Summary of A Kernelizable Primal-dual Formulation Of the Multilinear Singular Value Decomposition, by Frederiek Wesel et al.
A Kernelizable Primal-Dual Formulation of the Multilinear Singular Value Decomposition
by Frederiek Wesel, Kim Batselier
First submitted to arxiv on: 14 Oct 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Numerical Analysis (math.NA); Machine Learning (stat.ML)
GrooveSquid.com Paper Summaries
GrooveSquid.com’s goal is to make artificial intelligence research accessible by summarizing AI papers in simpler terms. Each summary below covers the same AI paper, written at different levels of difficulty. The medium difficulty and low difficulty versions are original summaries written by GrooveSquid.com, while the high difficulty version is the paper’s original abstract. Feel free to learn from the version that suits you best!
| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary The paper explores the connection between machine learning methods and primal-dual optimization problems, highlighting the importance of expressing learning tasks in terms of these two formulations. The authors demonstrate how popular methods like SVM, LS-SVM, Ridge Regression, Lasso Regression, PCA, and SVD can be defined either in terms of primal weights or dual Lagrange multipliers. The paper also derives a primal-dual formulation for Multilinear Singular Value Decomposition (MLSVD), which recovers PCA and SVD as special cases. Furthermore, the authors propose a nonlinear extension of MLSVD using feature maps, resulting in a kernel tensor in the dual problem. Potential applications include signal analysis and deep learning. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary The paper shows how different machine learning methods can be linked to two ways of solving problems: primal and dual optimization. It looks at well-known techniques like SVM and PCA, and explains how they can be understood using these two approaches. The authors also create a new way of doing MLSVD, which includes some special cases for PCA and SVD. This could help with analyzing signals and making deeper learning models. |
Keywords
» Artificial intelligence » Deep learning » Machine learning » Optimization » Pca » Regression
