A global geometric framework for nonlinear dimensionality reduction
A global geometric framework for nonlinear dimensionality reduction
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DOI：
10.1126/science.290.5500.2319
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发表时间：
2000-12-22
期刊：
影响因子：
56.9
通讯作者：
Langford, JC
中科院分区：
文献类型：
--
作者：
Tenenbaum, JB;de Silva, V;Langford, JC
研究大量高维数据的科学家，如全球气候模式、恒星光谱或人类基因分布，经常面临降维问题：寻找隐藏在高维观测中的有意义的低维结构。人类大脑在日常感知中也面临着同样的问题，从它的高维感觉输入中--30，000根听觉神经纤维或10（6）根视觉神经纤维--提取少量与感知相关的特征。在这里，我们描述了一种解决降维问题的方法，该方法使用易于测量的局部度量信息来学习数据集的底层全局几何结构。与经典的技术，如主成分分析（PCA）和多维尺度（MDS），我们的方法是能够发现的非线性自由度，复杂的自然观察，如人类的笔迹或图像的脸在不同的观看条件下。与以前的非线性降维算法相比，我们的算法有效地计算出全局最优解，并且对于一类重要的数据流形，保证渐近收敛到真实结构。
Scientists working with Large volumes of high-dimensional data, such as global climate patterns, stellar spectra, or human gene distributions, regularly confront the problem of dimensionality reduction: finding meaningful Low-dimensional structures hidden in their high-dimensional observations. The human brain confronts the same problem in everyday perception, extracting from its high-dimensional sensory inputs-30,000 auditory nerve fibers or 10(6) optic nerve fibers-a manageably small number of perceptually relevant features. Here we describe an approach to solving dimensionality reduction problems that uses easily measured local metric information to Learn the underlying global geometry of a data set. Unlike classical techniques such as principal component analysis (PCA) and multidimensional scaling (MDS), our approach is capable of discovering the nonlinear degrees of freedom that underlie complex natural observations, such as human handwriting or images of a face under different viewing conditions. In contrast to previous algorithms for nonlinear dimensionality reduction, ours efficiently computes a globally optimal solution, and, for an important class of data manifolds, is guaranteed to converge asymptotically to the true structure.