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I saw the following animation at making sense of PCA http://i.stack.imgur.com/lNHqt.gif, which shows blue data points.

I am reading a paper on Eigenfaces which says that:

"a typical image of size 256 by 256 becomes a vector of dimension 65536 or equivalently a point in 65536 dimensional space"

The paper is available at the following link: Eigenfaces for Recognition

My question is that in the context of Eigenfaces is each blue point an image?

Somebody please guide me.

Zulfi.

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  • $\begingroup$ Please follow the link "making sense of PCA" $\endgroup$
    – user2994783
    Nov 13, 2018 at 0:49
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    $\begingroup$ Yes, a point in 65536 dimensional space. $\endgroup$
    – Yves Daoust
    Mar 23 at 7:48

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Each blue data point in the animated picture stands for an image of a face whose dimension is much higher in the context of Eigenfaces for Recognition. They are the original data points. It does NOT mean Eigenfaces.

When the long swinging black solid rod becomes still under the "viscous friction" exerted by the red lines, its direction is the most significant eigenface in that context, which is defined as an eigenvector of the biggest eigenvalue of the covariance matrix of the face images. The projection of the blue points onto that long black rod viewed as vectors starting from the center of the blue points is the first principal component.

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  • $\begingroup$ Thanks Apass.Jack. I was asking "is each blue point an image?" and you have said " Each blue data point in the animated picture stands for an image of a face whose dimension is much higher". This means your answer is "Yes" . "They are the original data points. It does NOT mean Eigenfaces.". Yes Eigen faces are the Principal Components or Eigen Vectors. Thanks God bless you. $\endgroup$
    – user2994783
    Nov 13, 2018 at 3:58
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    $\begingroup$ I am afraid that you got mistaken. The Eigenfaces are Eigenvectors. However, Eigenvectors are NOT principal components. $\endgroup$
    – John L.
    Nov 13, 2018 at 5:37
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    $\begingroup$ For example, how does that popular answer at stats stack exchange describe principal components? "this new property is called 'first principal component'. And instead of saying 'property' or 'characteristic' we usually say 'feature' or 'variable'". Notice it is considered as a variable. $\endgroup$
    – John L.
    Nov 13, 2018 at 5:38
  • $\begingroup$ It is possible that some articles or some people may treat eigenvectors as principal components in some casual way. Indeed, they are so tightly related to each other it is almost impossible to mention one without mentioning the other. However, the general convention is that principal components are the projections of the original data onto the new axes. So, we will analyze the principle components (principle component analysis). $\endgroup$
    – John L.
    Nov 13, 2018 at 5:43
  • $\begingroup$ I got this from that stat site <We call these straight lines "principal components". There are as many principal components as there are variables. The first principal component is the best straight line you can fit to the data. The second principal component is the best straight line you can fit to the errors from the first principal component. The third principal component is the best straight line you can fit to the errors from the first and second principal components> Thanks for telling me that these are projections of blue points on to the principal axis. What we mean by variable here? $\endgroup$
    – user2994783
    Nov 13, 2018 at 6:01

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