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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)

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Open Access Green as soon as Postprint is submitted to ZB.

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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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