An alternative to EM for Gaussian mixture models: batch and stochastic Riemannian optimization

DOI10.1007/s10107-019-01381-4zbMath1441.62168arXiv1706.03267OpenAlexW2627006445WikidataQ115385318 ScholiaQ115385318MaRDI QIDQ2188245

Reshad Hosseini, Suvrit Sra

Publication date: 10 June 2020

Published in: Mathematical Programming. Series A. Series B (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1706.03267

zbMATH Keywords

stochastic optimizationpositive definite matricesretractionGaussian mixture modelsRiemannian optimizationnon-asymptotic rate of convergence

Mathematics Subject Classification ID

Statistics on manifolds (62R30) Classification and discrimination; cluster analysis (statistical aspects) (62H30) Stochastic programming (90C15) Applications of differential geometry to data and computer science (53Z50)

Related Items

Accelerated Optimization in the PDE Framework: Formulations for the Manifold of Diffeomorphisms ⋮ TLS-EM algorithm of mixture density models for exponential families ⋮ Fenchel conjugate via Busemann function on Hadamard manifolds ⋮ A trust region method for solving multicriteria optimization problems on Riemannian manifolds ⋮ Learning with symmetric positive definite matrices via generalized Bures-Wasserstein geometry ⋮ Recent Advances in Stochastic Riemannian Optimization ⋮ Nonconvex weak sharp minima on Riemannian manifolds ⋮ A Riemannian Newton trust-region method for fitting Gaussian mixture models ⋮ Large-sample properties of unsupervised estimation of the linear discriminant using projection pursuit

Uses Software

• Manopt
• PMTK
• k-means++
• PRMLT

Cites Work

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