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
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
آنالیز ریاضی
پیش نمایش صفحه اول مقاله
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
Journal: Journal of Mathematical Analysis and Applications - Volume 469, Issue 2, 15 January 2019, Pages 765-807
نویسندگان
Palle E.T. Jorgensen, Erin P.J. Pearse,