ABSTRACT
This chapter tries to extend cognition theory on the objective world in modern physics to cognition of the subjective world, and to introduce an interaction between data objects and the concept of field, so as to establish the cognitive field and formalize the description of the complex association between original, chaotic, and shapeless data objects. In the cognitive field, concepts, linguistic values, words, and even data points in domain space can be regarded as objects of interaction in field space. The cognitive process from quantitative data, to qualitative concept, to knowledge can be seen as study of interactions and relationships between these objects through the field at different granularities so as to mimic the human cognitive process. Knowledge discovery from ultra-large-scale relational databases is one of the frontiers in computer science. By learning from topology in mathematics and field theory in physics, the chapter proposes a topological potential method, that is, construction of virtual potential field in network topological space.
