Laplacian eigenmaps for dimensionality reduction and data representation
Laplacian eigenmaps for dimensionality reduction and data representation
复制标题
DOI：
10.1162/089976603321780317
复制
发表时间：
2003-06-01
影响因子：
2.9
通讯作者：
Niyogi, P
中科院分区：
文献类型：
--
作者：
Belkin, M;Niyogi, P
机器学习和模式识别的核心问题之一是为复杂数据开发适当的表示。我们考虑的问题，构建一个表示躺在一个低维流形嵌入在一个高维空间的数据。利用图形拉普拉斯算子、流形上的拉普拉斯Beltrami算子和热方程之间的对应关系，我们提出了一种几何激励算法来表示高维数据。该算法提供了一种计算效率高的方法，非线性降维，具有局部保持属性和聚类的自然连接。一些潜在的应用和说明性的例子进行了讨论。
One of the central problems in machine learning and pattern recognition is to develop appropriate representations for complex data. We consider the problem of constructing a representation for data lying on a low-dimensional manifold embedded in a high-dimensional space. Drawing on the correspondence between the graph Laplacian, the Laplace Beltrami operator on the manifold, and the connections to the heat equation, we propose a geometrically motivated algorithm for representing the high-dimensional data. The algorithm provides a computationally efficient approach to nonlinear dimensionality reduction that has locality-preserving properties and a natural connection to clustering. Some potential applications and illustrative examples are discussed.