6 papers
Locality Sensitive Hashing in Hyperbolic Space
Chengyuan Deng, Jie Gao, Kevin Lu +2
For a metric space , a family of locality sensitive hash functions is called sensitive if a randomly chosen function ha…
Johnson-Lindenstrauss Lemma Beyond Euclidean Geometry
Chengyuan Deng, Jie Gao, Kevin Lu +2
The Johnson-Lindenstrauss (JL) lemma is a cornerstone of dimensionality reduction in Euclidean space, but its applicability to non-Euclidean data has remained limited. This paper e…
On the Price of Differential Privacy for Hierarchical Clustering
Chengyuan Deng, Jie Gao, Jalaj Upadhyay +2
Hierarchical clustering is a fundamental unsupervised machine learning task with the aim of organizing data into a hierarchy of clusters. Many applications of hierarchical clusteri…
Neuc-MDS: Non-Euclidean Multidimensional Scaling Through Bilinear Forms
Chengyuan Deng, Jie Gao, Kevin Lu +3
We introduce Non-Euclidean-MDS (Neuc-MDS), an extension of classical Multidimensional Scaling (MDS) that accommodates non-Euclidean and non-metric inputs. The main idea is to gener…
Low Sensitivity Hopsets
Vikrant Ashvinkumar, Aaron Bernstein, Chengyuan Deng +2
Given a weighted graph , a -hopset is an edge set such that for any , where can reach in , there is a path from to in $G \…
The Discrepancy of Shortest Paths
Greg Bodwin, Chengyuan Deng, Jie Gao +3
The hereditary discrepancy of a set system is a certain quantitative measure of the pseudorandom properties of the system. Roughly, hereditary discrepancy measures how well one can…