融合局部和全局结构的流形学习

黄鸿; 李见为; 冯海亮

光学精密工程, 2009, 17 (3): 626, 网络出版: 2009-10-28

融合局部和全局结构的流形学习

Fusion of local and globle structures for manifold learning

论文大纲

黄鸿 ^1,*李见为 ^1,2冯海亮 ¹

作者单位

¹ 重庆大学光电技术及系统教育部重点实验室,重庆 400030

² 重庆工学院教授流动站,重庆 400050

维数约简流形学习全局几何结构局部全局保持嵌入 dimensionality reduction manifold learning global geometric structure Local and Global Preserving Embedding (LGPE)

摘要

提出了一种融合局部与全局结构的保持嵌入(LGPE)算法。该方法首先假定目标空间的整体映射函数,然后结合数据的全局几何结构分布信息进行数据重构,最后通过最小化准则函数来得到嵌入高维空间的低维子流形。LGPE方法在保持数据局部结构的同时保留了全局结构信息,在信噪比为10 dB的稀疏Swiss-roll(N=400)和COIL-20多姿态数据集上都取得了较好的维数约简效果。与其他局部流形学习方法相比,该方法在AT&T人脸图像库中,当嵌入特征矢量维数d<40时,其识别率提高了约15%。在人工与真实数据库的实验结果表明,本文方法对噪声和稀疏数据具有较好的鲁棒性。

Abstract

A new method called Local and Global Preserving Embedding (LGPE) is proposed for manifold learning. This method assumes a global embedding function in low dimensional space, then incorporates the relative compactness information of the data distributions on the global geometry to reconstruct sample data. Finally, the global low dimensional submanifold is obtained by minimizing the cost function.The LGPE preserves the local and global structures of the data points simultaneously, and can obtain better dimensionality reduction on the sparse Swiss-roll dataset with noises (N=400, SNR=10 dB) and COIL-20 multi-poses dataset.When it is used in the AT&T face dateset,the recognition rate can be improved by 15% as compared with that of other local manifold methods under condition of embedding dimension lower than 40. The experimental results on both synthetic and real data sets show that proposed method is effectiveness and robustness for noise and sparse data.

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黄鸿, 李见为, 冯海亮. 融合局部和全局结构的流形学习[J]. 光学精密工程, 2009, 17(3): 626. HUANG Hong, LI Jian-wei, FENG Hai-liang. Fusion of local and globle structures for manifold learning[J]. Optics and Precision Engineering, 2009, 17(3): 626.

融合局部和全局结构的流形学习

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