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:No. A least-squares fit minimizes (the squares of) the residuals, the vertical distances from the fit line (hyperplane) to the data. PCA minimizes the orthogonal projections to the hyperplane. (Or something like that; I don't really know what I'm talking about.) As for moments of inertia, well, physics isn't exactly my area of expertise. —[[User:Caesura|Caesura]][[User talk:Caesura|<sup>(t)</sup>]] 18:44, 14 December 2005 (UTC)
:PCA is equivalent to finding the principal axes of inertia for ''N'' point masses in ''m'' dimensions, and then throwing all but ''l'' of the new transformed co-ordinates away. It's also mathematically the same problem as [[Total Least Squares]] (errors in all variables), rather than [[Ordinary Least Squares]] (errors only in ''y'', not ''x''), ''if'' you can scale it so the errors in all the variables are uncorrelated and the same size. You're then finding the best ''l'' dimensional hyperplane through the ''m'' dimensional space that your data ought to sit on. The real power tool behind all of this to get a feel for is [[Singular Value Decomposition]]. PCA is just SVD applied to your data. -- [[User:Jheald|Jheald]] 19:40, 12 January 2006 (UTC).
== Derivation of PCA ==
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