# Semi-supervised Regression using Hessian energy with an application to semi-supervised dimensionality reduction

Kwang I. KimFlorian SteinkeMatthias Hein

Semi-supervised regression based on the graph Laplacian suffers from the fact that the solution is biased towards a constant and the lack of extrapolating power. Outgoing from these observations we propose to use the second-order Hessian energy for semi-supervised regression which overcomes both of these problems, in particular, if the data lies on or close to a low-dimensional submanifold in the feature space, the Hessian energy prefers functions which vary linearly with respect to the natural parameters in the data... (read more)

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