Matrix factorization methods for compressive sensing and multi-modal mutational signatures
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Abstract
In recent years the amount of data generated has grown exponentially from various sources. With the emergence of growing data sets leveraging, sifting through big data is more critical than ever before. This thesis focuses on two projects that address challenges with big data. The first project considers whether algorithmic choices in over-parameterized linear matrix factorization introduce implicit low-rank regularization. We prove that under certain conditions, our constraints are sufficient to lead to a unique low-rank matrix recovery without explicit or implicit regularization. The second project develops a method for integrating and deconvoluting multi-omics data to find mutational signatures. The Bayesian model, called Multi-Modal Non-negative Matrix Factorization, jointly estimates signatures across multiple mutation types. By jointly modeling the mutational modalities, it can improve the accuracy of the deconvolution results and more completely characterize the genomic fingerprint of each mutational process.