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PCA on fully centered data vs PCA on "centered around meaningful part of object"?

So usually PCA (in R at least) centers the data so that e.g. $(0,0,0)$ will be at the center of the data.

However, if one's data is such that it has an area relative to which one wants to produce the PCA, then how does one progress? I.e. how does one customize the centering so that PCA is relative to a part/point that one decides?

mavavilj
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  • Could you do PCA (i.e. with centering) then relocate the points to your desired center? Or do you specifically want the low rank decomposition performed at your desired center? – user257566 Jul 01 '21 at 18:04
  • @user257566 I did PCA with centering on my data and while the PC1 line is "promising" I'm not sure if it's pointing to the optimal direction compared to if the center was actually the point relative to which I want to study PCs. – mavavilj Jul 01 '21 at 18:06
  • @user257566 I'm not sure if that gives truthful direction for most variance? – mavavilj Jul 01 '21 at 18:07
  • See https://stats.stackexchange.com/q/22329/3277. Centering (i.e. moving the pivot of PCA-rotation) is _not_ a genuine part of PCA. You are in the right to put the origin to any location. Any you feel will make sense to you. But be aware that will change PCA results. – ttnphns Jul 01 '21 at 18:10
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    Check also this https://stats.stackexchange.com/a/16335/3277 where pics of different locations are shown as examples. – ttnphns Jul 01 '21 at 18:12
  • @ttnphns So I simply place the point relative to which I want PCA to $(0,0,0)$ and then let the algo work? – mavavilj Jul 01 '21 at 18:35
  • Using cartesian point of reference (the zero point) as the pivot for PCA amounts to doing PCA on the raw data values as they are. Simply order your pca function to omit doing the centering (if it has such option, usually they have it). – ttnphns Jul 01 '21 at 19:28

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