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Alternative TitleResearch and Applications of Subspace Learning
Thesis Advisor黄凯奇
Degree Grantor中国科学院研究生院
Place of Conferral中国科学院自动化研究所
Degree Discipline模式识别与智能系统
Keyword子空间学习 二维线性判别分析 局部权重投影回归 Pc-surf算法 Subspace Learning Two Dimensional Discriminant Analysis Locallly Weighted Projection Regression Pc-surf
Abstract随着科学技术的飞速发展,研究人员所收集到的数据高速增长, 体现在数据数量上的提高和维度上的增长。传统的统计学和机器学习方法可以很好的应对数据数量的增长,但是没有办法解决观测数据维度提高所带来的问题,这就迫切需要一种统计学方法能够从高维数据中提取有用信息。 子空间学习算法可以很好的应对高维数据分析问题,该方法将原始的高维数据投影到低维空间中,并保持某些特定的统计性质。 本文对于部分子空间学习算法展开学习和研究,主要工作和贡献包括: 1.介绍了基本的线性和非线性数据降维方法,包括:主成分分析算法、Fisher线性判别分析算法、偏最小二乘算法、MDS、局部线性嵌入算法等,并分析了这些算法的优缺点。 2.二维线性判别分析是对原始的Fisher线性判别分析算法加以改进,将线性判别分析从处理向量数据扩展到处理矩阵数据。但是二维线性判别分析算法的求解方法并不收敛,这为该方法的使用和推广带来了严重的问题。本文提出利用进化计算的方法来提供一个收敛的训练过程,即收敛的最优解搜索过程。基于变异和结合操作,进化算法可以对随机产生的投影矩阵进行迭代,并最终收敛到局部或全局最优解。我们在ORL和扩展YaleB人脸数据库上进行实验,证明算法的有效性。 3.增强现实是计算机视觉的重要应用领域之一,其目标是将虚拟的物体与真实的场景完美的结合,给人以身临其境的感觉。增强现实系统包括特征点检测、匹配和摄像机标定等部分。特征点匹配的结果对于系统的性能有非常重要的影响。子空间学习算法可以被成功的应用于特征点匹配模块。一方面,主成分分析算法可以用于特征点描述。将以特征点为中心,一定邻域内的图片结合位置信息,作为主成分分析算法的输入,其主成分可以作为特征点的主方向。我们用此方法改进SURF算法,提出了PC-SURF算法,实验证明PC-SURF具有更强的鲁棒性。另一方面,将特征点匹配问题看做分类问题,进化二维线性判别分析算法可以从特征点邻域提取具有辨别力的特征,用于特征点匹配问题。 4.子空间学习算法也可以应用于回归问题。我们将增量子空间学习算法局部权重投影回归应用于跟踪粒子滤波器框架,提出增量自调节粒子滤波器算法, 并将其应用于仿射群上的目标跟踪。我们利用SIFT描述子作为目标的特征描述,利用增量主成分分析算法来构造目标的自适应子空间表观模型,用于相似度度量。自调节粒子滤波器通过在线局部权重投影回归模型一步步调节粒子,实现最优的目标位置估计。实验证明增量自调节粒子滤波器在使用少量粒子的情况下,具有非常好的鲁棒性和准确性。 总的说来,本文对于子空间学习算法展开论述,针对二维线性判别分析算法不收敛的特性,提出了进化二维线性判别分析算法,提供了收敛的训练过程,并将该方法应用于特征点匹配问题。本文还将主成分分析算法应用于特征点描述工作,改进SURF算法,提出了更加鲁棒的SURF描述子。子空间学习算法不仅可以应用于分类问题,还可以处理回归问题。本文将局部权重投影回归模型这一增量子空间学习算法应用到目标跟踪问题上来, 取得了不错的效果。
Other AbstractWith the development of science and technology, more and more data are collected.The data volume booming can be reflected in two ways,the increase of the number and the dimension of observations.Traditional statistical methods can deal well with the former problem.However, these methods suffer from the later problem, which can be termed as the curse of dimensionality.It is essential to provide an effective method to deal with this problem. Subspace learning methods are effective tools to deal with the curse of dimensionality.A subspace learning algorithm projects the original high dimensional data space to a low dimensional subspace, wherein specific statistical properties can be well preserved. Subspace learning sheds light both on classification and regression problems. This paper focuses on some subspace learning methods, the main contributions are as follows: 1.This thesis first introduces the classical linear and nonlinear subspace learning methods, such as principal component analysis(PCA), Fisher's linear discriminant analysis (LDA), multi-dimension scaling and locally linear embedding algorithms and so on, then analysis its advantages and disadvantages. 2.Two dimensional discriminant analysis (2DLDA) extends the traditional linear discriminant analysis to matrix data representation. However, this method suffers from the non-convergent issue that the training stage is not convergent. This greatly limits the practical application of 2DLDA. In order to solve this problem, this thesis proposes a novel method to solve this problem. We employ evolutionary computation methods to provide a convergent training stage for 2DLDA. Based on mutation and combination operators, the evolutionary computation method can iteratively search the local optimal or global optimal solutions from randomly generated projection matrixes. Experiments on ORL and extended YaleB face databases prove the effectiveness of our method. 3.Augmented reality is one of the most important applications of computer vision, its purpose is to combine the virtual computer-generated imagery and the real-world environment to give people a sense of immersive. The augmented reality system includes feature detection module, feature matching module and camera calibration module and so on. Feature matching module plays a very important role in AR system. Subspace learning methods can be used for feature matching. PCA can be used for interest point descriptor. The neighbor region of the inter...
Other Identifier200728014628040
Document Type学位论文
Recommended Citation
GB/T 7714
陈伟. 子空间学习算法研究及其相关应用[D]. 中国科学院自动化研究所. 中国科学院研究生院,2010.
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