流形学习算法在人脸识别中的应用研究
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摘要
人脸是人类视觉中最常见的模式,人脸识别由于其自然、直观、非接触、安全、快捷等特点而倍受关注,已经成为最具发展潜力的生物特征识别技术之一,也是当前模式识别和人工智能领域的一个研究热点。但是,由于人脸结构的复杂性、人脸表情的多样性以及人脸成像过程的多变性等原因,人脸机器自动识别至今仍然被公认是一个具有挑战性的研究领域。一般认为,人脸从某种意义上来说是一种流形结构,人脸数据集是由某些内在变量控制形成的非线性流形,只要能从流形中寻找出光照、表情和姿态等控制变量,就能大幅降低观测空间的维数。
流形学习是近年来机器学习及模式识别等领域的一个研究热点,其主要目标是去发现高维观察数据空间的低维光滑流形。自从2000年Roweis和Saul提出LLE算法、Tenenbaum等人提出Isomap算法,特别是Donoho等人发现Isomap算法能够准确发现人脸图像流形潜在的参数空间、张长水等人将LLE算法用于人脸识别并取得了较好的识别效果之后,基于流形学习的人脸识别研究引起了人们的广泛关注。本文对流形学习算法在人脸识别中的应用问题进行研究,提出了3种新的基于流形学习的人脸识别算法,通过仿真实验验证了它们的有效性。主要工作和创新成果集中在以下几个方面:
1.简要介绍了流形学习研究中涉及的相关数学知识,如拓扑流形、微分流形、黎曼流形、测地线、Hausdorff距离等,为本文的研究提供理论支持。
2.分析讨论了流形学习在人脸识别应用中的一些关键问题。1)介绍了流形学习的研究动机、技术路线,主流流形学习算法的优势及存在不足。2)分析了人脸识别主要技术的优势及存在困难,指出了流形学习应用于人脸识别的可能性及可行性。3)针对人脸图像数据高维、非结构化的特点,分析讨论了高维空间的维数约简、维数灾难、数据稀疏性、空空间现象、胖尾现象等问题,从数学模型的角度讨论了流形学习与维数约简、本征维数估计、监督学习、半监督学习、监督流形学习及半监督流形学习等问题,揭示了它们的区别与联系。
3.构建模型、搭建实验平台,将主流流形学习算法应用于人脸识别。进行仿真实验,系统分析其应用的可能性,优势及存在的问题。1)线性流形学习算法人脸识别仿真实验:主成分分析(PCA)、线性判别分析算法(LDA)、局部保距投影(LPP)等。2)非线性流形学习算法人脸识别仿真实验:等距映射(Isomap),局部线性嵌入算法(LLE)、Laplacian特征映射(LE)、局部切空间排列(LTSA)等。
4.针对流形学习算法未能充分利用样本的类别信息,一般不适合用于分类,不能有效的消除图像中冗余信息;Isomap算法需要较多的训练样本来描述非线性流形结构,而人脸识别本身是一个小样本问题,通常训练样本不是很多,进而影响了识别效果。提出了一种新的人脸识别算法并在公开人脸数据库中验证了算法的有效性。
5.LTSA算法是著名的流形学习算法之一。但如果在模式识别时遇到相似的流形,两种流形相似的模型放在一起就构成了复杂流形,这时就很难用LTSA算法加以分类。针对这个问题,本文提出了一种新的人脸识别算法并在公开人脸数据库中验证了算法的有效性。
6.针对监督学习和非监督学习在利用样本信息方面存在的不足,提出了一种基于半监督流形学习的人脸表情识别方法,在部分有标签信息的人脸表情数据的情况下,通过利用人脸表情图像数据本身的非线性流形结构信息和部分标签信息来调整点与点之间的距离形成距离矩阵,而后基于被调整的距离矩阵进行线性近邻重建来实现维数约减,提取低维鉴别特征用于人脸表情识别。仿真实验验证了算法的有效性。
Human face is the most common visual part. Human face recognition has become not only a hot research topic in the field of artificial intelligence and model recognition, but also a most potential recognition technology by biometric characteristic for the merits of being natural, directly perceived, safe and convenient. However, due to the complexity of human face structure, the diversity of face expression and the changeable in face image formation process, computer face recognition technology is universally considered a challenging study topic. In a sense, it is commonly accepted that human face is a manifold structure. Face dataset is a non-linear manifold formed by some inner variables, such as illumination condition, face pose and facial expression. If some controlled variables can be seeked, space dimensionality could be reduced greatly.
In recent years, manifold learning become a hot study topic in the field of artificial intelligence and model recognition, and its aim is to seek low-dimensional smoothy manifold in high-dimensional observation data space. Since Roweis and Saul put forward LLE algorithm in 2000, Tenenbaum and his collegues proposed Isomap algorithm, especially after Donoho discovered Isomap algorithm can obtain the potential prameter space of face image manifold, Zhang Changshui and his collegues found LLE algorithm applied to face recognition can bring out better recognition effects, face recognition research based on manifold learning is attracting more and more attention. This dissertation focuses on the application of manifold learning in human face recognition, and proposed four novel algorithms based on manifold learning used for face recognition, and each algorithm’s effectiveness has been verified by experiments.
