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Published May 2015 | public
Journal Article

Representation of functions on big data: Graphs and trees

Abstract

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.

Additional Information

© 2014 Elsevier Inc. Received 20 March 2014; Received in revised form 3 June 2014; Accepted 22 June 2014; Available online 1 July 2014. We thank Professor K. Thirunavukkarasu (K.T. Arasu) at Wright State University for his comments on our graph theory related definitions. We also thank the anonymous reviewer for comments that helped us improve the presentation in the first draft of this paper. His research was supported by ARO Grant # W911 NF-11-1-0426.

Additional details

Created:
August 22, 2023
Modified:
October 23, 2023