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Stepwise functional refoundation of relational concept analysis

Created by
  • Haebom

Author

J er ome Euzenat (MOEX)

Outline

This paper presents a new understanding of the multi-context handling of relational concept analysis (RCA). RCA can generate multiple concept lattices from data with circular dependencies, but the conventional RCA has the problem of returning only one set of concept lattices. To solve this problem, this paper defines a set of concept lattices that satisfy three conditions: 'well-formed', 'saturated', and 'self-supported' as 'admissible solutions'. We consider the RCA process from a functional perspective, and define the space of admissible solutions and the expansion and contraction functions that operate on the space. We prove that admissible solutions are common fixed points of these two functions, and show that the conventional RCA returns the minimum element of the set of admissible solutions. Furthermore, we construct an operation that generates a maximum element, and show that the set of admissible solutions is a complete sublattice of the interval between these two elements. We study in detail how this structure and the defined functions explore this structure.

Takeaways, Limitations

Takeaways:
Strengthens the theoretical basis of RCA and clarifies its behavior in multi-context situations.
We explain why the output of RCA is restricted to a single set of concept grids, and define a set of acceptable solutions, allowing for a variety of solutions to be considered.
By analyzing the structure and properties of the set of acceptable solutions, we can better understand and interpret the results of RCA.
We present a method to find the minimum and maximum allowable solutions.
Limitations:
Further research is needed to determine whether the acceptable solution conditions presented in this paper are always appropriate in practical applications.
There is a lack of clear guidance on which of the various acceptable years to choose. Further research is needed on the appropriate criteria for selecting a year in a context-specific manner.
There is a lack of analysis on the computational complexity of the proposed functional approach. Its effectiveness when applied to real datasets needs to be evaluated.
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