Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

A Novel Nearest Neighbors Algorithm Based on Power Muirhead Mean

Kourosh Shahnazari, Seyed Moein Ayyoubzadeh

TL;DR

The paper addresses limitations of the traditional $K$-Nearest Neighbors classifier in handling outliers and complex, high-dimensional data by introducing PMM-KNN, which computes class-wise centroids via the Power Muirhead Mean. By integrating the adaptive PMM operator with per-class neighborhood aggregation, the method achieves robust centroid estimation and improved predictive accuracy across several benchmark datasets. Empirical results show statistically significant gains over baselines like GNB, SVM, and conventional KNN, especially on high-dimensional or structured data, with manageable computational overhead. The work suggests strong potential for real-world applications and points to automatic PMM parameter tuning as a promising direction for future research.

Abstract

This paper introduces the innovative Power Muirhead Mean K-Nearest Neighbors (PMM-KNN) algorithm, a novel data classification approach that combines the K-Nearest Neighbors method with the adaptive Power Muirhead Mean operator. The proposed methodology aims to address the limitations of traditional KNN by leveraging the Power Muirhead Mean for calculating the local means of K-nearest neighbors in each class to the query sample. Extensive experimentation on diverse benchmark datasets demonstrates the superiority of PMM-KNN over other classification methods. Results indicate statistically significant improvements in accuracy on various datasets, particularly those with complex and high-dimensional distributions. The adaptability of the Power Muirhead Mean empowers PMM-KNN to effectively capture underlying data structures, leading to enhanced accuracy and robustness. The findings highlight the potential of PMM-KNN as a powerful and versatile tool for data classification tasks, encouraging further research to explore its application in real-world scenarios and the automation of Power Muirhead Mean parameters to unleash its full potential.

A Novel Nearest Neighbors Algorithm Based on Power Muirhead Mean

TL;DR

The paper addresses limitations of the traditional -Nearest Neighbors classifier in handling outliers and complex, high-dimensional data by introducing PMM-KNN, which computes class-wise centroids via the Power Muirhead Mean. By integrating the adaptive PMM operator with per-class neighborhood aggregation, the method achieves robust centroid estimation and improved predictive accuracy across several benchmark datasets. Empirical results show statistically significant gains over baselines like GNB, SVM, and conventional KNN, especially on high-dimensional or structured data, with manageable computational overhead. The work suggests strong potential for real-world applications and points to automatic PMM parameter tuning as a promising direction for future research.

Abstract

This paper introduces the innovative Power Muirhead Mean K-Nearest Neighbors (PMM-KNN) algorithm, a novel data classification approach that combines the K-Nearest Neighbors method with the adaptive Power Muirhead Mean operator. The proposed methodology aims to address the limitations of traditional KNN by leveraging the Power Muirhead Mean for calculating the local means of K-nearest neighbors in each class to the query sample. Extensive experimentation on diverse benchmark datasets demonstrates the superiority of PMM-KNN over other classification methods. Results indicate statistically significant improvements in accuracy on various datasets, particularly those with complex and high-dimensional distributions. The adaptability of the Power Muirhead Mean empowers PMM-KNN to effectively capture underlying data structures, leading to enhanced accuracy and robustness. The findings highlight the potential of PMM-KNN as a powerful and versatile tool for data classification tasks, encouraging further research to explore its application in real-world scenarios and the automation of Power Muirhead Mean parameters to unleash its full potential.
Paper Structure (24 sections, 8 equations, 1 figure, 3 tables, 1 algorithm)

This paper contains 24 sections, 8 equations, 1 figure, 3 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Literature Review
  3. K-Nearest Neighbors Classifier
  4. Muirhead Mean Operator
  5. Power Average
  6. Power Muirhead Mean
  7. Methodology
  8. K-Nearest Neighbors based on Power Muirhead Mean
  9. Distance Computation
  10. Selecting K Nearest Neighbors
  11. Calculate Centroids Using Power Muirhead Mean
  12. Aggregating K Nearest Neighbors
  13. Predicting the Test Data Class
  14. Data And Testing
  15. Datasets
  16. ...and 9 more sections

Figures (1)

  • Figure 1: Flowchart of the PMM-KNN Algorithm