Browsing by Author "Liu, Alexander EJ"

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    Characterization of Stability of Non-Negative Matrix Factorization Models: An Application to Single-Cell Data
    (2023-08-21) Liu, Alexander EJ; Zhang, Qingrun; Wu, Jingjing; Xu, Yuan; Zhang, Qingrun
    The non-negative matrix factorization (NMF) is a powerful machine learning technique used in mathematics, computer science, and data science. This technique has applications in a wide range of fields including recommender systems, image processing, signal processing, machine learning and genetics. Recently, NMF has gained popularity in the analysis of single-cell gene expression data to identify cell types and gene expression patterns. In this thesis, we have studied the NMF, its rank estimation, classification, and stability using both simulated data and real single-cell gene expression data. We have designed two simulated data sets with desired features and tested two seeding methods, eight NMF algorithms and five rank estimation criteria. Additionally, a real single-cell gene expression data has been used to further characterize the NMF algorithms. We have also investigated the stability of NMF, first over the sample size consideration and then on initialization. The detailed conditions that have been revealed by this thesis may generate practical impact in directing the appropriate use of NMF in analyzing single-cell gene expression data.