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Attribute reduction algorithm of rough sets based on spatial optimization

Xuchang Guo, Houbiao Li

TL;DR

The paper addresses the problem that traditional rough set attribute reduction primarily minimizes the number of reduced attributes without considering spatial alignment with the decision attribute, potentially producing many rules and limited generality. It introduces a spatial optimization framework that uses spatial similarity between partitions and a spatially weighted metric, SPS, to guide attribute selection via SigSPS, culminating in a Spatial Optimal Rough Set attribute Reduction (SRS) algorithm. The approach combines cosine-based partition similarity and positive-region coverage to favor reductions that closely reflect the decision partition, and it demonstrates through experiments on 10 UCI datasets that SRS yields higher spatial similarity and often fewer rules than existing methods like MIBARK and AO. This work advances rough-set-based rule learning by producing more concise, generalizable rule sets and offers a scalable alternative to traditional discernibility-matrix–driven reductions.

Abstract

Rough set is one of the important methods for rule acquisition and attribute reduction. The current goal of rough set attribute reduction focuses more on minimizing the number of reduced attributes, but ignores the spatial similarity between reduced and decision attributes, which may lead to problems such as increased number of rules and limited generality. In this paper, a rough set attribute reduction algorithm based on spatial optimization is proposed. By introducing the concept of spatial similarity, to find the reduction with the highest spatial similarity, so that the spatial similarity between reduction and decision attributes is higher, and more concise and widespread rules are obtained. In addition, a comparative experiment with the traditional rough set attribute reduction algorithms is designed to prove the effectiveness of the rough set attribute reduction algorithm based on spatial optimization, which has made significant improvements on many datasets.

Attribute reduction algorithm of rough sets based on spatial optimization

TL;DR

The paper addresses the problem that traditional rough set attribute reduction primarily minimizes the number of reduced attributes without considering spatial alignment with the decision attribute, potentially producing many rules and limited generality. It introduces a spatial optimization framework that uses spatial similarity between partitions and a spatially weighted metric, SPS, to guide attribute selection via SigSPS, culminating in a Spatial Optimal Rough Set attribute Reduction (SRS) algorithm. The approach combines cosine-based partition similarity and positive-region coverage to favor reductions that closely reflect the decision partition, and it demonstrates through experiments on 10 UCI datasets that SRS yields higher spatial similarity and often fewer rules than existing methods like MIBARK and AO. This work advances rough-set-based rule learning by producing more concise, generalizable rule sets and offers a scalable alternative to traditional discernibility-matrix–driven reductions.

Abstract

Rough set is one of the important methods for rule acquisition and attribute reduction. The current goal of rough set attribute reduction focuses more on minimizing the number of reduced attributes, but ignores the spatial similarity between reduced and decision attributes, which may lead to problems such as increased number of rules and limited generality. In this paper, a rough set attribute reduction algorithm based on spatial optimization is proposed. By introducing the concept of spatial similarity, to find the reduction with the highest spatial similarity, so that the spatial similarity between reduction and decision attributes is higher, and more concise and widespread rules are obtained. In addition, a comparative experiment with the traditional rough set attribute reduction algorithms is designed to prove the effectiveness of the rough set attribute reduction algorithm based on spatial optimization, which has made significant improvements on many datasets.
Paper Structure (15 sections, 15 equations, 2 figures, 1 table, 4 algorithms)

This paper contains 15 sections, 15 equations, 2 figures, 1 table, 4 algorithms.

Table of Contents

  1. Introduction
  2. Related Work
  3. Preliminary
  4. Rough set theory
  5. Attribute reduction algorithms
  6. Discernibility matrix
  7. An attribute-oriented rough set approach
  8. MIBARK algorithm
  9. A spatial optimal rough set attribute reduction algorithm
  10. Spatial similarity
  11. Optimal spatial metric
  12. Feasibility analysis
  13. Spatial optimal rough set attribute reduction algorithm
  14. Experiments
  15. Conclusion

Figures (2)

  • Figure 1: Comparison of Attribute Numbers in Reduced Datasets
  • Figure 2: Comparison of Spatial Similarity of Reduced Datasets