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• W1988515501 abstract "Nonlinear dimensionality reduction embeddings computed from datasets do not provide a mechanism to compute the inverse map. In this paper, we address the problem of computing a stable inverse map to such a general bi-Lipschitz map. Our approach relies on radial basis functions (RBFs) to interpolate the inverse map everywhere on the low-dimensional image of the forward map. We demonstrate that the scale-free cubic RBF kernel performs better than the Gaussian kernel: it does not suffer from ill-conditioning, and does not require the choice of a scale. The proposed construction is shown to be similar to the Nystrom extension of the eigenvectors of the symmetric normalized graph Laplacian matrix. Based on this observation, we provide a new interpretation of the Nystrom extension with suggestions for improvement." @default.
• W1988515501 created "2016-06-24" @default.
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• W1988515501 creator A5029242127 @default.
• W1988515501 creator A5082106923 @default.
• W1988515501 date "2013-05-01" @default.
• W1988515501 modified "2023-09-27" @default.
• W1988515501 title "Inverting Nonlinear Dimensionality Reduction with Scale-Free Radial Basis Function Interpolation" @default.
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• W1988515501 hasPublicationYear "2013" @default.
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