Representation of functions on big data associated with directed graphs

Creators: Chui, Charles K.; Mhaskar, H. N.; Zhuang, Xiaosheng

Abstract

This paper is an extension of the previous work of Chui et al. (2015) [4], not only from numeric data to include non-numeric data as in that paper, but also from undirected graphs to directed graphs (called digraphs, for simplicity). Besides theoretical development, this paper introduces effective mathematical tools in terms of certain data-dependent orthogonal systems for function representation and analysis directly on the digraphs. In addition, this paper also includes algorithmic development and discussion of various experimental results on such data-sets as CORA, Proposition, and Wiki-votes.

Additional Information

© 2017 Elsevier Inc. Received 13 June 2016, Revised 12 November 2016, Accepted 21 December 2016, Available online 26 January 2017. Communicated by Zuowei Shen. The research of this author is supported by ARO Grant W911NF-15-1-0385. The research of this author is supported in part by the Research Grants Council of Hong Kong (Project No. CityU 11304414) and City University of Hong Kong (Project No.: 7200462 and 7004445). We thank Professors Percus and Hunter at Claremont Graduate University and Claremont McKenna College respectively for many useful discussions as well as their help in securing the Proposition data set, which was sent to us by Dr. Linhong Zhu at USC Information Sciences Institute in Marina Del Ray, California. We thank Dr. Garcia-Cardona for giving us a C code for the algorithm MBO.

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