期刊
BERNOULLI
卷 23, 期 1, 页码 288-328出版社
INT STATISTICAL INST
DOI: 10.3150/15-BEJ744
关键词
clustering; homology; kernel density estimation; topological data analysis
资金
- AFOSR [FA9550-10-1-0436, 113039]
- NSF [DMS-1127914, CCF-1049290]
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [1418261] Funding Source: National Science Foundation
We introduce a consistent estimator for the homology (an algebraic structure representing connected components and cycles) of level sets of both density and regression functions. Our method is based on kernel estimation. We apply this procedure to two problems: (1) inferring the homology structure of manifolds from noisy observations, (2) inferring the persistent homology (a multi-scale extension of homology) of either density or regression functions. We prove consistency for both of these problems. In addition to the theoretical results, we demonstrate these methods on simulated data for binary regression and clustering applications.
作者
我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。
推荐
暂无数据