کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
11010168 1812551 2019 43 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Continuum versus discrete networks, graph Laplacians, and reproducing kernel Hilbert spaces
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
پیش نمایش صفحه اول مقاله
Continuum versus discrete networks, graph Laplacians, and reproducing kernel Hilbert spaces
چکیده انگلیسی
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).
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Mathematical Analysis and Applications - Volume 469, Issue 2, 15 January 2019, Pages 765-807
نویسندگان
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