基于鲁棒判别式约束的字典学习算法研究

发布时间：2018-04-28 10:48

本文选题：字典学习 + 稀疏表示　；参考：《哈尔滨工业大学》2017年博士论文

【摘要】：字典学习已被广泛应用于图像处理、模式识别和计算机视觉等领域。判别字典学习是字典学习理论中一个重要的研究方向,其核心问题是如何设计判别式提高字典的判别性能。一般来说,判别式的设计可以分为两类。第一类是利用训练样本的特征结合编码系数构造判别式模型。但是,训练样本易受光照和遮挡等因素的影响,导致训练样本的特征与实际存在误差,影响判别式的鲁棒性,也降低了字典的判别性能。第二类是利用原子的自相关性特征设计判别式模型。虽然原子的自相关性特征具有一定的自适应性,如果数据的结构特征非线性的嵌入到高维空间中,基于原子自相关性特征约束的字典学习算法并不能真正地捕获训练样本的结构特征,也会降低字典的判别性能。因此,如何设计鲁棒的判别式模型,使字典尽可能地反映训练样本的特征并具有较强的判别性能,是字典学习理论中的一个重要研究方向,也是本文的研究重点。本文利用编码系数矩阵的行向量(profiles)和原子特征构建基于鲁棒判别式约束的字典学习模型,增强字典的判别性,提高字典学习算法的分类性能。利用原子构建拉普拉斯图表示它们的结构特征,并在此基础上利用流形学习理论构建鲁棒判别式模型,使其既能继承训练样本的结构特征,又能保持原子的结构和自相关性特征。此外,根据原子与profiles的一一对应关系,构建基于profiles的Fisher判别和局部结构特征约束的判别式模型,增强字典的判别性能。本文提出的基于鲁棒判别式约束的字典学习模型能在一定程度上解决判别字典学习算法中存在着判别式的鲁棒性和自适应性差以及字典判别性不强等问题。具体地说,本文的主要研究内容概括如下:(1)根据profiles的定义,给出其在理想字典学习模型中的描述,使得抽象的profiles更加直观和易于理解,并建立原子与profiles间的对应关系。利用理想情况下的字典学习模型推导出原子与profiles间的相似性关系。此外,本章还给出训练样本、编码系数、原子和profiles间的类标关系,并在此基础上提出一种利用profiles自适应地构造原子类标的方法。本章推导出的原子与profiles间的相似性定理以及原子类标构造方法,为设计鲁棒判别式模型提供一定的理论和算法基础。(2)提出一个基于自适应局部特征约束的字典学习算法(Adaptive Locality Constrained Dictionary Learning,ALC-DL)。ALC-DL算法利用字典中的原子构造拉普拉斯图,使其能够反映原子间的结构特征;然后,利用profiles衡量原子间的相似性,并构造基于自适应局部特征约束的判别式模型,使其能够继承训练样本的结构特征。由于原子和profiles在字典学习中不断的更新,基于自适应局部特征约束的判别式模型具有一定的鲁棒性。此外,本章还推导出基于原子局部特征约束的判别式与基于训练样本局部特征约束的判别式间的关系。实验结果表明ALC-DL算法比直接利用训练样本的局部特征约束的字典学习算法取得更好的分类性能。(3)针对目前字典学习算法中没有同时利用原子的局部特征和类标的情况,提出一个基于原子局部特征和类标嵌入约束的字典学习算法(Locality Constrained and Label Embedding Dictionary Learning,LCLE-DL)。首先,LCLE-DL算法利用特定类字典学习算法获得原子类标,并利用原子类标构造原子类标嵌入项,促使同类原子对应的profiles相似;然后,结合原子的自适应局部特征约束项设计双重构约束的字典学习算法,促使原子的局部特征与判别信息可以相互传递,增强判别式的鲁棒性。为了使得基于原子局部特征约束的编码系数和基于原子类标约束的编码系数尽可能的一致,利用2l范数对两种编码系数的差进行约束,并能够减少算法的复杂度。此外,本章还给出LCLE-DL算法与两种类标约束的字典学习算法的关系。实验结果表明LCLE-DL算法比单独利用类标或局部特征约束的字典学习算法取得更好的分类性能。(4)提出基于profiles的Fisher判别和局部特征约束的字典学习算法(Fisher Discriminative and Locality Constraint Dictionary Learning,FDLC-DL)。在FDLC-DL算法中,利用Fisher判别准则构造基于profiles的判别式模型,使得同类原子对应的profiles类内散度尽可能的小,不同类原子对应的profiles类间散度尽可能的大,增强编码系数的判别性能。此外,在FDLC-DL算法中,利用profiles构造拉普拉斯图保持profiles的局部特征,并利用原子衡量profiles间的相似性,在此基础上构造基于profiles局部特征约束的判别式模型。由于profiles矩阵是编码系数矩阵的转置矩阵,因此,基于profiles的局部特征约束项也能增强编码系数的判别性能。在字典学习过程中,profiles随着字典学习不断地更新,因此,FDLC-DL算法中的判别式也具有一定的鲁棒性。为了减少算法的复杂度,FDLC-DL算法也利用2l范数对编码系数进行约束。此外,本章还给出FDLC-DL算法与其它两种字典学习算法的关系。实验结果表明FDLC-DL算法能够有效地提高基于字典学习算法的分类性能。综上所述,为了提高判别式的鲁棒性,本文利用拉普拉斯图、流形学习和Fisher判别准则等方法,结合原子和profiles的特征,提出三种判别式模型,并成功的应用于判别字典学习中。经过大量的实验证明本文提出的三种基于鲁棒判别式约束的字典学习算法都有效地提高了模式分类的性能。
[Abstract]:Dictionary learning has been widely used in the fields of image processing, pattern recognition and computer vision. Discriminatory dictionary learning is an important research direction in dictionary learning theory. The core problem is how to design discriminant to improve the discriminant performance of dictionaries. Generally speaking, the design of discriminant can be divided into two categories. The first class is to use training. The characteristics of the sample are combined with the coding coefficients to construct a discriminant model. However, the training sample is easily affected by the factors such as illumination and occlusion, which leads to the error of the training sample and the actual existence, affects the robustness of the discriminant and the discriminant performance of the dictionary. The second kind is to design a discriminant model by using the autocorrelation characteristics of the original subunit. The autocorrelation feature of the atom has a certain adaptability. If the structural features of the data are embedded in the high dimensional space, the dictionary learning algorithm based on the autocorrelation characteristic of the atom can not really capture the structural features of the training