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arXiv research

A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.

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7 results for “sum-of-norms”

Recovery of a mixture of Gaussians by sum-of-norms clusteringcs.LG

Sum-of-norms clustering recovers mixtures of Gaussians even with infinite samples.

problem Recovering a mixture of Gaussians from a large number of samples.

method Sum-of-norms clustering with equal weights, convex optimization.

result Sum-of-norms clustering can recover mixtures of Gaussians even as the number of samples tends to infinity.

sum-of-norms clustering Gaussian mixture convex optimization infinite samples agglomeration conjecture

2019-02-19abs ↗pdf ↗

Local versions of sum-of-norms clusteringcs.LG

Localized sum-of-norms clustering separates balls in data.

problem Clustering arbitrarily close data points in multivariate data.

method Localized sum-of-norms optimization for clustering.

result Proves a bound on clustering error in stochastic ball model.

sum-of-norms clustering localization stochastic ball model clustering error

2021-09-20abs ↗pdf ↗

Certifying clusters from sum-of-norms clusteringcs.LG

This paper certifies cluster assignments from sum-of-norms clustering algorithms.

problem Certifying the correct cluster assignments from approximate solutions of sum-of-norms clustering.

method Presented a clustering test that identifies and certifies the correct cluster assignment from an approximate solution.

result The correct cluster assignment is guaranteed to be certified by a primal-dual path following algorithm after sufficient iterations.

sum-of-norms clustering clustering certification convex optimization subgradient descent ADMM

2020-06-19abs ↗pdf ↗

Recovery Bounds on Class-Based Optimal Transport: A Sum-of-Norms Regularization Frameworkcs.LG

Develops a new OT framework for class-based data with improved robustness.

problem Understand and recover class structure in optimal transport schemes.

method Proposes a convex OT program with sum-of-norms regularization and an accelerated proximal algorithm.

result The new regularizer preserves class structure better and is more robust to data geometry.

optimal transport class-based structure sum-of-norms regularization proximal algorithm

2019-03-09abs ↗pdf ↗

Re-embedding data to strengthen recovery guarantees of clusteringcs.LG

A new clustering method improves recovery guarantees by re-embedding data.

problem Improving recovery guarantees in clustering algorithms.

method Chaining four techniques: leapfrog distances, multidimensional scaling, spectral methods, and sum-of-norms clustering.

result Re-embedding data improves recovery guarantees of clustering.

clustering recovery guarantees sum-of-norms clustering spectral methods multidimensional scaling

2023-01-26abs ↗pdf ↗

Sum-of-norms regularized Nonnegative Matrix Factorizationcs.LG

SON-NMF estimates nonnegative rank on-the-fly for NMF.

problem Estimating the nonnegative rank of data in NMF.

method Sum-of-norms (SON) regularization to reduce rank, combined with a first-order BCD algorithm.

result SON-NMF can automatically estimate the rank from data without prior knowledge.

nonnegative matrix factorization rank estimation nonconvex optimization spectral variability graph-theoretic complexity

2024-06-30abs ↗pdf ↗

Convex Clustering: Model, Theoretical Guarantee and Efficient Algorithmcs.LG

Clustering is a fundamental problem in unsupervised learning. Popular methods like K-means, may suffer from poor performance as they are prone to get stuck in its local minima. Recently, the sum-of-norms (SON) model (also known as the clustering path) has been proposed in Pelckmans et al. (2005), Lindsten et al. (2011)…

2018-10-04abs ↗pdf ↗