Optimization algorithms for inference and classification of genetic profiles from undersampled measurements

In this thesis, we tackle three different problems, all related to optimization techniques for inference and classification of genetic profiles. First, we extend the deterministic Non-negative Matrix Factorization (NMF) framework to the probabilistic case (PNMF). We apply the PNMF algorithm to cluster and classify DNA microarrays data. The proposed PNMF is shown to outperform the deterministic NMF and the sparse NMF algorithms in clustering stability and classification accuracy. Second, we propose SMURC: Small-sample MUltivariate Regression with Covariance estimation. Specifically, we consider a high dimension low sample-size multivariate regression problem that accounts for correlation of the response variables. We show that, in this case, the maximum likelihood approach is senseless because the likelihood diverges. We propose a normalization of the likelihood function that guarantees convergence. Simulation results show that SMURC outperforms the regularized likelihood estimator with known covariance matrix and the state-of-the-art sparse Conditional Graphical Gaussian Model (sCGGM). In the third Chapter, we derive a new greedy algorithm that provides an exact sparse solution of the combinatorial l sub zero-optimization problem in an exponentially less computation time. Unlike other greedy approaches, which are only approximations of the exact sparse solution, the proposed greedy approach, called Kernel reconstruction, leads to the exact optimal solution.

Name thesis:degree_name

M.S. Electrical and Computer Engineering

Level thesis:degree_level

Thesis

Discipline thesis:degree_discipline

Electrical and Computer Engineering

Year dc:date.available

2014

Author dc:creator

• Bayar, Belhassen

Contributors dc:contributor

• Bouaynaya, Nidhal

• Signal processing--Mathematics; Gene regulatory networks
• Electrical and Computer Engineering

Repository record dc:identifier

https://rdw.rowan.edu/etd/410

OAI identifier oai:identifier

oai:rdw.rowan.edu:etd-1409