Summary of Low-rank Tensor Learning by Generalized Nonconvex Regularization, By Sijia Xia et al.
Low-Rank Tensor Learning by Generalized Nonconvex Regularization
by Sijia Xia, Michael K. Ng, Xiongjun Zhang
First submitted to arxiv on: 24 Oct 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: None
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| 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 proposes a nonconvex model for low-rank tensor learning, which is more effective in exploring the low-rankness of the underlying tensor compared to existing methods. The approach is based on transformed tensor nuclear norm and employs a family of nonconvex functions onto the singular values of all frontal slices of a tensor in the transformed domain. An error bound is established for the stationary point of the nonconvex model, and a proximal majorization-minimization (PMM) algorithm is designed to solve the resulting model. The paper demonstrates the effectiveness of the proposed method through numerical experiments on tensor completion and binary classification. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary The paper develops a new way to learn from tensors when only some data points are available. It uses a special type of function that helps find the underlying structure of the tensor, which is useful for many applications like image and video processing. The authors prove that their method works well by showing error bounds and conducting experiments on two different tasks. |
Keywords
* Artificial intelligence * Classification
