It is recognized that both sources of and solutions to the big data challenges are human collective intelligence. Data are an abstract representation of the quantity of realistic entities and perceived objects. Big data play an indispensable role not only in a wide range of engineering applications, but also in the cognitive mechanisms of both humans and cognitive robots such as sensation, quantification, qualification, estimation, memory, and reasoning. This keynote lecture presents online big data analytic theories by machine learning as well as knowledge extraction by cognitive robotics. Data, information, knowledge, and intelligence are the four hierarchical layers of cognitive objects in the brain and cognitive systems from the bottom up. It is discovered by the author that, although the cognitive unit of data is bit, that of knowledge is bir, i.e., a binary relation. A resent finding towards big data science is that big data systems in nature are a recursive n-dimensional typed hyperstructure (RNDTHS). This topological property of big data reveals that the mathematical foundation of big data science is underpinned by big data algebra (BDA), which is a denotational mathematical structure for efficiently dealing with the inherited complexities and unprecedented challenges in big data engineering. This leads to a coherent theory for big data modeling, analyses, mining, information elicitation, knowledge extraction, and intelligent generation for cognitive robots. Latest experiments demonstrate that cognitive robots may autonomously transform big data in vast linguistic databases (corpuses) into sophistic knowledge bases by cognitive machine learning.