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I have a set of 3D data points, indicated by the blue color in the picture below.

I then project them onto the x-y plane, i.e. setting z values of all the points to 0, shown by the yellow color below.

Then, I perform PCA on the 2D data points (the yellow ones).

I end up with the 1st Principal Component being the green line, and the 2nd being the yellow line.

enter image description here

As I am a newbie in PCA, I am not sure whether I have done something wrong or not.

Because in my intuitive, the 1st Principal Component should be like in the picture below:

enter image description here

I mean unlike the above picture given in wiki, my 1st component is NOT obvious and seems to make no sense. Did I do something wrong?

Edit:

To avoid the confusion, the 2D view from the above is as follows: enter image description here

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  • $\begingroup$ Two suggestions: could you explain why you project the data onto the xy plane (PCA can be done in 3-dimensional data too!)? If the third dimension is not really important to your problem, it would be better to post 2D plots - the 3D graph is hard to read. $\endgroup$ – pichenettes Jul 29 '13 at 9:14
  • $\begingroup$ @pichenettes yeah the 3rd dimension is not important to my purpose. Do u need me to post the 2D view (view from the top of x-y plane)? Thanks! $\endgroup$ – Sibbs Gambling Jul 29 '13 at 9:18
  • $\begingroup$ @pichenettes please see attached $\endgroup$ – Sibbs Gambling Jul 29 '13 at 9:24
  • $\begingroup$ A pure 2D view would have been better... $\endgroup$ – pichenettes Jul 29 '13 at 9:41
  • $\begingroup$ @pichenettes any idea? :) $\endgroup$ – Sibbs Gambling Jul 29 '13 at 9:43
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If the PCA was correct, than green and yellow line would be perpendicular. So something is wrong with your result.

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    $\begingroup$ I am almost sure that the green and yellow lines are perpendicular. The x and y axes do not have the same scale; and because this is a silly 3D projection, the gray grid in the background is not reliable (parallax error). $\endgroup$ – pichenettes Aug 1 '13 at 18:48
  • $\begingroup$ You are right, i missed the different scaling of the axes. $\endgroup$ – Twonky Aug 4 '13 at 9:00

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