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Analysis and Applications
Article . 2013 . Peer-reviewed
Data sources: Crossref
https://dx.doi.org/10.48550/ar...
Article . 2011
License: arXiv Non-Exclusive Distribution
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ON THE INCLUSION RELATION OF REPRODUCING KERNEL HILBERT SPACES

Authors: Haizhang Zhang; Liang Zhao;

ON THE INCLUSION RELATION OF REPRODUCING KERNEL HILBERT SPACES

Abstract

To help understand various reproducing kernels used in applied sciences, we investigate the inclusion relation of two reproducing kernel Hilbert spaces. Characterizations in terms of feature maps of the corresponding reproducing kernels are established. A full table of inclusion relations among widely-used translation invariant kernels is given. Concrete examples for Hilbert–Schmidt kernels are presented as well. We also discuss the preservation of such a relation under various operations of reproducing kernels. Finally, we briefly discuss the special inclusion with a norm equivalence.

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Keywords

Mathematics - Functional Analysis, FOS: Computer and information sciences, Computer Science - Machine Learning, FOS: Mathematics, Functional Analysis (math.FA), Machine Learning (cs.LG)

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    popularity
    This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
    Top 10%
    influence
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citations
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
6
Top 10%
Average
Average
Green
bronze