2013
NeurIPS
NeurIPS 2013
Cluster Trees on Manifolds
Abstract
We investigate the problem of estimating the cluster tree for a density $f$ supported on or near a smooth $d$-dimensional manifold $M$ isometrically embedded in $\mathbb{R}^D$. We study a $k$-nearest neighbor based algorithm recently proposed by Chaudhuri and Dasgupta. Under mild assumptions on $f$ and $M$, we obtain rates of convergence that depend on $d$ only but not on the ambient dimension $D$. We also provide a sample complexity lower bound for a natural class of clustering algorithms that use $D$-dimensional neighborhoods.
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Authors
Topics
Machine Learning > Core Methods > Clustering
Machine Learning > Learning Types > Unsupervised Learning
Machine Learning > Optimization & Theory > Learning Theory
Machine Learning > Optimization & Theory > Statistical Learning
Machine Learning > Optimization & Theory > Theory
Machine Learning > Core Methods > Dimensionality Reduction
Machine Learning > Optimization & Theory > Statistics
Machine Learning > Core Methods > Density Estimation