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arXiv · 2502.02668

Recovering Imbalanced Clusters via Gradient-Based Projection Pursuit

Martin Eppert·Satyaki Mukherjee·Debarghya Ghoshdastidar
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Abstract

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.

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Martin Eppert, Satyaki Mukherjee, Debarghya Ghoshdastidar. 2025-02-04. Recovering Imbalanced Clusters via Gradient-Based Projection Pursuit. https://arxiv.org/abs/2502.02668

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