Characterization of Stability of Non-Negative Matrix Factorization Models: An Application to Single-Cell Data

Liu, Alexander EJ

Characterization of Stability of Non-Negative Matrix Factorization Models: An Application to Single-Cell Data

dc.contributor.advisor	Zhang, Qingrun
dc.contributor.author	Liu, Alexander EJ
dc.contributor.committeemember	Wu, Jingjing
dc.contributor.committeemember	Xu, Yuan
dc.contributor.committeemember	Zhang, Qingrun
dc.date	2023-11
dc.date.accessioned	2023-09-08T15:46:39Z
dc.date.available	2023-09-08T15:46:39Z
dc.date.issued	2023-08-21
dc.description.abstract	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.
dc.identifier.citation	Liu, A. E. J. (2023). Characterization of stability of non-negative matrix factorization models: an application to single-cell data (Master's thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca.
dc.identifier.uri	https://hdl.handle.net/1880/116998
dc.identifier.uri	https://dx.doi.org/10.11575/PRISM/41842
dc.language.iso	en
dc.publisher.faculty	Graduate Studies
dc.publisher.institution	University of Calgary
dc.rights	University of Calgary graduate students retain copyright ownership and moral rights for their thesis. You may use this material in any way that is permitted by the Copyright Act or through licensing that has been assigned to the document. For uses that are not allowable under copyright legislation or licensing, you are required to seek permission.
dc.subject.classification	Statistics
dc.title	Characterization of Stability of Non-Negative Matrix Factorization Models: An Application to Single-Cell Data
dc.type	master thesis
thesis.degree.discipline	Mathematics & Statistics
thesis.degree.grantor	University of Calgary
thesis.degree.name	Master of Science (MSc)
ucalgary.thesis.accesssetbystudent	I do not require a thesis withhold – my thesis will have open access and can be viewed and downloaded publicly as soon as possible.