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• W2046292275 abstract "A common belief in high-dimensional data analysis is that data are concentrated on a low-dimensional manifold. This motivates simultaneous dimension reduction and regression on manifolds. We provide an algorithm for learning gradients on manifolds for dimension reduction for high-dimensional data with few observations. We obtain generalization error bounds for the gradient estimates and show that the convergence rate depends on the intrinsic dimension of the manifold and not on the dimension of the ambient space. We illustrate the efficacy of this approach empirically on simulated and real data and compare the method to other dimension reduction procedures." @default.
• W2046292275 created "2016-06-24" @default.
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• W2046292275 date "2010-02-01" @default.
• W2046292275 modified "2023-10-17" @default.
• W2046292275 title "Learning gradients on manifolds" @default.
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• W2046292275 doi "https://doi.org/10.3150/09-bej206" @default.
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