Recovering Imbalanced Clusters via Gradient-Based Projection Pursuit

• URL: http://arxiv.org/abs/2502.02668v1
• Date: Tue, 04 Feb 2025 19:18:17 GMT
• Title: Recovering Imbalanced Clusters via Gradient-Based Projection Pursuit
• Authors: Martin Eppert, Satyaki Mukherjee, Debarghya Ghoshdastidar,
• Abstract summary: We propose a method for recovering projections containing either Imbalanced Clusters or a Bernoulli-Rademacher distribution. 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. We experimentally evaluate our method's applicability to real-world data using FashionMNIST and the Human Activity Recognition dataset.
• Score: 7.141484637056533
• License:
• 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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