Big data are products of human collective intelligence that are exponentially increasing in all facets of quantity, complexity, semantics, distribution, and processing costs in computer science, cognitive informatics, web-based computing, cloud computing, and computational intelligence. This paper presents fundamental big data analysis and mining technologies in the domain of social networks as a typical paradigm of big data engineering. A key principle of computational sociology known as the characteristic opinion equilibrium is revealed in social networks and electoral systems. A set of numerical and fuzzy models for collective opinion analyses is formally presented. Fuzzy data mining methodologies are rigorously described for collective opinion elicitation and benchmarking in order to enhance the conventional counting and statistical methodologies for big data analytics.
Top1. Introduction
The hierarchy of human knowledge is categorized at the levels of data, information, knowledge, and intelligence [Debenham, 1989; Bender, 1996; Wang, 2006, 2014a]. Big data is one of the fundamental phenomena of the information era of human societies [Jacobs, 2009; Snijders et al., 2012; Wang, 2014a; Wang & Wiebe, 2014]. Almost all fields and hierarchical levels of human activities generate exponentially increasing data, information, and knowledge. Therefore, big data analytics has become one of the fundamental approaches to embody the abstraction and induction principles in rational inferences where discrete data represent continuous mechanisms and semantics.
Big data are extremely large-scaled data in terms of quantity, complexity, semantics, distribution, and processing costs in computer science, cognitive informatics, web-based computing, cloud computing, and computational intelligence. Big data and formal analytic theories are a pervasive demand across almost all fields of science, engineering, and everyday lives [Chicurel, 2000; Snijders et al., 2012; Wang, 2003, 2009a, 2014a]. Typical applications of big data methodologies in sciences are such as mathematics, number theories, neuroinformatics, computing systems, IT and web systems, brain science, memory capacity, genomes, linguistics, sociology, and management science [Wang, 2015; Wang & Berwick, 2012]. Paradigms of big data applications in engineering are such as Internet technologies, web systems, search engines, telecommunications, image processing, cognitive knowledge bases, multi-media databases, data mining, online text comprehension, machine translations, cognitive informatics, and cognitive robotics [Wang, 2003, 2007b, 2009b, 2009c, 2010, 2012a, 2013a, 2013b, 2015]. Big data in the modern society are fast approaching to the order of Petabyte (1015) per year [Wiki, 2012].
Big data analytics in sociology and collective opinion elicitation in social networks are identified as an important filed where data are often complex, vague, incomplete, and counting-based [Wang & Wiebe, 2014]. Censuses and general elections are the traditional and typical domains that demand efficient big data analytic theories and methodologies beyond number counting and statistics [Emerson, 2013; Saari, 2000]. Among modern digital societies and social networks, popular opinion collection via online polls and voting systems becomes necessary for policy confirmation in general elections.
This paper presents formal models and methodologies of big data analytics for collective opinions and representative equilibrium in social networks and electoral systems. The cognitive and computing properties of big data are explored in Section 2. Potential pitfalls of Conventional counting-based voting methods for collective opinion elicitation and the majority rule embodiment are analyzed in Section 3. The characteristic equilibrium of collective opinions in social networks is revealed via big data analyses and numerical algorithms in Section 4. A set of fuzzy models for collective opinion elicitation and aggregation are rigorously described in Section 5. Case studies on applications of the formal methodologies of big data analytics are demonstrated in big poll data mining, collective opinion elicitation, and characteristic equilibrium determination.