I have done this many times for factor analysis based factor scores, Ratna. The factor scores are first transformed to normal quantiles to reduce the effects of any existing outliers, followed by a factor analysis. For example, my graduate class created a quality of life index (QoL) that is based on 15 variables. The factor analysis reduced the dimensionality from 15  to fewer factors that explained a large proportion of the variability and that can be explained very well.  Factor analysis was an important tool and analyzing correlated data. We performed an exploratory factor analysis with all 15 variable.

Yes, the first componets have more information power the the original variates, and are orthogonal betwen them

yes it can be done. By using Factor Analysis you can estimate factor score for each respondent and then cluster analysis can be conducted.

If you use rotations of the factors, make sure to use a multivariate cluster analysis if the chosen rotation method is oblique. If you choose an orthogonal rotation, you can have separate cluster analysis for each factor. The beauty of doing a cluster analysis after a factor analysis is the ability to identify geographical clusters that are based on some interesting combination of variables. For example, we identified an area in Florida where the breast cancer rates were unusually high for white women with high income and high level of education who were smokers.

Sure this can be done, but please also consider the reverse procedure: First find your groups with cluster analysis and subsequently analyse each individual cluster with Principal Component Analysis (PCA). The reason for this is that the first few axes of your PCA do not at all need to be identical for the different groups you are interested in. If you picture your consumer groups as galaxies in the vast universe, it is easy to see that each galaxy has its own orientation (given by PCA) whereas the cluster analysis will have no trouble finding the individual galaxies. This is the result you get if you first cluster, and subsequently run PCA on the individual clusters. Running PCA first wil find the directions of biggest separation between galaxies, answering the question what linear combination of variables is crucial to distinguish them. Both options are useful.

Note: If you need the PCA to filter the data, this is my guess from your question, than you are misusing the procedure and you should either clean up your data some other way or, even better, switch to a more robust distance metric for your cluster analysis. PCA is a procedure that is extremely sensitive to outliers and running cluster analysis first can help filtering these out.

You can do that, that's for sure. I've used PCA prior to discriminant analysis to reduce multicolinearity of the data, but as someone else mentioned here the problem rises when you try to interpret the results of the second analysis. However, if your factors are meaningful enough, I think you shouldn't have trouble discussing your results.

Bas van der Geer wrote "the first few axes of your PCA do not at all need to be identical for the different groups you are interested in". An additional problem with PCA is that even though the axes explain subsequently most variance of the remaining variability, there is no guarantee that the the optimal clustering is in the space that explains most variance. Thus you may miss the clustering you seek by extracting a limited amount of principal components. Whether this happens is an empirical matter. J. D. Carroll and J. B. Kruskal have written about this problem.

Yes, you can

hello to all

cluster analysis can be done in several way. one is using factor scores. An important stage in cluster analysis is to test which is better? A multivariate should be don on clusters to see which kind of data make a big between subject? especially when we do a exploratory research.