I have this confusion related to PCA. Lets say I have a 100 dimensional data, then the projection into the first principal component is given by the average over all the dimensions.
How is it so?
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It is hard to tell what you are asking, because in theory any linear combination of the variables could be a principal component. Have you seen some of the explanations of PCA on this site, such as http://stats.stackexchange.com/questions/2691/making-sense-of-principal-component-analysis-eigenvectors-eigenvalues? – whuber Oct 08 '13 at 19:47
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@whuber. No I mean to say that if I have n dimensions then my first principal component will be $(1/n, 1/n....,1/n)$. So projecting my points on to this component will be taking the average of the n dimensions – user34790 Oct 08 '13 at 20:14
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3It is rare for that vector to be the first principal component, but it is possible. If your "no" is your response to my question, then that means you are missing out on the good information in the link I gave: please go read it. – whuber Oct 08 '13 at 20:42
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2user34790 - Under a particular set of circumstances, there's a tendency for the first principal component to load roughly equally. If the variances are all about equal (or you analyze the correlations instead of the covariances) and the correlations are all positive and fairly similar, then you tend to see roughly equal loading. – Glen_b Oct 09 '13 at 01:42