用梯度法找数据中难发现的不均衡聚类，小样本下更有效。
Recovering Imbalanced Clusters via Gradient-Based Projection Pursuit
- 基于梯度优化投影指标，自动发现隐藏的不均衡聚类结构。
- 在少量样本下仍能准确恢复不均衡聚类，比均衡情况更容易。
- 适用于真实数据集，尤其适合样本稀缺场景下的探索分析。
投影追踪是一种经典的数据探索方法，用于寻找数据集中有趣的投影方向。本文提出一种基于梯度的方法，用于恢复包含不均衡聚类或伯努利-雷姆达赫分布的投影。由于样本量是投影追踪的主要限制，我们在一个可植入向量（Planted Vector）设定下分析了算法的样本复杂度，发现不均衡聚类比均衡聚类更容易恢复。此外，我们给出了适用于多种数据分布和投影指标的广义结果，并将其与低次多项式框架中的计算下界进行比较。最后，在FashionMNIST和人类活动识别数据集上进行了实验，验证了该方法在仅少量样本时优于现有方法的有效性。
原文摘要 · Abstract (English)
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.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。