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The Rough Topology for Numerical Data

Uğur Yiğit

TL;DR

This paper generalizes the rough topology and the core to numerical data by classifying objects in terms of the attribute values and introduces a measurement criterion to determine whether an attribute belongs to the core.

Abstract

In this paper, we generalize the rough topology and the core to numerical data by classifying objects in terms of the attribute values. A new approach to finding the core for numerical data is discussed. Then a measurement to find whether an attribute is in the core or not is given. This new method for finding the core is used for attribute reduction. It is tested and compared by using eight different machine-learning algorithms. Also, it is discussed how this material is used to rank the importance of attributes in data classification. Finally, the algorithms and codes to convert data to pertinent data and to find the core is also provided.

The Rough Topology for Numerical Data

TL;DR

This paper generalizes the rough topology and the core to numerical data by classifying objects in terms of the attribute values and introduces a measurement criterion to determine whether an attribute belongs to the core.

Abstract

In this paper, we generalize the rough topology and the core to numerical data by classifying objects in terms of the attribute values. A new approach to finding the core for numerical data is discussed. Then a measurement to find whether an attribute is in the core or not is given. This new method for finding the core is used for attribute reduction. It is tested and compared by using eight different machine-learning algorithms. Also, it is discussed how this material is used to rank the importance of attributes in data classification. Finally, the algorithms and codes to convert data to pertinent data and to find the core is also provided.
Paper Structure (8 sections, 1 theorem, 4 equations, 3 figures, 1 table, 1 algorithm)

This paper contains 8 sections, 1 theorem, 4 equations, 3 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Rough Topology
  4. The Rough Topology for numerical data
  5. A topological method for big numerical data
  6. Applications
  7. An Application to Dataset with Categorical Decision Attribute
  8. Conclusion and Future Directions

Key Result

lemma 1

Tha The set $\beta_{R}=\{U, R_{\star}(X), B_{R}(X)\}$ is a basis for the rough topology $\tau_R$ on $U$ with respect to $X$.

Figures (3)

  • Figure 1: Comparison of Core Attributes and All Attributes for ML Algorithms
  • Figure 2: Confusion Matrix for the Hybrid Algorithm (The Core)
  • Figure 3: Confusion Matrix for the Hybrid Algorithm (All Attributes)

Theorems & Definitions (8)

  • definition 1
  • definition 2
  • definition 3
  • lemma 1
  • definition 4
  • definition 5
  • definition 6
  • remark 1