Mode and Ridge Estimation in Euclidean and Directional Product Spaces: A Mean Shift Approach
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2021
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| Acceso en línea: | |
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| _version_ | 1866910935313022976 |
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| author | Zhang, Yikun Chen, Yen-Chi |
| author_facet | Zhang, Yikun Chen, Yen-Chi |
| contents | The set of local modes and density ridge lines are important summary characteristics of the data-generating distribution. In this work, we focus on estimating local modes and density ridges from point cloud data in a product space combining two or more Euclidean and/or directional metric spaces. Specifically, our approach extends the (subspace constrained) mean shift algorithm to such product spaces, addressing potential challenges in the generalization process. We establish the algorithmic convergence of the proposed methods, along with practical implementation guidelines. Experiments on simulated and real-world datasets demonstrate the effectiveness of our proposed methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2110_08505 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Mode and Ridge Estimation in Euclidean and Directional Product Spaces: A Mean Shift Approach Zhang, Yikun Chen, Yen-Chi Machine Learning Methodology The set of local modes and density ridge lines are important summary characteristics of the data-generating distribution. In this work, we focus on estimating local modes and density ridges from point cloud data in a product space combining two or more Euclidean and/or directional metric spaces. Specifically, our approach extends the (subspace constrained) mean shift algorithm to such product spaces, addressing potential challenges in the generalization process. We establish the algorithmic convergence of the proposed methods, along with practical implementation guidelines. Experiments on simulated and real-world datasets demonstrate the effectiveness of our proposed methods. |
| title | Mode and Ridge Estimation in Euclidean and Directional Product Spaces: A Mean Shift Approach |
| topic | Machine Learning Methodology |
| url | https://arxiv.org/abs/2110.08505 |