Summary of Convex Relaxation For Solving Large-margin Classifiers in Hyperbolic Space, by Sheng Yang et al.
Convex Relaxation for Solving Large-Margin Classifiers in Hyperbolic Space
by Sheng Yang, Peihan Liu, Cengiz Pehlevan
First submitted to arxiv on: 27 May 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Optimization and Control (math.OC)
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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 A novel approach is proposed for extending Support Vector Machines (SVMs) to hyperbolic spaces, which exhibit superior performance in handling hierarchical data structures compared to Euclidean spaces. The traditional method of using projected gradient descent to solve hyperbolic SVMs is found to be sensitive to hyperparameters and initializations, often leading to suboptimal solutions. To address this challenge, the authors reformulate the problem as a polynomial optimization and apply semidefinite relaxation and sparse moment-sum-of-squares relaxation to approximate the optima. Experimental results demonstrate that these methods outperform projected gradient descent in various tasks. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary In this study, researchers find a new way to make machines learn from data with hierarchical structures better. This is important because some types of data have built-in patterns that are hard for computers to understand. The old way of solving this problem didn’t work well and needed adjustments to get good results. To fix this, the team changed the math behind the problem and used new techniques to find a solution. They tested their method with many different datasets and found it performed better than before. |
Keywords
» Artificial intelligence » Gradient descent » Optimization
