Continuous Semi-Supervised Nonnegative Matrix Factorization

Authors

Michael R. Lindstrom, The University of Texas Rio Grande ValleyFollow
Xiaofu Ding
Feng Liu
Anand Somayajula
Deanna Needell

Document Type

Article

Publication Date

3-30-2023

Abstract

Nonnegative matrix factorization can be used to automatically detect topics within a corpus in an unsupervised fashion. The technique amounts to an approximation of a nonnegative matrix as the product of two nonnegative matrices of lower rank. In certain applications it is desirable to extract topics and use them to predict quantitative outcomes. In this paper, we show Nonnegative Matrix Factorization can be combined with regression on a continuous response variable by minimizing a penalty function that adds a weighted regression error to a matrix factorization error. We show theoretically that as the weighting increases, the regression error in training decreases weakly. We test our method on synthetic data and real data coming from Rate My Professors reviews to predict an instructor’s rating from the text in their reviews. In practice, when used as a dimensionality reduction method (when the number of topics chosen in the model is fewer than the true number of topics), the method performs better than doing regression after topics are identified—both during training and testing—and it retrains interpretability.

Comments

© 2023 by the authors.

Recommended Citation

Lindstrom MR, Ding X, Liu F, Somayajula A, Needell D. Continuous Semi-Supervised Nonnegative Matrix Factorization. Algorithms. 2023; 16(4):187. https://doi.org/10.3390/a16040187

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Publication Title

Algorithms

DOI

10.3390/a16040187