Name
Abstract | ||
|---|---|---|
We explore the algebraic structure of the solution space of convex optimization problem Constrained Minimum Trace Factor Analysis (CMTFA), when the population covariance matrix Σ x has an additional latent graphical constraint, namely, a latent star topology. In particular, we have shown that CMTFA can have either a rank 1 or a rank n − 1 solution and nothing in between. The special case of a rank 1 solution, corresponds to the case where just one latent variable captures all the dependencies among the observables, giving rise to a star topology. We found explicit conditions for both rank 1 and rank n − 1 solutions for CMTFA solution of Σ x . As a basic attempt towards building a more general Gaussian tree, we have found a necessary and a sufficient condition for multiple clusters each having rank 1 CMTFA solution to satisfy a minimum probability, to combine together to build a Gaussian tree. |
Year | DOI | Venue |
|---|---|---|
2020 | 10.1109/ISIT44484.2020.9174323 | ISIT |
DocType | Citations | PageRank |
Conference | 0 | 0.34 |
References | Authors | |
0 | 3 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Mahmudul Hasan | 1 | 11 | 4.95 |
| Shuangqing Wei | 2 | 409 | 57.82 |
| Ali Moharrer | 3 | 7 | 4.56 |