Local versions of sum-of-norms clustering
This work addresses clustering challenges for data analysis by improving separation in close clusters, though it appears incremental as a localized variant of an existing method.
The authors tackled the problem of clustering multivariate data by proposing a localized version of sum-of-norms clustering, showing it can separate arbitrarily close balls in the stochastic ball model and proving a quantitative error bound in terms of datapoints and localization length.
Sum-of-norms clustering is a convex optimization problem whose solution can be used for the clustering of multivariate data. We propose and study a localized version of this method, and show in particular that it can separate arbitrarily close balls in the stochastic ball model. More precisely, we prove a quantitative bound on the error incurred in the clustering of disjoint connected sets. Our bound is expressed in terms of the number of datapoints and the localization length of the functional.