基于稀疏和低秩约束的模型学习研究

发布时间：2018-01-21 05:41

本文关键词： 低秩表示稀疏表示子空间聚类特征抽取线性回归模型学习　出处：《哈尔滨工业大学》2016年博士论文　论文类型：学位论文

【摘要】：稀疏约束和低秩约束是近年来出现的热点研究方向,目前已经被广泛地应用在机器学习和模式识别领域,如人脸识别、视频分析、图像分割等。从目前的研究中可以看出:1)稀疏和低秩约束能够有效地提高模型的鲁棒性。2)稀疏和低秩约束可以有效地提高子空间学习效率,例如提高维度约减的效率、抽取高效的特征以及提高子空间聚类的准确率。针对这两个方面的研究,学者们提出了一些新颖的基于稀疏或者低秩约束的模型,并且在一些实际应用中取得了令人满意的结果。同时,作为稀疏约束和低秩约束问题的推广,一些同时采用低秩和稀疏约束的新模型也引起了学者们的注意。本论文以提高模型的鲁棒性以及学习效率为研究目标,提出了一些新的基于稀疏和低秩约束的模型并成功应用于有监督学习、半监督学习和无监督学习。具体地说,本论文的主要工作概况如下。(1)提出一个基于低秩和稀疏嵌入的子空间学习框架以提高子空间的学习效率以及模型的鲁棒性。该框架将目前的子空间学习方法统一到低秩和稀疏的嵌入框架中。首先,将一些传统的子空间学习方法重写为一个统一的线性模型,然后将该模型并入到低秩和稀疏嵌入的子空间学习框架中,进而形成一系列新的子空间学习方法。该框架利用低秩和稀疏表示来并入数据的全局和局部结构到子空间学习中以提高子空间的学习效率。同时使用一个稀疏矩阵拟合噪声来提高模型对于不同的噪声数据的鲁棒性。实验证明,由该框架导出的新算法无论在有监督还是无监督的情形下都能够有效地提高分类准确率。(2)提出一个基于非负稀疏约束的图学习模型,利用非负稀疏约束来提高图的学习效率以及半监督聚类的准确率。具体地说,本文首先分析了传统半监督聚类方法的缺陷,即预先定义的图不能准确地传递标签信息。为处理这个问题,本文首先提出了一个新的非负稀疏图学习模型,该模型将非负稀疏约束引入图学习中并将图学习和半监督学习方法并入到一个学习框架中,使得该框架能够学习到一个最优的图结构,进而保证标签信息的准确传递。为了使得该框架具有处理新数据的能力,我们在该框架中引入一个线性回归模型,使得该框架不仅可以有效地提高半监督学习能力,而且可以有效地分类新的数据,即有效地解决了“out of sample”问题。(3)提出一个正则化的标签松弛线性回归模型和一个基于稀疏约束的鲁棒性正则化的标签松弛线性回归模型为解决传统的线性回归方法将所有的样本投影到一个二值化的标签矩阵,忽略了样本之间的差别的问题。模型不仅可以扩大不同类样本之间的距离,而且可以有效地解决模型的过拟合问题。为了增强模型的鲁棒性,本文引入一个新颖的稀疏约束,即?2,1范数到模型中进而提出鲁棒性正则化的标签松弛回归模型。由于使用了基于?2,1范数的损失函数,该模型可以有效地处理噪声数据。针对这两个模型,提出了两个对应的优化算法,使得分类更有效,运算更快捷。(4)提出一个基于稀疏约束的特征抽取模型为抽取高效的特征。模型通过一个简单的k近邻图来反映样本的局部结构,进而引导重构系数之间的相似性,并且引入一个基于行一致性稀疏的?2,1范数的投影矩阵来选择最相关的特征以保持数据的局部性和重构系数之间的相似性。通过理论分析和实验验证,该方法在没有标签信息的情况下可以选择鉴别性的特征并且选择的特征具有较好的稳定性。(5)为提高半监督子空间聚类的效率,提出了一个基于非负低秩表示的鲁棒性半监督子空间聚类模型。该模型通过1)利用类标签信息来指导仿射图的构建;2)将非负低秩表示框架和半监督子空间聚类函数并入到一个统一的框架下,使得学习到的仿射图可以准确地将数据划分到各自的子空间。为提高模型的鲁棒性,使用一个稀疏的矩阵来拟合噪声,使得模型对于不同的噪声具有较强的鲁棒性且可以准确地恢复被噪声污染或遮挡的图像。综上,为了提高模型的鲁棒性以及学习效率,本文提出五个基于稀疏和低秩约束的模型并成功应用在维度约减、特征抽取、分类和聚类上。大量公开数据库上的实验结果显示引入稀疏和低秩表示可以有效地提高模型的鲁棒性和学习效率。
[Abstract]:Sparse constraint and low rank constraint is a hot research direction in recent years. It has been widely used in the field of machine learning and pattern recognition, such as face recognition, video analysis, image segmentation and so on. From the present study shows that: 1) sparse and low rank constraint can improve the robustness of the.2 model) sparse and low rank subspace constraints can effectively improve the learning efficiency, such as to improve the efficiency of dimension reduction, feature extraction efficiency and improve the accuracy of subspace clustering. According to the two aspects of the research, scholars put forward some sparse or low rank constraint model based on the novel, and made satisfactory results in some practical applications. At the same time, as a generalization of sparse constraint and low rank constraint problems, some with low rank and sparse constraints a new model has attracted attention of scholars. This thesis In order to improve the robustness of the model and the learning efficiency as the research target, and puts forward some new based on sparse and low rank constraint model is successfully applied to supervised learning, semi supervised learning and unsupervised learning. Specifically, the main work of this dissertation is outlined as follows. (1) proposed a low rank and sparse embedded subspace learning based framework to improve subspace learning efficiency and robustness of the model. The framework of the current subspace learning method to uniform embedding framework and sparse low rank. First of all, some of the traditional subspace learning method is rewritten as a unified linear model, then the model is incorporated into the to the low rank and sparse embedding subspace learning framework, and then formed a series of new subspace learning method. It uses low rank and sparse representation to incorporate the data of the global and local structure subspace learning In order to improve the learning efficiency. At the same time subspace using a sparse matrix fitting model to improve the noise robustness to different noise data. Experiments show that the new algorithm is derived by the framework in supervised or unsupervised situations can effectively improve the