Computing minimal sets of descriptive conditions for binary data

@article{Belohlvek2014ComputingMS,
  title={Computing minimal sets of descriptive conditions for binary data},
  author={Radim Belohl{\'a}vek and Vil{\'e}m Vychodil},
  journal={International Journal of General Systems},
  year={2014},
  volume={43},
  pages={521 - 534}
}
Suppose we are given a set of binary attributes. Each attribute is described by a finite set of objects to which the attribute applies. We consider the following problem. Is it possible to find a small set of conditions, or factors, associated to the attributes in such a way that an attribute applies to an object if and only if the object satisfies all conditions associated to the attribute? In this sense, we look for minimal sets of descriptive conditions for a set of binary attributes. We… 

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References

SHOWING 1-10 OF 23 REFERENCES

Discovery of optimal factors in binary data via a novel method of matrix decomposition

Optimal triangular decompositions of matrices with entries from residuated lattices

  • R. Belohlávek
  • Mathematics, Computer Science
    Int. J. Approx. Reason.
  • 2009

Triadic concept lattices of data with graded attributes

This paper shows how triadic concept analysis is developed in a setting in which the ternary relationship between objects, attributes, and modi is a matter of degree rather than a yes-or-no relationship.

The Discrete Basis Problem

This paper describes a matrix decomposition formulation for Boolean data, the Discrete Basis Problem, and gives a simple greedy algorithm for solving it and shows how it can be solved using existing methods.

Boolean Factor Analysis for Data Preprocessing in Machine Learning

  • J. Outrata
  • Computer Science
    2010 Ninth International Conference on Machine Learning and Applications
  • 2010
Two input data preprocessing methods for machine learning (ML) that utilize formal concept analysis and boolean factor analysis in that the new attributes are defined by so-called factor concepts computed from input data table.

The role mining problem: finding a minimal descriptive set of roles

The role mining problem (RMP) is defined as the problem of discovering an optimal set of roles from existing user permissions, and its theoretical bounds are analyzed to show that RMP is an NP-complete problem.

Formal concept analysis and linguistic hedges

It is argued that linguistic hedges represent mathematically and computationally a feasible way to parameterize methods for knowledge extraction from data that enable one to emphasize or to suppress extracted patterns while keeping their interpretation.

Relational-product architectures for information processing

Tiling Databases

This paper considers 0/1 databases and provides an alternative way of extracting knowledge from such databases using tiles, and develops an approximation algorithm for finding tilings which approximates the optimal solution within reasonable factors.

What is the Dimension of Your Binary Data?

This work considers the problem of defining a robust measure of dimension for 0/1 datasets, and shows that the basic idea of fractal dimension can be adapted for binary data.