Neighborhood preserving embedding
Neighborhood preserving embedding
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DOI：
10.1109/iccv.2005.167
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发表时间：
2005-10
期刊：
影响因子：
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通讯作者：
Xiaofei He;Deng Cai;Shuicheng Yan;HongJiang Zhang
中科院分区：
文献类型：
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作者：
Xiaofei He;Deng Cai;Shuicheng Yan;HongJiang Zhang
最近有很多的兴趣在几何动机的方法来分析数据在高维空间。我们考虑的情况下，数据是从抽样的概率分布，支持或附近的一个子流形的欧几里得空间。在本文中，我们提出了一种新的子空间学习算法称为邻域保持嵌入（NPE）。与主成分分析（PCA）的目标是保持全局欧氏结构不同，NPE的目标是保持数据流形上的局部邻域结构。因此，NPE对离群值的敏感性低于PCA。此外，与最近提出的流形学习算法（如Isomap和局部线性嵌入）相比，NPE是在任何地方定义的，而不仅仅是在训练数据点上。此外，NPE可以在原始空间或数据点映射到的再生核希尔伯特空间中进行。这就产生了内核NPE。在人脸数据库上的实验证明了该算法的有效性
Recently there has been a lot of interest in geometrically motivated approaches to data analysis in high dimensional spaces. We consider the case where data is drawn from sampling a probability distribution that has support on or near a submanifold of Euclidean space. In this paper, we propose a novel subspace learning algorithm called neighborhood preserving embedding (NPE). Different from principal component analysis (PCA) which aims at preserving the global Euclidean structure, NPE aims at preserving the local neighborhood structure on the data manifold. Therefore, NPE is less sensitive to outliers than PCA. Also, comparing to the recently proposed manifold learning algorithms such as Isomap and locally linear embedding, NPE is defined everywhere, rather than only on the training data points. Furthermore, NPE may be conducted in the original space or in the reproducing kernel Hilbert space into which data points are mapped. This gives rise to kernel NPE. Several experiments on face database demonstrate the effectiveness of our algorithm