Geometric Optimization in Machine Learning

DOI10.1007/978-3-319-45026-1_3zbMath1401.68269OpenAlexW2528306447MaRDI QIDQ2954275

Suvrit Sra, Reshad Hosseini

Publication date: 12 January 2017

Published in: Algorithmic Advances in Riemannian Geometry and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-319-45026-1_3

Mathematics Subject Classification ID

Learning and adaptive systems in artificial intelligence (68T05)

Uses Software

• Manopt
• PMTK
• Matrix Means Toolbox
• MixEst
• k-means++

Cites Work

• Matrix power means and the Karcher mean
• Determinantal processes and independence
• Redescending \(M\)-estimates of multivariate location and scatter
• Computing the Karcher mean of symmetric positive definite matrices
• Means of Hermitian positive-definite matrices based on the log-determinant \(\alpha\)-divergence function
• A survey and comparison of contemporary algorithms for computing the matrix geometric mean
• Geometric means of structured matrices
• Positive definite matrices
• Convex analysis and optimization in Hadamard spaces
• Introduction to Smooth Manifolds
• Nonlinear Perron–Frobenius Theory
• Optimization Methods on Riemannian Manifolds and Their Application to Shape Space
• Manopt, a Matlab toolbox for optimization on manifolds
• A Broyden Class of Quasi-Newton Methods for Riemannian Optimization
• Mixture Densities, Maximum Likelihood and the EM Algorithm
• Efficient Greedy Learning of Gaussian Mixture Models
• Unified Framework to Regularized Covariance Estimation in Scaled Gaussian Models
• Complex Elliptically Symmetric Distributions: Survey, New Results and Applications
• Geodesic Convexity and Covariance Estimation
• Conic Geometric Optimization on the Manifold of Positive Definite Matrices
• A Differential Geometric Approach to the Geometric Mean of Symmetric Positive-Definite Matrices
• Invariant metrics, contractions and nonlinear matrix equations
• On Certain Contraction Mappings in a Partially Ordered Vector Space
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