Mapping a Manifold of Perceptual Observations
Mapping a Manifold of Perceptual Observations
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发表时间：
1997-12
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通讯作者：
J. Tenenbaum
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作者：
J. Tenenbaum
非线性降维在这里被表述为试图找到一组观测的欧几里得特征空间嵌入的问题，该嵌入尽可能接近地保留其内在度量结构-沿着测地线路径测量的观测流形上的点之间的距离。我们的等距特征映射过程，或isomap，是能够可靠地恢复低维非线性结构在现实的感知数据集，如流形的人脸图像，传统的全局映射方法只能找到局部极小值。恢复的地图提供了一组规范的全局有意义的功能，它允许感知转换，如插值，外推和类比-在原始观察空间中的高度非线性变换-在特征空间中使用简单的线性运算来计算。
Nonlinear dimensionality reduction is formulated here as the problem of trying to find a Euclidean feature-space embedding of a set of observations that preserves as closely as possible their intrinsic metric structure - the distances between points on the observation manifold as measured along geodesic paths. Our isometric feature mapping procedure, or isomap, is able to reliably recover low-dimensional nonlinear structure in realistic perceptual data sets, such as a manifold of face images, where conventional global mapping methods find only local minima. The recovered map provides a canonical set of globally meaningful features, which allows perceptual transformations such as interpolation, extrapolation, and analogy - highly nonlinear transformations in the original observation space - to be computed with simple linear operations in feature space.