Re: fit plane to xz axis of data

• To: mathgroup at smc.vnet.net
• Subject: [mg89808] Re: fit plane to xz axis of data
• From: Ray Koopman <koopman at sfu.ca>
• Date: Sat, 21 Jun 2008 05:29:58 -0400 (EDT)
• References: <g3fvnb\$klg\$1@smc.vnet.net>

```On Jun 20, 3:10 am, will parr <willpower... at hotmail.com> wrote:
>> On Jun 14, 2:33 am, will parr
>> <willpower... at hotmail.com> wrote:
>>> [...]
>>> Additionally, is it possible to compute a vector running parallel
>>> to the long side (long axis of the SVD plane) of the computed
>>> plane, originating at the mean (centroid) of the data, with a
>>> length of 1?
>>> [...]
>>
>> v rotates the {x,y,z} axes to the principal axes of the centered
>> data: (#-m&/@data).v == u.w , which contains the projections of
>> the centered points onto their principal axes.  u is orthonormal,
>> and w is diagonal, so you want  u[[All,1]] .
>
> Thanks very much, but did you mean v[[All,1]]? as this gives
> an answer in the form {x,y,z} (ie a 3D vector), specifically:
>
> {-0.722734, -0.690915, -0.0170901},
>
> whereas u[[All,1]] gives a long list of values (ie not a vector).
>
> thanks again for your help,
>
> Will
>

It depends on what you think "vector" means. One of its meanings
is a list of values, as in the Mathematica function VectorQ.

u[[All,1]] is such a vector. It contains the normalized projections
of the points onto the first principal axis of the centered data.

v[[All,1]] contains the cosines of the first principal axis
with the original {x,y,z} axes.

```

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