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Representation of functions on big data associated with directed graphs

Chui, Charles K. and Mhaskar, H. N. and Zhuang, Xiaosheng (2018) Representation of functions on big data associated with directed graphs. Applied and Computational Harmonic Analysis, 44 (1). pp. 165-188. ISSN 1063-5203. http://resolver.caltech.edu/CaltechAUTHORS:20170526-090358440

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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.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1016/j.acha.2016.12.005DOIArticle
http://www.sciencedirect.com/science/article/pii/S1063520317300027PublisherArticle
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 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.
Funders:
Funding AgencyGrant Number
Army Research Office (ARO)W911NF-15-1-0385
Research Grants Council of Hong KongCityU 11304414
City University of Hong Kong7200462
City University of Hong Kong7004445
Record Number:CaltechAUTHORS:20170526-090358440
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20170526-090358440
Official Citation:Charles K. Chui, H.N. Mhaskar, Xiaosheng Zhuang, Representation of functions on big data associated with directed graphs, Applied and Computational Harmonic Analysis, Volume 44, Issue 1, January 2018, Pages 165-188, ISSN 1063-5203, https://doi.org/10.1016/j.acha.2016.12.005. (http://www.sciencedirect.com/science/article/pii/S1063520317300027)
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:77798
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:26 May 2017 16:41
Last Modified:06 Oct 2017 16:25

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