n-dimension rotation: Data rotation

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mavadati.mohammad@gmail.com
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n-dimension rotation: Data rotation

Postby mavadati.mohammad@gmail.com » Wed May 22, 2013 4:55 pm UTC

How can I rotate/align n-dimensional data into specific set of basis vector ? I have two set of data in high-dimensional space (e.g. 4D) and want to rotate one to another, in a way they become closer

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z4lis
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Re: n-dimension rotation: Data rotation

Postby z4lis » Thu May 23, 2013 10:18 pm UTC

You need to define closer, and what aspects of the data you want to be preserved under the transformation.
What they (mathematicians) define as interesting depends on their particular field of study; mathematical anaylsts find pain and extreme confusion interesting, whereas geometers are interested in beauty.

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mavadati.mohammad@gmail.com
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Re: n-dimension rotation: Data rotation

Postby mavadati.mohammad@gmail.com » Thu May 23, 2013 11:30 pm UTC

The assumption is that we have two set of data which have the same data arrangement (i.e. two cloud points that have the same shape. Two almost the same objects which has been translation and rotated) . I am looking for the transformation, which can preserve the ratio of distances between the high-dimensional data points and also the angle between them.

Tchebu
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Re: n-dimension rotation: Data rotation

Postby Tchebu » Fri May 24, 2013 12:55 am UTC

The orthogonal group seems like the thing you're looking for.
Our universe is most certainly unique... it's the only one that string theory doesn't describe.

DeGuerre
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Re: n-dimension rotation: Data rotation

Postby DeGuerre » Mon May 27, 2013 4:11 am UTC

mavadati.mohammad@gmail.com wrote:The assumption is that we have two set of data which have the same data arrangement (i.e. two cloud points that have the same shape. Two almost the same objects which has been translation and rotated) . I am looking for the transformation, which can preserve the ratio of distances between the high-dimensional data points and also the angle between them.

Are the points in one-to-one correspondence? If so, do you know the correspondence?


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