形来描述。输入数据样本在其空间中所具备的流形约束,是数据的本征特征,是人来识别目标的重要信息。然而,多核分类方法尚未充分利用输入数据样本的流形约束信息。为了利用输入数据样本的流形约束信息,本文提出了一种具有输入数据样本流形约束信息的监督型的流形正则化多核分类模型。为获取输入数据样本在其空间中的流形约束信息,需要描述它们在空间中的近邻关系程度,本文应用了能细致地评价数据间近邻关系的Hellinge r(?)巨离；同时,考虑了输出数据所表达的类别标号信息作用,即同类别数据间的近邻关系程度比不同类数据间的近邻关系程度较高的一般性知识。最后,本文给出了考虑标号信息的监督型的输入数据样本流形约束的流形正则项,将其引入监督型的多核分类模型,建立了一种具有输入数据样本流形约束的监督型的流形正则化多核分类模型,给出了该模型的求解算法。监督分类仿真试验对比的结果表明,本文提出的一种具有输入数据样本流形约束的监督型的流形正则化多核分类模型是有效的。针对实际工程中,数据的输出部分普遍是有标号和无标号同时存在的事实,本文将具有输入数据样本流形约束的监督型的流形正则化多核分类模型拓展成为一种半监督的分类模型。首先,通过欧氏距离来获取全体输入数据样本之间的近邻关系,并以此得到输入数据样本的流形约束信息；然后,扩展监督型的流形正则化多核分类模型中的多核函数在全体输入数据样本下的矩阵并计算全体输入数据样本的流形约束信息的流形正则信息；从而,拓展模型成为能够综合利用有标号和无标号数据样本的一种半监督型的流形正则化多核分类模型。本文给出了这种半监督型的流形正则化多核分类模型的求解算法、误差分析和半监督分类仿真试验对比,试验结果表明了该模型在半监督分类中的有效性。针对本文给出的一种半监督型的流形正则化多核分类模型,一方面为提高该模型的自适应性和分类准确性,本文提出了半监督型的流形正则化多核分类模型中的多核函数的参数的自动选择方法；另一方面,本文改进了半监督型的流形正则化多核分类模型中的多核组合权值的约束形式,给出p范数约束多核组合权值的模型一般解。在提出的多核函数中的参数自动选择方面,本文通过改进半监督型的流形正则化多核分类模型的数学表达式并设计求解算法,将待选的核函数参数值转化为算法的解,实现自动地确定核函数参数的具体取值。在改进多核组合权值的约束方面,通过将半监督型的流形正则化多核分类模型中的多核组合权值的固定的1范数约束,改进为一般性的p范数约束,并给出了p范数约束多核组合权值的半监督流形正则化多核分类模型的求解定理及其证明。对于两方面改进后的半监督分类模型,本文分别做了半监督分类仿真试验对比。试验结果表明,本文提出的核函数参数自动选择的半监督流形正则化多核分类模型和p范数约束多核组合权值的半监督流形正则化多核分类模型是有效的。
[Abstract]:Data classification is one of the most basic learning tasks of machine learning. With the development of networked information, the data complexity of the required classification is getting higher and higher. Multi-core learning is an effective method for classification of complex data sets due to the strong ability of describing data features. From a classification point of view, the data set is divided into an input data portion, a spatial or attribute information of the data, and a corresponding output data portion, which is the category label information of the data. Input data samples, from natural world or engineering, often have inherent constraints or constraints, which can be described in nature by a mathematical manifold. The manifold constraints of the input data samples in their space are the intrinsic characteristics of the data and are important information for people to identify the target. However, the multi-core classification method has not fully utilized the manifold constraint information of the input data samples. In order to use the manifold constraint information of the input data samples, this paper presents a supervised manifold regularization multi-core classification model with input data sample manifold constraint information. In order to obtain the manifold constraint information of the input data samples in their space, it is necessary to describe their neighbor relation degree in space. ) At the same time, the class label information, which is expressed by the output data, is considered, that is, the degree of neighbor relation between the same class data is higher than that of the neighbor relation among the different class data. In the end, this paper gives a manifold regularized multi-core classification model with a supervised type of input data sample manifold constraint, considering the manifold regular term of the supervised type input data sample manifold constraint of the reference label information, and establishing a supervised type manifold regularized multi-core classification model with input data sample manifold constraint. The algorithm of this model is given. The results of the comparison of supervised classification simulation tests show that a supervised manifold regularization multi-core classification model with input data sample manifold constraints is effective. In the actual project, the output part of the data is generally the fact that the reference number and the no-label are present at the same time. In this paper, a supervised type manifold regularization multi-core classification model with input data sample manifold constraints is expanded into a semi-supervised classification model. First, the neighbor relation between all input data samples is obtained by the Euclidean distance, and the manifold constraint information of the input data sample is obtained; and then, the multi-kernel function in the extended-supervised manifold regularized multi-core classification model is used for the matrix of all input data samples and the manifold regular information of the manifold constraint information of all the input data samples is calculated; therefore, The expansion model is a kind of semi-supervised manifold regularized multi-core classification model which can comprehensively utilize the data samples with the label and the no-label. In this paper, the solution algorithm, the error analysis and the semi-supervised classification simulation test of the semi-supervised manifold regularized multi-core classification model are presented. The results show the effectiveness of the model in the semi-supervised classification. In order to improve the self-adaptability and classification accuracy of the model, a semi-supervised manifold regularized multi-core classification model is presented in this paper. On the one hand, the automatic selection method of the parameters of a multi-kernel function in a semi-supervised manifold regularization multi-core classification model is proposed. On the other hand, In this paper, the constrained form of multi-core combined weight in a semi-supervised manifold regularized multi-core classification model is improved, and a model general solution of a p-norm constrained multi-core combined weight is given. In this paper, by improving the mathematical expression of the semi-supervised manifold regularization multi-core classification model and designing the solution algorithm, the kernel function parameter value to be selected is transformed into the solution of the algorithm. And the specific value of the kernel function parameter is automatically determined. in the aspect of improving the constraint of the multi-core combined weight, the general p-norm constraint is improved by the fixed 1-norm constraint of the multi-core combination weight in the semi-supervised manifold regularization multi-core classification model, The solution theorem of the semi-supervised manifold regularized multi-core classification model with p-norm constrained multi-core combined weight and its proof are given. In this paper, the semi-supervised and semi-supervised classification model is compared with the two-aspect improved semi-supervised classification model. The experimental results show that the semi-supervised manifold regularized multi-core classification model and the semi-supervised manifold regularized multi-core classification model of the auto-selected semi-supervised manifold regularized multi-core classification model and the p-norm constrained multi-core combined weight are effective.
【学位授予单位】：北京科技大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：TP181

【相似文献】