Summary of Rmlr: Extending Multinomial Logistic Regression Into General Geometries, by Ziheng Chen et al.
RMLR: Extending Multinomial Logistic Regression into General Geometries
by Ziheng Chen, Yue Song, Rui Wang, Xiaojun Wu, Nicu Sebe
First submitted to arxiv on: 28 Sep 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Artificial Intelligence (cs.AI)
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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 This paper proposes a framework for designing Riemannian multinomial logistic regression (MLR) over general geometries, referred to as RMLR. The approach builds upon Euclidean MLR and extends it to Riemannian spaces, enabling its use with various manifolds. The authors showcase their framework on the Symmetric Positive Definite (SPD) manifold and special orthogonal group, developing five families of SPD MLRs under different power-deformed metrics. They also propose Lie MLR for rotation matrices based on a bi-invariant metric. Experimental results validate the effectiveness of RMLR on various Riemannian backbone networks. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper helps us better understand how to classify things that are not points in space, but rather shapes or curves. It’s like trying to figure out what kind of animal an object is based on its features. The authors came up with a new way to do this using special math called Riemannian geometry. They tested their method on different kinds of shapes and it worked really well! This could be useful for things like recognizing pictures of animals or identifying sounds. |
Keywords
* Artificial intelligence * Logistic regression
