Download Algebraic Graph Theory based Astronomical Big Data Analysis

AlGrABA: Algebraic Graph Theory based
Astronomical Big Data Analysis
Amit Kumar Mishra
Electrical Engineering Department
University of Cape Town, South Africa
Email: [email protected]
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Introduction
Applying algebra to study the properties of graphs is a classic area of research in mathematics. With the advent of big-data type challenges the use of graph is gathering
interest amongst the data processing engineers. This follows from the fact that bigdata mostly originates because of a large number of sensing nodes. Some of the recent
works have looked into developing signal processing framework based on graphs [1,2].
Tools, inspired by such work, has shown much promise [3, 4].
Representing astronomical data as a graph at each instant of data-capture is intuitive. Hence, we hypothesize that by exploring ways to 1) represent (e.g. [5]) and 2)
manipulate (e.g. [6]) the astronomical recordings in a graph framework will help not
only in presenting an elegant framework to handle and store massive amount of data,
it will also help in making the data analytics processes more robust and less prone to
noisy and false recognition-results.
In this proposed PhD project the student will work on the hypothesis that using
algebraic graph theory based approaches will make astronomical data handling and
processing faster and more robust.
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Existing Expertise at UCT
UCT hosts the SKA Research Chair in Big Data Analysis. In addition we have some
very good mathematicians working in the domain of algebraic graph theory [7]. The
proposer also has close ties with some of the best mathematicians in the domain of
algebraic graph theory [8]. As a research team we have long standing experience in
handling signal processing for huge amount of data generated from radar and radio
telescopes. These and the existing rich link our group has with SKA-SA makes us the
best place to host a study on the use of algebraic graph theory to analyse astronomical
big-data.
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Conclusion
Bigdata analysis is a rich field with manifold of approaches in it. Algebraic graph
theory can be one of the best ways to handle big-data. Hence the proposed project will
not only have very high probability to become a tool that will really be used by SKA,
it can also be a major engineering spin-off of the SKA project.
References
[1] A. Sandryhaila and J. M. Moura, “Big data analysis with signal processing on
graphs: Representation and processing of massive data sets with irregular structure,” IEEE Signal Processing Magazine, vol. 31, no. 5, pp. 80–90, 2014.
[2] D. Conte, P. Foggia, C. Sansone, and M. Vento, “Thirty years of graph matching
in pattern recognition,” International journal of pattern recognition and artificial
intelligence, vol. 18, no. 03, pp. 265–298, 2004.
[3] A. Bifet, “Mining big data in real time,” Informatica, vol. 37, no. 1, 2013.
[4] Y. Low, J. E. Gonzalez, A. Kyrola, D. Bickson, C. E. Guestrin, and J. Hellerstein, “Graphlab: A new framework for parallel machine learning,” arXiv preprint
arXiv:1408.2041, 2014.
[5] M. Belkin and P. Niyogi, “Laplacian eigenmaps for dimensionality reduction and
data representation,” Neural computation, vol. 15, no. 6, pp. 1373–1396, 2003.
[6] P. J. Slater, “Centers to centroids in graphs,” Journal of Graph Theory, vol. 2, no. 3,
pp. 209–222, 1978.
[7] P. Dankelmann, D. Erwin, W. Goddard, S. Mukwembi, and H. C. Swart, “Eccentric counts, connectivity and chordality,” Information Processing Letters, vol. 112,
no. 24, pp. 944–947, 2012.
[8] R. B. Bapat, Graphs and matrices.
Springer, 2010.
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