Contents
Why is rotation of components necessary in PCA?
Is rotation necessary in PCA? Yes, rotation (orthogonal) is necessary to account the maximum variance of the training set. If we don’t rotate the components, the effect of PCA will diminish and we’ll have to select more number of components to explain variance in the training set.
What are loading scores in PCA?
Factor loadings (factor or component coefficients) : The factor loadings, also called component loadings in PCA, are the correlation coefficients between the variables (rows) and factors (columns). PC scores: Also called component scores in PCA, these scores are the scores of each case (row) on each factor (column).
How are component scores used in a PCA?
Terminology: First of all, the results of a PCA are usually discussed in terms of component scores, sometimes called factor scores (the transformed variable values corresponding to a particular data point), and loadings (the weight by which each standardized original variable should be multiplied to get the component score).
Is it possible to rotate raw scores in PCA?
It is possible to consider an alternative rotation procedure, where TT⊤ is inserted between US and V⊤. This would rotate raw scores and eigenvectors (instead of standardized scores and loadings). The biggest problem with this approach is that after such a “rotation”, scores will not be uncorrelated anymore, which is pretty fatal for PCA.
What is the best way to scale parameters before running a PCAS?
For Garbor Borgulya – you mentioned data measured with a normally distributed error – does this mean log-transforming and giving the data a more normal distribution before scaling is a good choice if my data is variable? I understand logging data for PCAs can help with outliers as well.
Is it still PCA after an orthogonal rotation?
After an orthogonal rotation (such as varimax), the “rotated-principal” axes are not orthogonal, and orthogonal projections on them do not make sense. So one should rather drop this whole axes/projections point of view. It would be weird to still call it PCA (which is all about projections with maximal variance etc.).