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The basic idea i'm trying is to model the data with factor analysis, assuming a latent variable structure that underlies the observations. Labels for "real" anomalies are available and used for validation. Another important note is that the data does not have a "very" Gaussian nature.

Then, projecting the observations onto the new subspace found, and looking for outliers - i.e. finding the observations that digress from the underlying structure, assuming the anomalies i'm looking for will be more prevalent there.

Using R's factanal, with varimax (or oblimin) rotations, i have encountered the following result, which i'm not sure about :

  • When projecting the normalized data (z-score) using the FA model found, classification/detection is poor ; but since factanal scales the data in advance, i believe this is the correct way(?)
  • When projecting the original data (not normalized) using the same FA model, detection is much improved.

Could this be due to projecting the observations onto a subspace that assumes a low variance, much more "normal" distribution, thereby "aggravating" any anomalous points?

Would appreciate help/insight as to what i'm missing!

Thank you.

Update: - LX yields much better classification than LX*, where L is the loadings matrix, X is the data matrix, and X* is the standardized data matrix. LX also yields better classification than in the following. https://stat.ethz.ch/pipermail/r-help/2002-April/020278.html

Could the LX transformation be related to LDA?

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    $\begingroup$ It has nothing to do with normality. Simply factor analysis perfomed on standardized data (=correlations), centered data (=covariances), scaled data (=cosines) or raw data (=dot-products) often leaves quite different results. You shouldn't rely on default specification but think over what type of data narmalization will suit your task $\endgroup$
    – ttnphns
    Commented Nov 9, 2012 at 11:03
  • $\begingroup$ Thanks. Could you possibly reference me to some sources describing those differences? $\endgroup$
    – mrquestion
    Commented Nov 9, 2012 at 11:07
  • $\begingroup$ These needn't be described because the differences aren't systematic but depend on the data at hand, and the subject is obvious: supposing you're familiar with how FA works, then just use imagination. $\endgroup$
    – ttnphns
    Commented Nov 9, 2012 at 11:20
  • $\begingroup$ Is there perhaps any relation to LDA? $\endgroup$
    – mrquestion
    Commented Nov 10, 2012 at 1:06
  • $\begingroup$ FA is as such fairly distant from LDA. And LDA always works on centered or standardized data whereas FA/PCA sometimes (rarely) are performed on uncentered data. $\endgroup$
    – ttnphns
    Commented Nov 10, 2012 at 6:32

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