【作者】 杨茂龙；

【导师】 夏德深；

【作者基本信息】 南京理工大学 ， 模式识别与智能系统， 2011， 博士

【摘要】 特征抽取是模式识别领域最基本的问题之一。通过特征抽取,以较少的维数表示数据,用更为稳定的表达方式提高分类性能。近几十年来,在主成分分析、线性鉴别分析等线性鉴别特征抽取方法的基础上,典型相关分析(Canonical Correlation Analysis, CCA)、偏最小二乘(Partial Least Squares, PLS)等相关投影分析方法在数据处理与分析、回归分析与预测、鉴别信息抽取与融合等各个领域得到了广泛应用。特别是伴随着对相关投影分析的本质认识的不断深入,CCA、PLS与主成分分析(Principal Component Analysis, PCA)、线性鉴别分析(Linear Discriminant Analysis,LDA)之间的关系已被发现,前人的研究将利用相关投影分析抽取鉴别信息、进行信息融合的理论推到了一个新的阶段,具体的应用则更扩展到了模式分类与识别、图像重构与压缩、信息检索、回归分析等各个领域。正是因为相关投影分析在各个领域的成功应用,使其成为模式识别研究中最有活力、最有应用前景的领域之一。另一方面,相关投影分析从基础理论到具体应用,都有一些重要问题尚未解决,这激励着人们争相参与到此项研究中去。CCA是实现信息融合的有力工具。随着用CCA抽取典型成分作为鉴别特征及用于多特征融合进行模式识别的成功应用,该方法又被推广到图像鉴别特征抽取中,并建立了CCA抽取鉴别特征的理论框架。PLS回归分析提供了单因变量或多因变量对多自变量的回归建模方法,在回归建模的同时,不仅实现了原始数据的压缩,也消除了对系统无解释意义的干扰信息(噪声)。由于PLS解决了以往用普通多元回归分析方法无法解决的难题,因此该方法的理论研究进展非常迅速,应用领域已扩展到机械、生物、地质、医学、社会学以及经济学等领域。PLS模型的鲁棒性使其成为回归分析、维数压缩和分类技术的有力工具之一。本文工作主要包括如下内容：(1)进一步完善了基于CCA和PLS的相关投影分析,并且用于单特征、组合特征抽取和图像分类与识别的理论框架。讨论了CCA抽取鉴别特征的原则和特征组合,以及在正交约束和统计不相关约束条件下CCA和PLS抽取特征的性能,并与传统方法如PCA、LDA进行了对比。实验结果表明,相关投影分析能够更有效地抽取鉴别特征,特别是对称性的双特征,如人的左右眼、左右手掌的鉴别特征抽取有着更好的表现。(2)在介绍基于图像矩阵的二维相关投影分析的基础上,引入二维典型相关分析(Two-dimensional Canonical Correlation Analysis,2DCCA)和二维偏最小二乘(Two-dimensional Partial Least Squares,2DPLS)的基本理论,深入讨论了2DCCA与(Two-dimensional Linear Discriminant Analysis,2DLDA)的关系,证明了在两类类标编码情况下,二者仍存在等价关系。(3)分析了基于类标号的相关投影分析的缺陷,在此基础上提出了基于样本标号的相关投影分析,并将其推广到二维情况。基于同样原因,提出了模糊相关投影分析。实验结果表明,两种改进算法都可以有效地提高鉴别特征抽取性能。在ORL、AR等人脸图像数据库、中科院自动化所掌纹图像库(CASIA-Palmprint)、香港理工大学掌纹图像库(PolyU Palmprint)的实验基础上,在构建的战斗机卫星图像数据集上进一步验证了本文算法的有效性,也为统计模式识别在基于遥感图像的重要目标识别做了有益的尝试。(4)基于回归分析理论,从分析与预测的实际出发,运用PLSR对美国大选建模,寻找候选人得票率与国民经济发展等因素的相关关系。从而成功地将PLSR应用到辅助分析中去,拓展了分析与预测的研究方法和手段。更多还原

【Abstract】 Discriminant feature extraction is one of the basic problems of pattern recognition. Data can be described with fewer dimension information by feature extraction, which can improve recognition rate effectively with more steady data description. Recently, on the basis of linear discriminant feature extraction methods such as principal component analysis (PCA), linear discriminant analysis (LDA), correlation projection analysis methods such as canonical correlation analysis (CCA), partial least squares (PLS) have been used widely in many fields:data processing and analysis, regression analysis and prediction, discriminant feature extraction and fusion and so on. Especially, with the deepening understanding to the essence of correlation projection analysis, people have found the relations between CCA, PLS, PCA and LDA. Earlier study of correlation projection analysis has put the theory of discriminant feature extraction and information fusion to a new stage. The applications have also expanded to pattern classification and recognition, image compression and reconstruction, information retrieval, regression analysis, and so on. As the result of its successful application in many fields, correlation projection analysis has been one of the most lively and potential fields. On the other hand, there are many important problems from basic theory to application to be solved, which inspirit people to participate in the studies.As we know, CCA is effective means for information fusion. By the successful application of discriminant feature extraction and multi-feature fusion with CCA, it has also expanded to image’s discriminant feature extraction, and the theoretic frameworks have been established.PLS regression analysis provides a regression modeling method for single/multi dependent variables with independent ones. On the course of regression modeling, original data are compressed, and interfering information (noise) is removed at the same time. PLS has solved the problems which cannot be solved with classical multivariate analysis methods, so the theoretic research of this method has developed rapidly. Its applying fields have extended to mechanics, biology, geology, medicine, sociology and economics. The robustness of PLS makes it become one of the most effective tools for regression analysis, dimension reduction and classifying technique.Our work mainly includes the following parts:(1) On the basis of other persons’ work, we further perfect the theoretical framework of single/combined feature extraction and image classification & recognition with correlation projection analysis based on CCA&PLS. We discuss the principle of feature extraction and feature combine with CCA, and the capability of feature extraction with CCA&PLS under orthogonal constraints or statistical uncorrelative (conjugate orthogonal) constraints, then compare with classical methods such as PCA and LDA. The results of experiments show that correlation projection analysis is more efficient in discriminant feature extraction, especially in the case of symmetrical dual-features such as human being’s dual-eyes, dual-palmprints, and we will get more ideal results.(2)On the basis of two-dimensional correlation projection analysis based on image matrices, we introduce the basic theory of 2DCCA and 2DPLS, and discuss the relationship between 2DLDA and 2DCCA. We prove that they are equivalent in c and c-1 class label encoding cases for discriminant feature extraction.(3)We analyze the defects of correlation projection analysis based on class label encoding, then introduce correlation projection analysis based on sample label encoding, and further expand it to two-dimensional cases. For the same reason, we introduce fuzzy correlation projection analysis and give new algorithms. The results of experiments show that both methods can improve the performance of feature extraction. On the basis of experiments on ORL and AR face databases, CASIA-Palmprint and PolyU Palmprint databases, combining with our practical work, we build a remote sense image database of fighters. Experiment results on it show that our algorithms are efficient and robust. Moreover it is an attempt for important targets recognition in remote sense images.(4)On the basis of regression theories and for the purpose of analysis and prediction, we use PLSR to model US presidential election in order to explore the relationship between candidates’ votes and domestic economic development and other factors. As a result, we can deal with analysis and prediction with PLS successfully, and achieve preferable results. We get the purpose of "quantitating qualitative problems, and qualitatively analyzing quantitative results", and enrich the means for analysis and prediction.更多还原