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Spectral Clustering on Large Datasets: When Does it Work? Theory from Continuous Clustering and Density Cheeger-Buser
We provide theoretically-informed intuition about spectral clustering on large data sets drawn from probability densities, by proving when a continuous form of spectral clustering considered by past researchers (the unweighted spectral cut of a probability density) finds good clusters of the underlying density itself.
Metric Transforms and Low Rank Matrices via Representation Theory of the Real Hyperrectangle
This completes the theory of Manhattan to Manhattan metric transforms initiated by Assouad in 1980.
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