Journal article
Use of operator defect identities in multi-channel signal plus residual-analysis via iterated products and telescoping energy-residuals: Applications to kernels in machine learning
Journal of mathematical analysis and applications, Vol.565(1), 130935
01/01/2027
DOI: 10.1016/j.jmaa.2026.130935
Abstract
We present a new operator theoretic framework for analysis of complex systems with intrinsic subdivisions into components, taking the form of “residuals” in general, and “telescoping energy residuals” in particular. We prove new results which yield admissibility/effectiveness, and new a priori bounds on energy residuals. Applications include infinite-dimensional Kaczmarz theory for λn-relaxed variants, and λn-effectiveness. And we give applications of our framework to generalized machine learning algorithms, greedy Kernel Principal Component Analysis (KPCA), which provides an exact telescoping residual identity and explicit finite-step energy decomposition, which are not usually available in standard PCA/KPCA analyses.
Details
- Title: Subtitle
- Use of operator defect identities in multi-channel signal plus residual-analysis via iterated products and telescoping energy-residuals: Applications to kernels in machine learning
- Creators
- Palle E.T. Jorgensen - University of IowaMyung-Sin Song - Southern Illinois University EdwardsvilleJames Tian - Mathematical Reviews, 535 W. William St, Suite 210, Ann Arbor, MI 48103, USA
- Resource Type
- Journal article
- Publication Details
- Journal of mathematical analysis and applications, Vol.565(1), 130935
- DOI
- 10.1016/j.jmaa.2026.130935
- ISSN
- 0022-247X
- eISSN
- 1096-0813
- Publisher
- Elsevier Inc
- Language
- English
- Date published
- 01/01/2027
- Academic Unit
- Mathematics
- Record Identifier
- 9985183130502771
Metrics
1 Record Views