Gaussian Latent Factor Analysis under Graphical Constraints
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In this paper we explored the algebraic structure of the solution space of Constrained Minimum Trace Factor Analysis (CMTFA) and Constrained Minimum Determinant Factor Analysis (CMDFA). We imposed graphical constraint on the generation model of the population matrix Σ_x and make it star structured. We have explicitly shown that there can be only two distinct solutions possible for CMTFA for such Σ_x one of which is a star. We found the sufficient and necessary conditon for both the solutions. We have also found the necessary and sufficient conditions under which CMDFA solution of such star structured population matrices is also a star.
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