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We develop a convex relaxation of maximum a posteriori estimation of a mixture of regression models. Although our relaxation involves a semidefinite matrix variable, we reformulate the problem to eliminate the need for general semidefinite programming. In particular, we provide two reformulations that admit fast algorithms. The first is a max-min spectral reformulation exploiting quasi-Newton descent. The second is a min-min reformulation consisting of fast alternating steps of closed-form updates. We evaluate the methods against Expectation-Maximization in a real problem of motion segmentation from video data.

The increasing complexity of automotive electronics has put considerable pressure on automotive communication networking to accommodate in-vehicle information flows. The use of power lines has been a promising alternative to in-vehicle communications because of elimination of extra data cables. In this paper, we focus on the latest HomePlug Green PHY (HPGP) which has been promoted by major automotive manufacturers for green communications with electric vehicles, and study its worst-case access delay performance in supporting delaycritical in-vehicle applications using both theoretical analysis and the simulation. Specifically, we apply Network Calculus as a deterministic modeling approach to evaluate the worst delay and further verify its performance using the OMNeT++ simulation. Evaluation results are also supplemented to compare with legacy methods and provide useful guidelines for developing HPGP based vehicular power line communication systems.