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I was reading this method related to proximal newton methods

http://machinelearning.wustl.edu/mlpapers/paper_files/NIPS2012_0388.pdf. I came across this page

enter image description here

I didn't get what this part means

$ \frac{1}{2}||y-x||^2_H $ what does H signify here and how do I calculate $ \frac{1}{2}||y-x||^2_H $ given x and y.

user12331
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    My guess is that as $H$ is a positive definite matrix, it induces a norm by means of the quadratic form $||x||_H = \sqrt{x^T H x}$. You can easily verify that this satisfies the properties of a norm. So $||\cdot||_H$ would is the norm with respect to this quadratic form. – rnegrinho Jun 18 '14 at 18:04
  • Yep, that's exactly what it is. – Michael Grant Jun 19 '14 at 20:27

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