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I would like to know how do I reconstruct the data using only the first principal component of the PCA?

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  • $\begingroup$ You can't. PCA is a dimension reduction technique. It discards information. You can only recover the original data if you have all principal components. $\endgroup$ – S. Kolassa - Reinstate Monica Nov 7 '15 at 14:09
  • $\begingroup$ I meant..reconstruct the data using only the first principal component..it'll not be the original data..but a "version" of it using the 1PC $\endgroup$ – Ana Nov 7 '15 at 14:37
  • $\begingroup$ @amoeba ... and therein lies the problem with answers that rely on a particular software language for their explanations: their value is limited to those who are familiar with the software. For instance, the accepted answer in your first link is an effective one, but because it isn't actually explained--it's only illustrated with R code--it is less widely useful than it might otherwise be. $\endgroup$ – whuber Nov 7 '15 at 14:42
  • $\begingroup$ @whuber: I couldn't agree more. In fact, I noticed this situation before (because this question reappears often enough), but having several old, well upvoted threads with highly voted & accepted answers somehow puts me off from composing an answer myself (I wouldn't even know which thread to post this answer in). What would you suggest? $\endgroup$ – amoeba says Reinstate Monica Nov 7 '15 at 14:46
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    $\begingroup$ @amoeba It's not an easy choice. I would be tempted to edit one of the answers you referenced. By choosing a thread (and an answer within it) that appears most likely to come up in future searches, you would maximize the visibility of your edit. (My experience is that new answers to old questions with accepted answers are usually overlooked, undervoted, and get little attention.) $\endgroup$ – whuber Nov 7 '15 at 14:50

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