On the Numerical Rank of Radial Basis Function Kernels in High Dimensions

DOI10.1137/17M1135803zbMath1455.65068arXiv1706.07883WikidataQ128719408 ScholiaQ128719408MaRDI QIDQ4644416

Ruoxi Wang, Yingzhou Li, Eric Darve

Publication date: 7 January 2019

Published in: SIAM Journal on Matrix Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1706.07883

zbMATH Keywords

Fourier expansionradial basis functionshigh-dimensional datalow-rank approximationChebyshev expansionkernel matrices

Mathematics Subject Classification ID

Factorization of matrices (15A23) Best approximation, Chebyshev systems (41A50) Eigenvalues, singular values, and eigenvectors (15A18) Multidimensional problems (41A63) Approximation by polynomials (41A10) Fourier coefficients, Fourier series of functions with special properties, special Fourier series (42A16) Numerical methods for low-rank matrix approximation; matrix compression (65F55)

Related Items (5)

Kernel Approximation on Algebraic Varieties ⋮ Randomized approximate class-specific kernel spectral regression analysis for large-scale face verification ⋮ HODLR\(d\)D: a new black-box fast algorithm for \(N\)-body problems in \(d\)-dimensions with guaranteed error bounds. Applications to integral equations and support vector machines ⋮ Spectral Properties of Kernel Matrices in the Flat Limit ⋮ Block Basis Factorization for Scalable Kernel Evaluation

Uses Software

• rbf_qr

Cites Work

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