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I see a lot of talks/papers where Principal Component Analysis (PCA) scatter plots have axes that go from numbers OTHER than -1 to 1.

I thought that for PCA, the data MUST be unit variance transformed and mean-centered, which should always produce axes that vary from -1 to 1.

When people show scatter plots that have points at values like -4,3 or 15,-2 does this mean that they did not properly perform the PCA?

kjetil b halvorsen
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SBoother
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    the values of the scores do only depend on how good the data can be represented in terms of the corresponding principal component. the value of the scores do not need to be valued between $-1$ and $1$ - neither do standardized variables. – BloXX Mar 05 '19 at 11:54
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    There are _raw PC scores_ and _standardized (to unit variance) PC scores_. The raw scores you get when you compute them directly by the eigenvectors (which form the matrix of the orthogonal rotation of the data into the PCs). If you then z-standardize the PC scores you get standardized PC scores. But the latter are also what you get if you use the matrix of _loadings_ (https://stats.stackexchange.com/q/143905/3277) rather than eigenvectors to compute PC scores. – ttnphns Mar 05 '19 at 14:06

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Answered in comments:

The values of the scores do only depend on how good the data can be represented in terms of the corresponding principal component. the value of the scores do not need to be valued between −1 and 1 - neither do standardized variables.

– BloXX

There are raw PC scores and standardized (to unit variance) PC scores. The raw scores you get when you compute them directly by the eigenvectors (which form the matrix of the orthogonal rotation of the data into the PCs). If you then z-standardize the PC scores you get standardized PC scores. But the latter are also what you get if you use the matrix of loadings (Loadings vs eigenvectors in PCA: when to use one or another?) rather than eigenvectors to compute PC scores.

– ttnphns

kjetil b halvorsen
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