Quote:
Originally Posted by pouramini
Thank you, yes that seems helpful if we regard all points in Z space, but I thought it speaks about the points in Z which are the mapping of a point in data set D.
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Hm, in my understanding, the quote "some points in the
Z space may not be valid transforms of any x E X" regards all the points in the Z space. For example: If
![z = \Phi (x) = [1, x^{2}_{1}, x^{2}_{2}]](/vblatex/img/ffecf9a16569d17d6fac65051babad78-1.gif "z = \Phi (x) = [1, x^{2}_{1}, x^{2}_{2}]")
, then the point
![z = [1, -3, -5]](/vblatex/img/589017a58811363c19ecc1f52f573b2d-1.gif "z = [1, -3, -5]")
in the Z space cannot be a valid transform of any
.