"Factor analysis is used to find the variability among observed, correlated variables in terms of a potentially lower number of unobserved variables called factors." It is often used as a dimension reduction with a better data modeling. Unlike PCA, there is no orthogonality constraint for the factors. In addition to this, noise term is explicit in the factor analysis. Having said this, PCA and FA are primarily seen as unsupervised learning algorithms. I would like to know if there is any supervised alternative for Factor analysis. As in, is there any algorithm which not only accounts for the inherent noise in the data, but also assumes correlation among the variables and still can result in discriminating features.
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you might be interested in
http://www.faculty.ucr.edu/~taelee/paper/sfm.pdf
http://kyb.tuebingen.mpg.de/fileadmin/user_upload/files/publications/attachments/sppca_kdd2006_4069%5B0%5D.pdf
and references therein
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Dear Vikram Shenoy Handiru,
You can also look at Linear Discriminant Analysis and related work. LDA is also closely related to principal component analysis (PCA) and factor analysis in that they both look for linear combinations of variables which best explain the data.
Best regards
Ludovic
What you are describing fits "Exploratory Factor Analysis" or EFA. One could argue that the "supervised" fashion of Factor Analysis is "Confirmatory Factor Analysis" or CFA. Often these are done in a Structural Equations Modeling (SEM) framework where you can specify the factor structures and relationships between latent and observed variables.
Some people take a mixed approach by using EFA to fit an initial model and then tweak things using CFA so that things make theoretical sense.
Yes you can read this paper about supervised PCA :
"Supervised principal component analysis: Visualization, classification and regression on subspaces and submanifolds" - http://www.sciencedirect.com/science/article/pii/S0031320310005819
"Prediction by Supervised Principal Components" - https://web.stanford.edu/~hastie/Papers/spca_JASA.pdf
you try also to perform a "supervised clsutering" and then the analysis of the obtained clusters
Vincent
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