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Poster
Cluster Trees on Manifolds
Sivaraman Balakrishnan · Srivatsan Narayanan · Alessandro Rinaldo · Aarti Singh · Larry Wasserman

Thu Dec 05 07:00 PM -- 11:59 PM (PST) @ Harrah's Special Events Center, 2nd Floor
in Poster Session »
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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Author Information

Sivaraman Balakrishnan (CMU)
Srivatsan Narayanan (CMU)
Alessandro Rinaldo (CMU)
Aarti Singh (CMU)
Larry Wasserman (Carnegie Mellon University)

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