The major research work in the dissertation contains the following seven aspects:
1.A brief introduction is made on some closely relative mathmatics theories used in manifold learning as the theoretic supporting which include topology manifold, differential manifold, Riemann manifold, geodesic, Hausdorff distance.
2.A analysis is made on some important issues when manifold learning is applied to face recognition. 1)A brief account of manifold learning’s research motive, technology support, as well as some mainstream algorithm’s advantages and shortcomings. 2) Based on the analysis on the advantages and disvantages of main face recognition techniques, this dissertation put forward the possibility and feasibility of applying manifold learning to face recognition. 3) In accordance with face image features of high-dimensional data and non-structural, some key issues such as dimensionality reduction, dimensionality curses, data sparity, empty space phenommnnon and fat tailed distribution are studied. The differences and relations between manifold learning and dimensionality reduction, intrinsic dimensionality estimation, supervised learning, semi-supervised learning, supervised manifold learning, semi-supervised manifold learning are revealed from the perspective of mathematic pattern.
3.Constructing a model and experimental platform to applying mainstream maniflod learning algorithms to face recognition. The possibility, advantages and dificiency are studied systematically through experiments. 1) face recognition experiment with linear manifold learning algorithm: PCA, LDA, LPP. 2) face recognition experiments with non-linear manifold learning, algorithm: Isomap, LLE, LE, LTSA.
4.Because manifold learning can’t make full use of sample’s information and can’t remove the unnecessary image information. Isomap algorithm requires a large quantity of training samples to describle non-linear manifold structure. However, face recognition itself is a small sample, for the lack of training samples, the recognition effects are lowered. This dissertation proposed a novel face recognition method. And its effects has been verified in open huamn face data base.
5.LTSA is a famous manifold learning algorithm. However, during the process of model recognition, if two similar manifold modeds come together, a more complex manifold will be formed, where LTSA algorithm is difficult to process and classify the information. To solve the above problem, a new face recognition approach is proposed and the experimental results on open huamn face data base has showed its effectiveness.
6. To solve the weakpoints which occur during the period of supervised and semi-supervised learning processing sample information, a novel face expression recognition approach is proposed based on semi-supervised manifold learning. In this approach, firstly, the distance between two points is adjusted to form distance matrix by nonlinear structure information and some label’s information from face expression image data. Secondly, low-dimensionality discriminant property useful for face expression recognition can be extracted by reconstructing neighbouring linear and dimensionality reduction. Experimental results has indicated its effective performance.
流形学习是近年来机器学习及模式识别等领域的一个研究热点,其主要目标是去发现高维观察数据空间的低维光滑流形。自从2000年Roweis和Saul提出LLE算法、Tenenbaum等人提出Isomap算法,特别是Donoho等人发现Isomap算法能够准确发现人脸图像流形潜在的参数空间、张长水等人将LLE算法用于人脸识别并取得了较好的识别效果之后,基于流形学习的人脸识别研究引起了人们的广泛关注。本文对流形学习算法在人脸识别中的应用问题进行研究,提出了3种新的基于流形学习的人脸识别算法,通过仿真实验验证了它们的有效性。主要工作和创新成果集中在以下几个方面:
1.简要介绍了流形学习研究中涉及的相关数学知识,如拓扑流形、微分流形、黎曼流形、测地线、Hausdorff距离等,为本文的研究提供理论支持。
2.分析讨论了流形学习在人脸识别应用中的一些关键问题。1)介绍了流形学习的研究动机、技术路线,主流流形学习算法的优势及存在不足。2)分析了人脸识别主要技术的优势及存在困难,指出了流形学习应用于人脸识别的可能性及可行性。3)针对人脸图像数据高维、非结构化的特点,分析讨论了高维空间的维数约简、维数灾难、数据稀疏性、空空间现象、胖尾现象等问题,从数学模型的角度讨论了流形学习与维数约简、本征维数估计、监督学习、半监督学习、监督流形学习及半监督流形学习等问题,揭示了它们的区别与联系。
3.构建模型、搭建实验平台,将主流流形学习算法应用于人脸识别。进行仿真实验,系统分析其应用的可能性,优势及存在的问题。1)线性流形学习算法人脸识别仿真实验:主成分分析(PCA)、线性判别分析算法(LDA)、局部保距投影(LPP)等。2)非线性流形学习算法人脸识别仿真实验:等距映射(Isomap),局部线性嵌入算法(LLE)、Laplacian特征映射(LE)、局部切空间排列(LTSA)等。
4.针对流形学习算法未能充分利用样本的类别信息,一般不适合用于分类,不能有效的消除图像中冗余信息;Isomap算法需要较多的训练样本来描述非线性流形结构,而人脸识别本身是一个小样本问题,通常训练样本不是很多,进而影响了识别效果。提出了一种新的人脸识别算法并在公开人脸数据库中验证了算法的有效性。
5.LTSA算法是著名的流形学习算法之一。但如果在模式识别时遇到相似的流形,两种流形相似的模型放在一起就构成了复杂流形,这时就很难用LTSA算法加以分类。针对这个问题,本文提出了一种新的人脸识别算法并在公开人脸数据库中验证了算法的有效性。
6.针对监督学习和非监督学习在利用样本信息方面存在的不足,提出了一种基于半监督流形学习的人脸表情识别方法,在部分有标签信息的人脸表情数据的情况下,通过利用人脸表情图像数据本身的非线性流形结构信息和部分标签信息来调整点与点之间的距离形成距离矩阵,而后基于被调整的距离矩阵进行线性近邻重建来实现维数约减,提取低维鉴别特征用于人脸表情识别。仿真实验验证了算法的有效性。
