Convex Relaxation for Solving Large-Margin Classifiers in Hyperbolic Space
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866913365016707072 |
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| author | Yang, Sheng Liu, Peihan Pehlevan, Cengiz |
| author_facet | Yang, Sheng Liu, Peihan Pehlevan, Cengiz |
| contents | Hyperbolic spaces have increasingly been recognized for their outstanding performance in handling data with inherent hierarchical structures compared to their Euclidean counterparts. However, learning in hyperbolic spaces poses significant challenges. In particular, extending support vector machines to hyperbolic spaces is in general a constrained non-convex optimization problem. Previous and popular attempts to solve hyperbolic SVMs, primarily using projected gradient descent, are generally sensitive to hyperparameters and initializations, often leading to suboptimal solutions. In this work, by first rewriting the problem into a polynomial optimization, we apply semidefinite relaxation and sparse moment-sum-of-squares relaxation to effectively approximate the optima. From extensive empirical experiments, these methods are shown to perform better than the projected gradient descent approach. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_17198 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Convex Relaxation for Solving Large-Margin Classifiers in Hyperbolic Space Yang, Sheng Liu, Peihan Pehlevan, Cengiz Machine Learning Optimization and Control Hyperbolic spaces have increasingly been recognized for their outstanding performance in handling data with inherent hierarchical structures compared to their Euclidean counterparts. However, learning in hyperbolic spaces poses significant challenges. In particular, extending support vector machines to hyperbolic spaces is in general a constrained non-convex optimization problem. Previous and popular attempts to solve hyperbolic SVMs, primarily using projected gradient descent, are generally sensitive to hyperparameters and initializations, often leading to suboptimal solutions. In this work, by first rewriting the problem into a polynomial optimization, we apply semidefinite relaxation and sparse moment-sum-of-squares relaxation to effectively approximate the optima. From extensive empirical experiments, these methods are shown to perform better than the projected gradient descent approach. |
| title | Convex Relaxation for Solving Large-Margin Classifiers in Hyperbolic Space |
| topic | Machine Learning Optimization and Control |
| url | https://arxiv.org/abs/2405.17198 |