I've been studying PCA, and some of the terminology isn't very clear. I do not understand what they mean when they refer to a "principal component". One definition I have seen calls it the new coordinates after the transformation the original data. Another calls these new coordinates the principal component scores. Clarification would be greatly appreciated.
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"Principal components" are linear combinations of original variables. If you plot your data on a (hyper)plane (one observarion = one point), these combinations can be interpreted as "new coordinates" of points. Here, "new coordinates" and so "principal components" mean "formulas to calculate new values from the old ones".
On the other hand, each point now has new coordinates. These new coordinates of points (results of applying formulas mentioned above to original points) are called "principal component scores".
To sum up:
"principal components" are formulas
"principal components scores" are values obtained from these formulas
Both can be called "new coordinates". In a first case we mean "formulas to calculate new coordinates" in latter case we mean "values of new coordinates for our points".
Łukasz Deryło
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