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Data are the most fundamental and pervasive cognitive objects in the brain that link the real-world entities and attributes to mental abstractions via sensation and quantification. Data are an abstract representation of the quantity of realistic entities or abstract objects against specific measurement scales (von Neumann, 1946; Ullman & Widom, 1997; Tucker, 1992; Lewis & Papadimitriou, 1998; Sternberg, 1998; Chicurel, 2000; Chapra & Canale, 2002; Jacobs, 2009; Hassanien et al., 2015; Wang, 2003, 2007, 2015a, 2016c).
Big data are extremely large-scaled heterogeneous data in quantity, complexity, retain, retrieval, semantics, cognition, distribution, maintenance, and processing costs. Big data are pervasively manipulated across contemporary science disciplines such as computer science, information science, cognitive informatics, web-based computing, cloud computing, social networks and computational intelligence (Wang, 2015a). The inherent complexity of big data and the exponentially increasing demands on big data have create unprecedented problems in all aspects and phases of big data engineering. The challenges stem from not only the oversized magnificent and complexity of datasets beyond classical handling capacity of theories and technologies, but also the extended domain of big data out of the traditional domain of real numbers (R) (Wang, 2016c).
Basic characteristics of big data are unstructured, heterogeneous, monotonous growing, mostly nonverbal, hybrid, unclear semantics, decay in consistency, and increase in entropy over time (Wang, 2006, 2016b). Big data plays an indispensable role not only in a wide range of engineering applications, but also in the cognitive mechanisms of human sensation, quantification, qualification, estimation, memory, and reasoning (Jacobs, 2009; Snijders et al., 2012; Wang, 2015a; Wang et al., 2016, 2017). The taxonomy of cognitive objects represented in human brains can be classified into four forms known as data, information, knowledge, and intelligence in a hierarchical structure from the bottom up according to their levels of abstraction (Berkeley, 1954; Turing, 1950; Shannon, 1956; von Neumann, 1958; McCarthy et al. 1955; McCulloch, 1965; Debenham, 1989; Bender, 2000; Hassanien et al., 2015; Wang, 2009a, 2010, 2014a, 2015a, 2015c, 2016a, 2016d). It is recognized that almost all fields and hierarchical levels of human activities generate exponentially increasing data, because data plays an indispensable role in fundamental cognitive mechanisms of humans such as sensation, quantification, qualification, estimation, memory, reasoning, and knowledge generation.