Human face is the most common visual part. Human face recognition has become not only a hot research topic in the field of artificial intelligence and model recognition, but also a most potential recognition technology by biometric characteristic for the merits of being natural, directly perceived, safe and convenient. However, due to the complexity of human face structure, the diversity of face expression and the changeable in face image formation process, computer face recognition technology is universally considered a challenging study topic. In a sense, it is commonly accepted that human face is a manifold structure. Face dataset is a non-linear manifold formed by some inner variables, such as illumination condition, face pose and facial expression. If some controlled variables can be seeked, space dimensionality could be reduced greatly.
In recent years, manifold learning become a hot study topic in the field of artificial intelligence and model recognition, and its aim is to seek low-dimensional smoothy manifold in high-dimensional observation data space. Since Roweis and Saul put forward LLE algorithm in 2000, Tenenbaum and his collegues proposed Isomap algorithm, especially after Donoho discovered Isomap algorithm can obtain the potential prameter space of face image manifold, Zhang Changshui and his collegues found LLE algorithm applied to face recognition can bring out better recognition effects, face recognition research based on manifold learning is attracting more and more attention. This dissertation focuses on the application of manifold learning in human face recognition, and proposed four novel algorithms based on manifold learning used for face recognition, and each algorithm’s effectiveness has been verified by experiments.
The major research work in the dissertation contains the following seven aspects:
1.A brief introduction is made on some closely relative mathmatics theories used in manifold learning as the theoretic supporting which include topology manifold, differential manifold, Riemann manifold, geodesic, Hausdorff distance.
2.A analysis is made on some important issues when manifold learning is applied to face recognition. 1)A brief account of manifold learning’s research motive, technology support, as well as some mainstream algorithm’s advantages and shortcomings. 2) Based on the analysis on the advantages and disvantages of main face recognition techniques, this dissertation put forward the possibility and feasibility of applying manifold learning to face recognition. 3) In accordance with face image features of high-dimensional data and non-structural, some key issues such as dimensionality reduction, dimensionality curses, data sparity, empty space phenommnnon and fat tailed distribution are studied. The differences and relations between manifold learning and dimensionality reduction, intrinsic dimensionality estimation, supervised learning, semi-supervised learning, supervised manifold learning, semi-supervised manifold learning are revealed from the perspective of mathematic pattern.
3.Constructing a model and experimental platform to applying mainstream maniflod learning algorithms to face recognition. The possibility, advantages and dificiency are studied systematically through experiments. 1) face recognition experiment with linear manifold learning algorithm: PCA, LDA, LPP. 2) face recognition experiments with non-linear manifold learning, algorithm: Isomap, LLE, LE, LTSA.
4.Because manifold learning can’t make full use of sample’s information and can’t remove the unnecessary image information. Isomap algorithm requires a large quantity of training samples to describle non-linear manifold structure. However, face recognition itself is a small sample, for the lack of training samples, the recognition effects are lowered. This dissertation proposed a novel face recognition method. And its effects has been verified in open huamn face data base.
5.LTSA is a famous manifold learning algorithm. However, during the process of model recognition, if two similar manifold modeds come together, a more complex manifold will be formed, where LTSA algorithm is difficult to process and classify the information. To solve the above problem, a new face recognition approach is proposed and the experimental results on open huamn face data base has showed its effectiveness.
6. To solve the weakpoints which occur during the period of supervised and semi-supervised learning processing sample information, a novel face expression recognition approach is proposed based on semi-supervised manifold learning. In this approach, firstly, the distance between two points is adjusted to form distance matrix by nonlinear structure information and some label’s information from face expression image data. Secondly, low-dimensionality discriminant property useful for face expression recognition can be extracted by reconstructing neighbouring linear and dimensionality reduction. Experimental results has indicated its effective performance.
引文
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