[1]BAO Yanke,WANG Peizhuang,GUO Sicong.Structure of factor space and the dual convolution theorem[J].CAAI Transactions on Intelligent Systems,2018,13(4):656-664.[doi:10.11992/tis.201706057]
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Structure of factor space and the dual convolution theorem
CAAI Transactions on Intelligent Systems[ISSN 1673-4785/CN 23-1538/TP] Volume:
13
Number of periods:
2018 4
Page number:
656-664
Column:
学术论文—人工智能基础
Public date:
2018-07-05
- Title:
- Structure of factor space and the dual convolution theorem
- Keywords:
- factor space; structure; staggered automorphism transform; convolution lattice; dual convolution theorem
- CLC:
- TP18;O29
- DOI:
- 10.11992/tis.201706057
- Abstract:
- Based on two expressions consistency and the reverse-change relation of conceptual connotation and extension, as well as the dialectical unity of summary and parsing in the concept formation process, in this paper, we present a detailed discussion of the mathematical structure of factor space. We systematically identify the basic concepts and core propositions of factor space, as constructed by the principle of cognitive ontology, and provide a new ideological framework for both the theoretical and technological research of knowledge discovery based on factor space. We propose novel concepts related to the staggered automorphism transform and the convolution lattice, prove the dual entanglement theorem of factor space, and introduce a geometrical representation of the mathematical structure of factor space as a Mobius strip, thereby establishing a new mathematical model for illustrating the dynamics mechanism of the formation of human thinking and conceptualization.
- References:
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Last Update:
2018-08-25