文件名称:
A Global Geometric Framework for Nonlinear Dimensionality Reduction
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文件大小: 628kb
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上传时间: 2009-10-09
详细说明： Scientists working with large volumes of high-dimensional data, such as global climate patterns, stellar spectra, or human gene distributions, regularly con- front the problem of dimensionality reduction: Þnding meaningful low-dimen- sional structures hidden in their high-dimensional observations. The human brain confronts the same problem in everyday perception, extracting from its high-dimensional sensory inputsÑ30,000 auditory nerve Þbers or 106 optic nerve ÞbersÑa 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 com- plex 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 efÞciently computes a globally optimal solution, and, for an important class of data manifolds, is guaranteed to converge asymptotically to the true structure. ...展开收缩
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