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Chui, C.K.* ; Filbir, F. ; Mhaskar, H.N.*

Representation of functions on big data: Graphs and trees.

Appl. Comput. Harmon. Anal. 38, 489-509 (2014)
Open Access Green as soon as Postprint is submitted to ZB.
Many current problems dealing with big data can be cast efficiently as function approximation on graphs. The information in the graph structure can often be reorganized in the form of a tree; for example, using clustering techniques. The objective of this paper is to develop a new system of orthogonal functions on weighted trees. The system is local, easily implementable, and allows for scalable approximations without saturation. A novelty of our orthogonal system is that the Fourier projections are uniformly bounded in the supremum norm. We describe in detail a construction of wavelet-like representations and estimate the degree of approximation of functions on the trees.
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Publication type Article: Journal article
Document type Scientific Article
Keywords Analysis On Graphs And Trees ; Big Data ; Function Approximation On Big Data ; Wavelet-like Representation; Diffusion Maps; Laplacian; Wavelets; Frames
ISSN (print) / ISBN 1063-5203
e-ISSN 1096-603X
Quellenangaben Volume: 38, Issue: 3, Pages: 489-509 Article Number: , Supplement: ,
Publisher Academic Press
Publishing Place San Diego, Calif. [u.a.]
Reviewing status Peer reviewed