Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4605060 | Applied and Computational Harmonic Analysis | 2015 | 21 Pages |
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.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
C.K. Chui, F. Filbir, H.N. Mhaskar,