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08/23/2023
How to Protect Copyright Data in Optimization of Large Language Models?
Large language models (LLMs) and generative AI have played a transformat...
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05/11/2023
Spectral Clustering on Large Datasets: When Does it Work? Theory from Continuous Clustering and Density Cheeger-Buser
Spectral clustering is one of the most popular clustering algorithms tha...
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11/23/2020
Functions that Preserve Manhattan Distances
What functions, when applied to the pairwise Manhattan distances between...
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11/04/2020
Algorithms and Hardness for Linear Algebra on Geometric Graphs
For a function 𝖪 : ℝ^d×ℝ^d→ℝ_≥ 0, and a set P = { x_1, …, x_n}⊂ℝ^d of n ...
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04/20/2020
Weighted Cheeger and Buser Inequalities, with Applications to Clustering and Cutting Probability Densities
In this paper, we show how sparse or isoperimetric cuts of a probability...
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08/16/2018
Constant Arboricity Spectral Sparsifiers
We show that every graph is spectrally similar to the union of a constan...
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05/30/2018
Graph Sparsification, Spectral Sketches, and Faster Resistance Computation, via Short Cycle Decompositions
We develop a framework for graph sparsification and sketching, based on ...
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09/22/2017
Intrinsic Metrics: Exact Equality between a Geodesic Metric and a Graph metric
Some researchers have proposed using non-Euclidean metrics for clusterin...
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09/22/2017