6.15 Image classi cation kernel. For 0, the kernel K : (x; x0) 7! XN k=1...
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6.15 Image classication kernel. For 0, the kernel K : (x; x0) 7!
XN k=1 min(jxkj; jx0kj) (6.30)
over RN RN is used in image classication. Show that K is PDS for all
0. To do so, proceed as follows.
(a) Use the fact that (f; g) 7!
R +1 t=0 f(t)g(t)dt is an inner product over the set of measurable functions over [0;+1) to show that (x; x0) 7! min(x; x0) is a PDS kernel. (Hint: associate an indicator function to x and another one to x0.)
(b) Use the result from
(a) to rst show that K1 is PDS and similarly that K with other values of is also PDS.
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Related Book For
Foundations Of Machine Learning
ISBN: 9780262351362
2nd Edition
Authors: Mehryar Mohri, Afshin Rostamizadeh
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