classification accuracy. (2) proposed a the learning model of non negative sparse constraint graphs based on the accuracy of non negative sparse constraints to improve the learning efficiency of graph and semi supervised clustering. Specifically, this paper first analyzes the defects of the traditional semi supervised clustering method, namely a predefined map can not accurately transfer label information. To deal with this problem in this paper. We propose a new non negative sparse graph learning model, the model will be non negative constraint graph learning and graph learning and semi supervised learning method into a learning framework, this framework can make Enough to learn an optimal structure, and ensure accurate transfer of label information. In order to make the framework has the ability to deal with the new data, we introduce a linear regression model in this framework, the framework can not only effectively improve semi supervised learning ability, and can effectively classify new data, i.e. to effectively solve the "out of sample". (3) proposed a regularized label relaxation linear regression model and a linear relaxation based on label robustness regularized sparse constraint regression model to solve the traditional linear regression method to sample all the projection to a value of two of the label matrix. Ignoring the difference between the sample problem. The model can not only expand the distance between samples of different classes, and can effectively solve the problem of over fitting model. In order to enhance the robustness of the model in this paper. The introduction of a novel sparse constraint, namely? 2,1 norm to the model and then put forward the label relaxation robustness regularized regression model. Based on the loss function due to the use of the? 2,1 norm, the model can effectively deal with noisy data. According to the two models, two corresponding optimization algorithm is proposed, which makes the classification more effective and more efficient operation. (4) proposed a feature extraction model based on sparse constraint for feature extraction and efficient model. Through a simple k neighbor graph to reflect the local structure of the data, and then guide the similarity coefficient between the reconstruction, and the introduction of a consistency based on sparse projection? The 2,1 matrix norm to select the most relevant features to keep the similarity between the data locality and reconstruction coefficient. Through theoretical analysis and experimental verification, this method can choose the identification in case of no label information The characteristics and the selection of the characteristics of a good stability. (5) in order to improve the efficiency of semi supervised subspace clustering, proposed a representation of non negative low rank based robust semi supervised subspace clustering model. This model through 1) constructed using class label information to guide the affine graph; 2) will non negative low rank representation framework and semi supervised subspace clustering function is incorporated into a unified framework, the affine map learning that can accurately divide data into each subspace. In order to improve the robustness of the model, a sparse matrix is used to fit the noise, and the model has strong robustness and can accurately recover the polluted by noise or occlusion of image for different noise. To sum up, in order to improve the model's robustness and learning efficiency, this paper proposes five based on sparse and low rank constraint model is successfully applied in the dimension of about Reduction, feature extraction, classification and clustering. Experimental results on a large number of open databases show that introducing sparse and low rank representation can effectively improve the robustness and learning efficiency of the model.

【学位授予单位】：哈尔滨工业大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：TP391.41;TP181

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