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On the Cognitive and Theoretical Foundations of Big Data Science and Engineering

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  • Yingxu Wang

    (International Institute of Cognitive Informatics and Cognitive Computing (ICIC), Department of Electrical and Computer Engineering, Schulich School of Engineering and Hotchkiss Brain Institute, University of Calgary, 2500 University Drive NW, Calgary, AB, Canada T2N 1N4, Canada2Information Systems Lab, Stanford University, Stanford, CA 94305, USA)

Abstract

Big data play an indispensable role not only in the cognitive mechanisms of human sensation, quantification, qualification, estimation, memory, and reasoning, but also in a wide range of engineering applications. A basic study on the theoretical foundations of big data science is presented with a coherent set of general principles and analytic methodologies for big data systems. Cognitive foundations of big data are explored in order to formally explain the origination and nature of big data. A set of mathematical models of big data are created that rigorously elicit the general essences and patterns of big data across pervasive domains in sciences, engineering, and societies. A significant finding towards big data science is that big data systems in nature are a recursive n-dimensional-typed hyperstructure (RNTHS) rather than pure numbers. The fundamental topological property of big data reveals a set of denotational mathematical solutions for dealing with inherited complexities and unprecedented challenges in big data engineering.

Suggested Citation

  • Yingxu Wang, 2017. "On the Cognitive and Theoretical Foundations of Big Data Science and Engineering," New Mathematics and Natural Computation (NMNC), World Scientific Publishing Co. Pte. Ltd., vol. 13(02), pages 101-117, July.
    • Handle: RePEc:wsi:nmncxx:v:13:y:2017:i:02:n:s1793005717400026
    DOI: 10.1142/S1793005717400026
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    References listed on IDEAS

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    1. Yingxu Wang, 2016. "On Cognitive Foundations and Mathematical Theories of Knowledge Science," International Journal of Cognitive Informatics and Natural Intelligence (IJCINI), IGI Global, vol. 10(2), pages 1-25, April.
    2. Yingxu Wang, 2011. "Inference Algebra (IA): A Denotational Mathematics for Cognitive Computing and Machine Reasoning (I)," International Journal of Cognitive Informatics and Natural Intelligence (IJCINI), IGI Global, vol. 5(4), pages 61-82, October.
    3. Yingxu Wang, 2015. "On the Mathematical Theories and Cognitive Foundations of Information," International Journal of Cognitive Informatics and Natural Intelligence (IJCINI), IGI Global, vol. 9(3), pages 42-64, July.
    4. Yingxu Wang, 2012. "Inference Algebra (IA): A Denotational Mathematics for Cognitive Computing and Machine Reasoning (II)," International Journal of Cognitive Informatics and Natural Intelligence (IJCINI), IGI Global, vol. 6(1), pages 21-47, January.
    5. Marina Chicurel, 2000. "Databasing the brain," Nature, Nature, vol. 406(6798), pages 822-825, August.
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    Cited by:

    1. Zhaohao Sun & Paul P. Wang, 2017. "Big Data, Analytics, and Intelligence: An Editorial Perspective," New Mathematics and Natural Computation (NMNC), World Scientific Publishing Co. Pte. Ltd., vol. 13(02), pages 75-81, July.

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