Nonnegative Matrix Factorization with Group and Basis Restrictions

Phillip Shreeves (), Jeffrey L. Andrews (), Xinchen Deng, Ramie Ali-Adeeb and Andrew Jirasek ()
Additional contact information
Phillip Shreeves: University of British Columbia - Okanagan
Jeffrey L. Andrews: University of British Columbia - Okanagan
Xinchen Deng: University of British Columbia - Okanagan
Ramie Ali-Adeeb: University of British Columbia - Okanagan
Andrew Jirasek: University of British Columbia - Okanagan

Statistics in Biosciences, 2023, vol. 15, issue 3, No 5, 608-632

Abstract: Abstract Nonnegative matrix factorization (NMF) is a popular method used to reduce dimensionality in data sets whose elements are nonnegative. It does so by decomposing the data set of interest, X, into two lower rank nonnegative matrices multiplied together. These two matrices can be described as the latent factors, represented in the rows of H, and the scores of the observations on these factors that are found in the rows of W. This paper provides an extension of this method which allows one to specify prior knowledge of the data, including both group information and possible underlying factors. This is done by further decomposing the matrix, H, into matrices A and S multiplied together. These matrices represent an ’auxiliary’ matrix and a semi-constrained factor matrix, respectively. This method and its updating criterion are proposed, followed by its application on both simulated and real-world examples displaying different uses of the algorithm.

Keywords: Nonnegative matrix factorization; Semi-supervised learning; Raman spectroscopy; Dimensionality reduction (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s12561-023-09398-2 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:stabio:v:15:y:2023:i:3:d:10.1007_s12561-023-09398-2

Ordering information: This journal article can be ordered from
http://www.springer.com/journal/12561

DOI: 10.1007/s12561-023-09398-2

Access Statistics for this article

Statistics in Biosciences is currently edited by Hongyu Zhao and Xihong Lin

More articles in Statistics in Biosciences from Springer, International Chinese Statistical Association
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().