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Subject:

Re: question

From:

Benjamin Rubinstein <[log in to unmask]>

Reply-To:

The Support Vector Machine discussion list <[log in to unmask]>

Date:

Thu, 3 Feb 2005 20:58:06 -0800

Content-Type:

text/plain

Parts/Attachments:

Parts/Attachments

text/plain (47 lines)

Hi Monika,

The word "image" has a usage more general than kernel methods, refering
to the output of a function/mapping on a point, or the outputs of a
function on a set of points.

That is, if we defined a function f: X -> Y (taking points from set X
into set Y), and x and a point in X and S a subset of X, then we refer
to the familiar f(x) as the "image of x in Y under f", and f(S) :=
{f(x)|x in S} as the "image of S in Y under f" (f wasn't strictly
defined on subsets of X, we use f(S) as short-hand).

You can also talk about the "preimage" of a subset S of (or point in) Y
under f as the set of points in X that are mapped by f into S.

The image of the data is simply the set of points in feature space
mapped by the feature mapping from input space.

Cheers,
Ben

--------------------------------------
Benjamin I. P. Rubinstein
PhD student, Berkeley Computer Science
http://www.cs.berkeley.edu/~benr
--------------------------------------


Monika Ray wrote:
> Hello,
>
> This is a very silly question..but I think I got tangled up somewhere..and
> I need help.
>
> IN the mapping from low dimension to high dimension, the "image" of the
> data in the input space is in the high dimensional feature space.  Can
> someone tell me what is the meaning of this "image"?
>
> thanks
> monika
> ***********************************************************************
> The sweetest songs are those that tell of our saddest thought...
>
> Computational Intelligence Centre, Washington University St. louis, MO
> **********************************************************************
>

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