Journal article
Continuum versus discrete networks, graph Laplacians, and reproducing kernel Hilbert spaces
Journal of mathematical analysis and applications, Vol.469(2), pp.765-807
01/15/2019
DOI: 10.1016/j.jmaa.2018.09.035
Abstract
Motivated by applications to machine learning, we construct a reversible and irreducible Markov chain whose state space is a certain collection of measurable sets of a chosen l.c.h. space X. We study the resulting network (connected undirected graph), including transience, Royden and Riesz decompositions, and kernel factorization. We describe a construction for Hilbert spaces of signed measures which comes equipped with a new notion of reproducing kernels and there is a unique solution to a regularized optimization problem involving the approximation of L2 functions by functions of finite energy. The latter has applications to machine learning (for Markov random fields, for example).
Details
- Title: Subtitle
- Continuum versus discrete networks, graph Laplacians, and reproducing kernel Hilbert spaces
- Creators
- Palle E.T Jorgensen - University of Iowa, Iowa City, IA 52246-1419, USAErin P.J Pearse - California State Polytechnic University, San Luis Obispo, CA 93405-0403, USA
- Resource Type
- Journal article
- Publication Details
- Journal of mathematical analysis and applications, Vol.469(2), pp.765-807
- DOI
- 10.1016/j.jmaa.2018.09.035
- ISSN
- 0022-247X
- eISSN
- 1096-0813
- Publisher
- Elsevier Inc
- Language
- English
- Date published
- 01/15/2019
- Academic Unit
- Mathematics
- Record Identifier
- 9983985913302771
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