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《Journal of Software》 2005-09
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A Better Scaled Local Tangent Space Alignment Algorithm

YANG Jian1,2+, LI Fu-Xin1,2, WANG Jue1 1(Institute of Automation, The Chinese Academy of Sciences, Beijing 100080, China) 2(Graduate School, The Chinese Academy of Sciences, Beijing 100049, China)  
Recently, a new manifold learning algorithm, LTSA (local tangent space alignment), has been proposed. It is efficient for many nonlinear dimension reduction problems but unfit for large data sets and newcome data. In this paper, an improved algorithm called partitional local tangent space alignment (PLTSA) is presented, which is based on VQPCA (vector quantization principal component analysis) and LTSA. In the algorithm, the sample space is first divided into overlapping blocks using the X-Means algorithm. Then each block is projected to its local tangent space to get local low-dimensional coordinates of the points in it. At last, the global low-dimensional embedded manifold is obtained by local affine transformations. PLTSA is better than VQPCA in that it gives the global coordinates of the data. It works on a much smaller optimization matrix than that of LTSA and leads to a better-scaled algorithm. The algorithm also provides a set of transformations that allow to calculate the global embedded coordinates of the newcome data. Experiments illustrate the validity of this algorithm.
【Fund】: 国家自然科学基金;; 国家重点基础研究发展规划(973)~~
【CateGory Index】: TP18
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