samples, but also reduces the discriminant performance of the dictionary. Therefore, how to design a robust discriminant? The model, which makes the dictionary as much as possible to reflect the characteristics of the training samples and has strong discriminative performance, is an important research direction in the dictionary learning theory, and is also the focus of this paper. In this paper, the dictionary learning model based on robust discriminant constraint is constructed by using the line vector (Profiles) and the atomic characteristics of the coding coefficient matrix to enhance the character of the word. The discriminability of the dictionary improves the classification performance of the dictionary learning algorithm. Using the atomic construction Laplasse graph to represent their structural features, the robust discriminant model is constructed by the manifold learning theory, so that it can not only inherit the structural features of the training samples, but also maintain the structure and autocorrelation of the atoms. With the one-to-one correspondence between the sub and the profiles, the discriminant model based on the Fisher discrimination and the local structural feature constraint based on profiles is constructed to enhance the discriminant performance of the dictionary. The dictionary learning model based on the robust discriminant constraint can solve the discriminant robustness and self of the discriminant algorithm to a certain extent. In particular, the main contents of this paper are summarized as follows: (1) according to the definition of profiles, the description in the ideal dictionary learning model is given, which makes the abstract profiles more intuitive and easy to understand, and establishes the correspondence between the original and the profiles. The dictionary learning model derives the similarity relation between the atom and the profiles. In addition, this chapter gives the training sample, the coding coefficient, the class relation between the atom and the profiles. On this basis, a method of using profiles to construct the atomic class standard is proposed. The similarity theorem between the atom and the profiles is derived in this chapter. The subclass standard construction method provides a certain theoretical and algorithm basis for the design of robust discriminant model. (2) a dictionary learning algorithm (Adaptive Locality Constrained Dictionary Learning, ALC-DL).ALC-DL algorithm based on adaptive local feature constraints is proposed to use the atomic structure of the Laplasse graph in the dictionary to reflect the atom. The structural characteristics of the interatomic structure; then, using profiles to measure the similarity between atoms, and construct a discriminant model based on adaptive local feature constraints, so that they can inherit the structural features of the training samples. Because of the constant updating of the atom and the profiles in the dictionary learning, the discriminant model based on the adaptive local characteristic constraints has a certain degree. In addition, this chapter also derives the relationship between the discriminant based on the local characteristic constraints of the atom and the discriminant based on the local feature constraint based on the training sample. The experimental results show that the ALC-DL algorithm achieves better classification performance than the dictionary learning algorithm using the local feature constraint directly using the training sample. (3) for the current dictionary learning calculation. In the method, a dictionary learning algorithm (Locality Constrained and Label Embedding Dictionary