Multidimensional scaling of noisy high dimensional data

DOI10.1016/j.acha.2020.11.006zbMath1461.62235arXiv1801.10229OpenAlexW3106887080MaRDI QIDQ2659741

Matan Gavish, Erez Peterfreund

Publication date: 26 March 2021

Published in: Applied and Computational Harmonic Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1801.10229

zbMATH Keywords

dimensionality reductionmultidimensional scalingEuclidean embeddingsingular value thresholdingoptimal shrinkageMDS+

Mathematics Subject Classification ID

Computational methods for problems pertaining to statistics (62-08) Estimation in multivariate analysis (62H12) Statistical aspects of big data and data science (62R07)

Related Items

Design-free estimation of integrated covariance matrices for high-frequency data

Uses Software

• MNIST

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Reconstruction of a low-rank matrix in the presence of Gaussian noise
• Fluctuations of the extreme eigenvalues of finite rank deformations of random matrices
• The singular values and vectors of low rank perturbations of large rectangular random matrices
• Minimax risk of matrix denoising by singular value thresholding
• Convergence and prediction of principal component scores in high-dimensional settings
• Spectral analysis of large dimensional random matrices
• Developments of the generative topographic mapping
• Modern multidimensional scaling: theory and applications
• On the distribution of the largest eigenvalue in principal components analysis
• Optimal shrinkage of eigenvalues in the spiked covariance model
• Diffusion maps
• A generalized solution of the orthogonal Procrustes problem
• Phase transition of the largest eigenvalue for nonnull complex sample covariance matrices
• Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis
• Nonmetric multidimensional scaling. A numerical method
• Multidimensional scaling. I: Theory and method
• Random Matrix Methods for Wireless Communications
• The Optimal Hard Threshold for Singular Values is <inline-formula> <tex-math notation="TeX">\(4/\sqrt {3}\) </tex-math></inline-formula>
• Non-Parametric Detection of the Number of Signals: Hypothesis Testing and Random Matrix Theory
• Metric Learning
• Optimal Shrinkage of Singular Values
• DISTRIBUTION OF EIGENVALUES FOR SOME SETS OF RANDOM MATRICES
• Some distance properties of latent root and vector methods used in multivariate analysis