Recovering Imbalanced Clusters via Gradient-Based Projection Pursuit
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866911028938276864 |
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| author | Eppert, Martin Mukherjee, Satyaki Ghoshdastidar, Debarghya |
| author_facet | Eppert, Martin Mukherjee, Satyaki Ghoshdastidar, Debarghya |
| contents | Projection Pursuit is a classic exploratory technique for finding interesting projections of a dataset. We propose a method for recovering projections containing either Imbalanced Clusters or a Bernoulli-Rademacher distribution using a gradient-based technique to optimize the projection index. As sample complexity is a major limiting factor in Projection Pursuit, we analyze our algorithm's sample complexity within a Planted Vector setting where we can observe that Imbalanced Clusters can be recovered more easily than balanced ones. Additionally, we give a generalized result that works for a variety of data distributions and projection indices. We compare these results to computational lower bounds in the Low-Degree-Polynomial Framework. Finally, we experimentally evaluate our method's applicability to real-world data using FashionMNIST and the Human Activity Recognition Dataset, where our algorithm outperforms others when only a few samples are available. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_02668 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Recovering Imbalanced Clusters via Gradient-Based Projection Pursuit Eppert, Martin Mukherjee, Satyaki Ghoshdastidar, Debarghya Machine Learning Projection Pursuit is a classic exploratory technique for finding interesting projections of a dataset. We propose a method for recovering projections containing either Imbalanced Clusters or a Bernoulli-Rademacher distribution using a gradient-based technique to optimize the projection index. As sample complexity is a major limiting factor in Projection Pursuit, we analyze our algorithm's sample complexity within a Planted Vector setting where we can observe that Imbalanced Clusters can be recovered more easily than balanced ones. Additionally, we give a generalized result that works for a variety of data distributions and projection indices. We compare these results to computational lower bounds in the Low-Degree-Polynomial Framework. Finally, we experimentally evaluate our method's applicability to real-world data using FashionMNIST and the Human Activity Recognition Dataset, where our algorithm outperforms others when only a few samples are available. |
| title | Recovering Imbalanced Clusters via Gradient-Based Projection Pursuit |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2502.02668 |