2014/11/06 by Xiaoyu Chen, Dongming Wang, Chen, Xiaoyu +1
Computer Science · #Artificial Intelligence (cs.AI) #Data Management and Algorithms #FOS: Computer and information sciences #Rough Sets and Fuzzy Logic #Topological and Geometric Data Analysis #cs.AI
paper · pdf · doi:10.48550/arxiv.1411.1497
14 pages
arxiv created 2014/11/06 · openalex publication_date 2014/11/06 · arxiv updated 2014/11/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the data space D of any given data set X and explain how functions and relations are defined over D. From D and for a specific domain Δ we construct the information space I of X by interpreting variables, functions, and explicit relations over D in Δ and by including other relations that D implies under the interpretation in Δ. Then from I we build up the knowledge space K of X as the product of two spaces KT and KP, where KT is obtained from I by using the induction principle to generalize propositional relations to quantified relations, the deduction principle to generate new relations, and standard mechanisms to validate relations and KP is the space of specifications of methods with operational instructions which are valid in KT. Through our construction of the three topological spaces the following key observation is made clear: the retrieval of information from the given data set for Δ consists essentially in mining domain objects and relations, and the discovery of knowledge from the retrieved information consists essentially in applying the induction and deduction principles to generate propositions, synthesizing and modeling the information to generate specifications of methods with operational instructions, and validating the propositions and specifications. Based on this observation, efficient approaches may be designed to discover profound knowledge automatically from simple data, as demonstrated by the result of our study in the case of geometry.