Teaching Reform of Singular Value Decomposition Based on the Exploratory Typical Case

DOI

10.2991/978-94-6463-058-9_117How to use a DOI?

Keywords

matrix; tensor; singular value decomposition; typical case

ABSTRACT

Singular value decomposition is an important way of matrix decomposition, which has many important applications in the fields of machine learning, signal processing and statistics. However, the singular value decomposition in the matrix computations course focuses on the theoretical teaching of basic concepts and calculation methods. Students can’t understand the importance of singular value decomposition and how to use singular value decomposition. Therefore, an exploratory typical case is designed and implemented in this paper based on singular value decomposition theorem. The typical case is about image compression and student-friendly, which mainly includes gray-image compression matrix model, color-image compression matrix model and color-image compression tensor model. The realization of gray-image compression matrix model is helpful for students to understand and master the significance and application of the singular value decomposition. The analysis of the two color-image compression models is helpful for students to explore the similarities and difference between tensor singular value decomposition and matrix singular value decomposition. In the teaching process of singular value decomposition, discussion teaching is adopted to implement this teaching case, which has received good teaching feedback, mobilized students' enthusiasm in learning mathematics, and improved the teaching effect of matrix computations course.

Copyright

© 2023 The Author(s)

Open Access

Open Access This chapter is licensed under the terms of the Creative Commons Attribution-NonCommercial 4.0 International License (http://creativecommons.org/licenses/by-nc/4.0/), which permits any noncommercial use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

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TY  - CONF
AU  - Le Han
PY  - 2022
DA  - 2022/12/27
TI  - Teaching Reform of Singular Value Decomposition Based on the Exploratory Typical Case
BT  - Proceedings of the 2nd International Conference on Internet, Education and Information Technology (IEIT 2022)
PB  - Atlantis Press
SP  - 749
EP  - 753
SN  - 2352-538X
UR  - https://doi.org/10.2991/978-94-6463-058-9_117
DO  - 10.2991/978-94-6463-058-9_117
ID  - Han2022
ER  -