Nonlinear Dimensionality Reduction by Local Orthogonality Preserving Alignment

CORC > 北京大学 > 信息科学技术学院

	Nonlinear Dimensionality Reduction by Local Orthogonality Preserving Alignment
	Lin Tong ; Liu Yao ; Wang Bo ; Wang Liwei ; Zha Hongbin
刊名	Journal of Computer Science and Technology
	2016
关键词	manifold learning dimensionality reduction semi-definite programming Procrustes measure
英文摘要	We present a new manifold learning algorithm called Local Orthogonality Preserving Alignment (LOPA). Our algorithm is inspired by the Local Tangent Space Alignment (LTSA) method that aims to align multiple local neighborhoods into a global coordinate system using affine transformations. However, LTSA often fails to preserve original geometric quantities such as distances and angles. Although an iterative alignment procedure for preserving orthogonality was suggested by the authors of LTSA, neither the corresponding initialization nor the experiments were given. Procrustes Subspaces Alignment (PSA) implements the orthogonality preserving idea by estimating each rotation transformation separately with simulated annealing. However, the optimization in PSA is complicated and multiple separated local rotations may produce globally contradictive results. To address these difficulties, we first use the pseudo-inverse trick of LTSA to represent each local orthogonal transformation with the unified global coordinates. Second the orthogonality constraints are relaxed to be an instance of semi-definite programming (SDP). Finally a two-step iterative procedure is employed to further reduce the errors in orthogonal constraints. Extensive experiments show that LOPA can faithfully preserve distances, angles, inner products, and neighborhoods of the original datasets. In comparison, the embedding performance of LOPA is better than that of PSA and comparable to that of state-of-the-art algorithms like MVU and MVE, while the runtime of LOPA is significantly faster than that of PSA, MVU and MVE.; supported by the National Basic Research 973 Program of China,the National Natural Science Foundation of China under Grant,the Seeding Grant for Medicine and Information Sciences of Peking University of China; 中国科技核心期刊(ISTIC); 中国科学引文数据库(CSCD); 3; 512-524; 31
语种	英语
内容类型	期刊论文
源URL	[http://ir.pku.edu.cn/handle/20.500.11897/449865]
专题	信息科学技术学院
推荐引用方式 GB/T 7714	Lin Tong,Liu Yao,Wang Bo,et al. Nonlinear Dimensionality Reduction by Local Orthogonality Preserving Alignment[J]. Journal of Computer Science and Technology,2016.
APA	Lin Tong,Liu Yao,Wang Bo,Wang Liwei,&Zha Hongbin.(2016).Nonlinear Dimensionality Reduction by Local Orthogonality Preserving Alignment.Journal of Computer Science and Technology.
MLA	Lin Tong,et al."Nonlinear Dimensionality Reduction by Local Orthogonality Preserving Alignment".Journal of Computer Science and Technology (2016).