Nonlinear Dimensionality Reduction by Local Orthogonality Preserving Alignment
Nonlinear Dimensionality Reduction by Local Orthogonality Preserving Alignment
复制标题
通过保持对齐的局部正交性进行非线性降维
DOI：
10.1007/s11390-016-1644-4
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发表时间：
2016-05
影响因子：
0.7
通讯作者：
Zha Hong-Bin
中科院分区：
文献类型：
--
作者：
Lin Tong;Liu Yao;Wang Bo;Wang Li-Wei;Zha Hong-Bin
提出了一种新的流形学习算法--局部正交性保持对齐算法(LOPA)。我们的算法受到局部切线空间对齐(LTSA)方法的启发，该方法旨在使用仿射变换将多个局部邻域对齐到一个全局坐标系中。然而，LTSA往往不能保持原始的几何量，如距离和角度。虽然LTSA的作者提出了一种保持正交性的迭代比对过程，但没有给出相应的初始化和实验。Procrstes子空间排列算法通过模拟退火法分别估计每个旋转变换，实现了保持正交性的思想。然而，PSA中的优化问题比较复杂，多个分离的局部旋转可能产生全局矛盾的结果。为了解决这些困难，我们首先使用LTSA的伪逆技巧来用统一的全局坐标来表示每个局部正交变换。其次，将正交性约束放宽为半定规划的一个实例。最后，采用两步迭代的方法进一步减少了正交约束的误差。大量的实验表明，LOPA能够忠实地保持原始数据集的距离、角度、内积和邻域。相比之下，LOPA的嵌入性能优于PSA，与MVU、MVE等先进算法相当，而运行时间明显快于PSA、MVU和MVE。
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.
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DOI：
10.1109/tpami.2011.39
发表时间：
2011-09
期刊：
IEEE Trans. on Pattern Analysis and Machine Intelligence
影响因子：
--
作者：
Shufu Xie, Shiguang Shan, Xilin Chen, Jie Chen
通讯作者：
Shufu Xie, Shiguang Shan, Xilin Chen, Jie Chen
DOI：
--
发表时间：
2007-03
期刊：
--
影响因子：
--
作者：
B. Shaw;Tony Jebara
通讯作者：
B. Shaw;Tony Jebara
DOI：
--
发表时间：
2007-07
期刊：
--
影响因子：
--
作者：
Golub Gene H. Et.Al
通讯作者：
Golub Gene H. Et.Al
黎曼流形学习
DOI：
10.1109/tpami.2007.70735
发表时间：
2008-05-01
影响因子：
23.6
作者：
Lin, Tong;Zha, Hongbin
通讯作者：
Zha, Hongbin
影响因子：
2.7
作者：
Wen, Zaiwen;Yin, Wotao
通讯作者：
Yin, Wotao