An Introduction to the Application of Tensorial Manifold Learning Methods in the Digital Image Processing and Computer Vision
- Department of Mathematics, Payame Noor University (PNU), P.O. Box 19395-3697, Tehran, Iran
- Department of Mathematics, Faculty of Sciences, Imam Hossein Comprehensive University, Tehran, Iran.
Received: 22-07-2021
Accepted: 20-01-2022
Published in Issue 30-03-2022
Copyright (c) 2024 International Journal of Mathematical Modeling & Computations

This work is licensed under a Creative Commons Attribution 4.0 International License.
How to Cite
Yazdani, H., & Shojaeifard, A. R. (2022). An Introduction to the Application of Tensorial Manifold Learning Methods in the Digital Image Processing and Computer Vision. International Journal of Mathematical Modelling & Computations, 12(1), 27-35. https://doi.org/10.30495/ijm2c.2022.1936139.1224
Abstract
Tensors as vector fields structures and manifolds as great geometrical-topological structures have many applications in the fields of big data analysis. Types of norms, metrics and scalable structures have been defined from various aspects. Nowadays, the hybrid methods between tensorial algorithms and manifold learning (MaL) methods have been attracted some attention. In image and signal processing, from image recovery to face recognition, these methods have appeared very excellent. According to our experiments by MATLAB R2021a, the hybrid algorithms are powerful other than algorithms based on the efficient popular parameters.References
- C. G. Baker, P. A. Absil and K. A. Gallivan, An implicit trust-region method on Riemannian
- manifolds, IMA Journal of Numerical Analysis, 28 (2008) 665–689.
- E. J. Candes and B. Recht, Exact matrix completion via convex optimization, Foundations of Computational Mathematics, 9 (2009) 717, doi:10.1007/s10208-009-9045-5.
- M. Kurucz, A. Benczur and K. Csalogany, Methods for large scale svd with missing values, KDD
- Cup, (2007) 31–38, ACM 978-1-59593-834-3/07/0008.
- J. M. Lewis, L. J. P. van der Maaten and V. R. de Sa. A behavioral investigation of dimensionality
- reduction, In Proceedings of the Cognitive Science Society (CSS), (2012) 671–676.
- J. Liu, P. Musialski , P. Wonka and J. Ye, Tensor completion for estimating missing values in visual
- data, IEEE Transactions on Pattern Analysis and Machine Intelligence, 1 (35) (2013) 208–220.
- B. ONeil, Semi-Riemannian Geometry With Application to Relativity, Academic Press, (1983).
- L. Qi, The spectral theory of tensors, arXiv, (2012), doi:10.48550/ARXIV.1201.3424.
- A. Rovi, Analysis of 2-Tensors, MAI mathematics: Master thesis, Linkopings University, (2010).
- A. R. Shojaiefard and H. R. Yazdani, A hybrid method based on the completely positive-tensors
- and PCA for face recognition, communicated to Neural Processing Letters, (2021).
- A. R. Shojaiefard, H. R. Yazdani and M. Shahrezaei, Apply tensor completion based on the denoising
- by inequality constrained convex optimization for recovering images, communicated to Wavelets and
- Linear Algebra, (2021).
- A. R. Shojaiefard, H. R. Yazdani and M. Shahrezaei, Detecting 3D-facial shape recovery by tensor
- representation and HoSVD, communicated to Journal of Computer and Knowledge Engineering,
- (2021).
- Q. Song, H. Ge, J. Caverlee and X. Hu, Tensor completion algorithms in big data analytics, ACM
- Transactions on Knowledge Discovery from Data (TKDD), 6 (13) (2019) 1–48.
- L. J. P. Van der Maaten, E. O. Postma and H. J. Van den Herik, Dimensionality reduction: A
- comparative review, Technical Report TiCC TR, 5 (2009).
10.30495/ijm2c.2022.1936139.1224