Locality Preserving Kernel PCA
首发时间:2015-01-06
Abstract:Dimensionality reduction is widely used in image understanding and machine learning tasks. Among these dimensionality reduction methods such as LLE, Isomap, etc., PCA is a powerful and efficient approach to obtain the linear low dimensional space embedded in the original high dimensional space. Furthermore, Kernel PCA (KPCA) is proposed to capture the nonlinear structure of the data in the projected space using "emph{Kernel Trick}". However, KPCA fails to consider the locality preserving constraint which requires the neighboring points nearer in the reduced space. The locality constraint is natural and reasonable and thus can be incorporated into KPCA to improve the performance. In this paper, a novel method, which is called Locality Preserving Kernel PCA (LPKPCA) is proposed to reduce the reconstruction error and preserve the neighborhood relationship simultaneously. We formulate the objective function and solve it mathematically to derive the analytical solution. Several datasets have been used to compare the performance of KPCA and our novel LPKPCA including ORL face dataset, Yale Face Dataset B and Scene 15 Dataset. All the experimental results show that our method can achieve better performance on these datasets.
keywords: Locality Preserving Constraint, Kernel PCA, Dimensionality Reduction
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基于局部保持的核主成分分析
摘要:降维在图像理解和机器学习中扮演重要的角色。在众多的降维方法当中,PCA是一种有效的线性方法之一。而核PCA能够在PCA的基础上进一步捕捉非线性的关系。然而,核PCA方法没有考虑局部保持性质。在本文中,我们提出局部保持的核PCA方法,并且在ORL人脸库,Yale B人脸库,以及Scene15数据库上验证了核PCA方法的有效性。
关键词: 局部保持,核PCA, 降维
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No.4626085102208614****
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