Representation of functions on big data: Graphs and trees

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 orthogon...

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Bibliographic Details
Published in:Applied and computational harmonic analysis 2015-05, Vol.38 (3), p.489-509
Main Authors: Chui, C.K., Filbir, F., Mhaskar, H.N.
Format: Article
Language:English
Subjects:
Analysis on graphs and trees
Big data
Function approximation on big data
Wavelet-like representation
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Summary: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.
ISSN:1063-5203
1096-603X
DOI:10.1016/j.acha.2014.06.006