HSSR Hessian based semi supervised regression and dimensionality reduction 1.0

Kwang In Kim, Florian Steinke, Matthias Hein — Tue, 15 Dec 2009 19:21:59 -0000

This package contains Matlab code for semi-supervised regression using the Hessian energy.

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 (cf. project web for examples). Based on these observations, we propose using the second-order Hessian energy for semi-supervised regression which overcomes both these problems. If the data lies on or close to a low-dimensional submanifold in feature space, the Hessian energy prefers functions whose values vary linearly with respect to geodesic distance, which makes it particulary suited for semi-supervised dimensionality reduction.

The code provides a more stable estimate of the Hessian operator as the one used in ‘Hessian eigenmaps’ proposed by Donoho and Grimes and thus using its eigenvectors can also be used for unsupervised dimensionality reduction.

mloss.org HSSR Hessian based semi supervised regression and dimensionality reduction

HSSR Hessian based semi supervised regression and dimensionality reduction 1.0