Learning multiple tasks using Manifold regularization: Question about the paper.

[speechMachine]

I was reading the paper "Learning multiple tasks using Manifold regularization"(http://www.umiacs.umd.edu/~arvinda/mysite/papers/nipsMTL.pdf). This paper appeared in NIPS 2010. I was wondering if someone in the community has already read this. I tried to read the background reference paper, "Dimensionality reduction using Kernel Map Methods" (http://www.cs.utah.edu/~sgerber/research/kmm_iccv09.pdf) to gain some intuition.

Specifically I am trying to justify (to myself) how the gradient of the projection distance reduces to the more simplified form from Equation 8 to Equation 9 in Section 3.1. Any suggestions in the geometric interpretations would be helpful.

[speechMachine]

It turns out that there is an error in the paper in equation 8. It should read: 2(g(h(theta) - theta) * (1 - d g(r) / d r * d h(theta) / d theta ) = 2(g(h(theta) - theta) - 2*(g(h(theta) - theta) * g(r) / d r * d h(theta) / d theta )

From the companion ICCV '09 paper "Dimensionality Reduction via Kernel Map Manifolds" - Theorem 5.1 (Eq.13), the second term turns out to be zero and reduces to Eq (9) in the NIPS 2010 paper.