Complex Interpolation of Matrices with an application to Multi-Manifold Learning
Not on the map. Why?
Abstract (arXiv)
Given two symmetric positive-definite matrices A, B ∈ ℝn × n, we study the spectral properties of the interpolation A1-x Bx for 0 ≤ x ≤ 1. The presence of `common structures' in A and B, eigenvectors pointing in a similar direction, can be investigated using this interpolation perspective. Generically, exact log-linearity of the operator norm |A1-x Bx| is equivalent to the existence of a shared eigenvector in the original matrices; stability bounds show that approximate log-linearity forces principal singular vectors to align with leading eigenvectors of both matrices. These results give rise to and provide theoretical justification for a multi-manifold learning framework that identifies common and distinct latent structures in multiview data.
Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 6 of its 25 references that are in the map. First posted on arXiv 15 Apr 2026.
Builds on
6 of 25 references.
References · 6
- 2015Nonparametric Canonical Correlation Analysiscited by 22
- 2016Latent common manifold learning with alternating diffusion: analysis and applicationscited by 16
- 2018Recovering Hidden Components in Multimodal Data with Composite Diffusion Operatorscited by 10
- 2022Spatiotemporal Analysis Using Riemannian Composition of Diffusion Operatorscited by 6
- 2020Spectral Discovery of Jointly Smooth Features for Multimodal Datacited by 5
- 2021A common variable minimax theorem for graphscited by 5
Built on by
Not cited yet.