Learning, LCLE-DL) is proposed, which is based on the local characteristics of the atom and the embedding constraint of the class standard. First, the LCLE-DL algorithm uses a specific class dictionary learning algorithm to obtain the atomic class standard and uses the original method. The subclass standard constructs the embedded term of the atomic class standard to promote the similarity of the profiles of the same atom. Then, the dictionary learning algorithm, which combines the adaptive local characteristic constraint of the atom, is designed to promote the local characteristics of the atom and the discriminant information to communicate with each other and enhance the robustness of the discriminant. In order to make the local feature based on the atom. The coding coefficients of the constraints and the coding coefficients based on the constraints of the atomic class are as consistent as possible. The 2l norm is used to restrain the difference between the two coding coefficients, and the complexity of the algorithm can be reduced. In addition, the relationship between the LCLE-DL algorithm and the dictionary learning algorithm with the two type constraint is also given. The experimental results show that the LCLE-DL algorithm is more than single. Dictionary learning algorithm that uses class or local feature constraints to achieve better classification performance. (4) a dictionary learning algorithm based on Fisher discrimination and local feature constraints (Fisher Discriminative and Locality Constraint Dictionary Learning, FDLC-DL) is proposed. In FDLC-DL algorithm, a Fisher discrimination criterion is used to construct a profiles based algorithm. The discriminant model of Les makes the corresponding profiles class as small as possible, and the divergence of the profiles classes corresponding to different classes of atoms is as large as possible and enhances the discriminant performance of the coding coefficients. In addition, in the FDLC-DL algorithm, the local characteristics of the profiles are preserved by the Laplasse graph, and the profile is used to measure the profile. Based on the similarity between S, a discriminant model based on profiles local feature constraints is constructed. Because the profiles matrix is the transposed matrix of the coding coefficient matrix, the local feature constraint based on the profiles can also enhance the discriminant performance of the coding coefficients. In the dictionary learning process, profiles is constantly updated with the dictionary learning, Therefore, the discriminant in the FDLC-DL algorithm also has a certain robustness. In order to reduce the complexity of the algorithm, the FDLC-DL algorithm also uses the 2l norm to restrain the coding coefficients. In addition, the relationship between the FDLC-DL algorithm and the other two kinds of dictionary learning algorithms is also given. The experimental results show that the FDLC-DL algorithm can effectively improve the lexicography based on the dictionary. In summary, in order to improve the robustness of the discriminant, in order to improve the robustness of the discriminant, this paper uses Laplasse graph, manifold learning and Fisher criterion, combined the characteristics of atomic and profiles, to propose three discriminant models, and successfully applied to discriminant dictionary learning. After a large number of experiments, three kinds of bases proposed in this paper have been proved. The dictionary learning algorithm with robust discriminant constraints effectively improves the performance of pattern classification.

【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】：2017
【分类号】：TP391.41;TP181

【相似文献】