Nonlinear dimensionality reduction by locally linear embedding
Nonlinear dimensionality reduction by locally linear embedding
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DOI：
10.1126/science.290.5500.2323
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发表时间：
2000-12-22
期刊：
影响因子：
56.9
通讯作者：
Saul, LK
中科院分区：
文献类型：
--
作者：
Roweis, ST;Saul, LK
许多科学领域依赖于探索性数据分析和可视化。分析大量多变量数据的需要提出了降维的基本问题：如何发现高维数据的紧凑表示。在这里，我们介绍了局部线性嵌入（LLE），这是一种无监督学习算法，可以计算高维输入的低维，邻域保留嵌入。与局部降维的聚类方法不同，LLE将其输入映射到一个较低维度的全局坐标系中，并且其优化不涉及局部极小值。通过利用线性重建的局部对称性，LLE能够学习非线性流形的全局结构，例如由人脸图像或文本文档生成的流形。
Many areas of science depend on exploratory data analysis and visualization. The need to analyze Large amounts of multivariate data raises the fundamental problem of dimensionality reduction: how to discover compact representations of high-dimensional data. Here, we introduce Locally Linear embedding (LLE), an unsupervised Learning algorithm that computes Low-dimensional, neighborhood-preserving embeddings of high-dimensional inputs. Unlike clustering methods for Local dimensionality reduction, LLE maps its inputs into a single global coordinate system of lower dimensionality, and its optimizations do not involve Local minima. By exploiting the local symmetries of Linear reconstructions, LLE is able to Learn the global structure of nonlinear manifolds, such as those generated by images of faces or documents of text.