Orthogonal neighborhood preserving projections
Orthogonal neighborhood preserving projections
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DOI：
10.1109/icdm.2005.113
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发表时间：
2005-11
期刊：
影响因子：
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通讯作者：
E. Kokiopoulou;Y. Saad
中科院分区：
文献类型：
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作者：
E. Kokiopoulou;Y. Saad
正交邻域保持投影（ONPP）是一种线性降维技术，它试图同时保留数据样本的内在邻域几何结构和全局几何结构。所提出的技术构建了一个加权数据图，其中权重是以数据驱动的方式构建的，类似于局部线性嵌入（LLE）。与标准LLE的一个主要区别在于，标准LLE中输入空间和降维空间之间的映射是隐式的，而ONPP在两者之间采用了显式的线性映射。因此，与LLE不同的是，处理新的数据样本变得很直接，因为这相当于一个简单的线性变换。ONPP具有局部保持投影（LPP）的一些特性。ONPP和LPP都依赖于k - 近邻图来捕捉数据拓扑结构。然而，我们的算法继承了LLE在保留局部邻域结构方面的特性，而LPP旨在仅保留局部性，而没有特别针对保留几何结构。这一特性使ONPP成为一种有效的数据可视化方法。我们提供了大量的实验证据，使用著名的合成测试案例以及来自计算生物学和计算机视觉的实际数据来证明ONPP的优势特性。
Orthogonal neighborhood preserving projections (ONPP) is a linear dimensionality reduction technique which attempts to preserve both the intrinsic neighborhood geometry of the data samples and the global geometry. The proposed technique constructs a weighted data graph where the weights are constructed in a data-driven fashion, similarly to locally linear embedding (LLE). A major difference with the standard LLE where the mapping between the input and the reduced spaces is implicit, is that ONPP employs an explicit linear mapping between the two. As a result, and in contrast with LLE, handling new data samples becomes straightforward, as this amounts to a simple linear transformation. ONPP shares some of the properties of locality preserving projections (LPP). Both ONPP and LPP rely on a k-nearest neighbor graph in order to capture the data topology. However, our algorithm inherits the characteristics of LLE in preserving the structure of local neighborhoods, while LPP aims at preserving only locality without specifically aiming at preserving the geometric structure. This feature makes ONPP an effective method for data visualization. We provide ample experimental evidence to demonstrate the advantageous characteristics of ONPP, using well known synthetic test cases as well as real life data from computational biology and computer vision.