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Weighted p-norm distance t kernel SVM classification algorithm based on improved polarization.

Wenbo Liu1,2, Shengnan Liang3,4, Xiwen Qin5

  • 1School of Mathematics and Statistics, Qiannan Normal University for Nationalities, Duyun, 558000, Guizhou, China. 874717829@qq.com.

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This summary is machine-generated.

This study introduces a novel weighted p-norm distance t kernel for Support Vector Machines (SVM). This enhanced kernel improves classification prediction performance on complex datasets compared to traditional methods.

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Area of Science:

  • Machine Learning
  • Pattern Recognition
  • Data Mining

Background:

  • Support Vector Machines (SVM) rely on kernel functions for linear segmentation in high-dimensional feature spaces.
  • The choice of kernel function critically impacts SVM's classification accuracy, especially for linearly inseparable data.
  • Existing kernel methods may have limitations in applicability and predictive performance across diverse datasets.

Purpose of the Study:

  • To propose an improved Support Vector Machine (SVM) classification algorithm using a novel weighted p-norm distance t kernel.
  • To enhance the applicability and classification prediction accuracy of SVM for various real-world datasets.
  • To investigate the impact of improved polarization techniques on kernel parameter optimization.

Main Methods:

  • Construction of a t-class kernel function based on the t-distribution probability density function, with theoretical validation.
  • Extension of the t-class kernel to a p-norm distance kernel to identify optimal mapping spaces.
  • Implementation of improved local kernel polarization to determine optimal kernel weights and parameters for weighted kernel combinations.
  • Stratified sampling for training data and redefinition of the affinity matrix.

Main Results:

  • The proposed weighted p-norm distance t kernel demonstrates improved classification prediction performance compared to traditional kernel functions across 6 real-world datasets.
  • Statistical comparison tests (10x fivefold cross-validation) confirm the significant impact of different p-norms on SVM classification performance.
  • The weighted combination of different kernel functions, optimized through improved polarization, leads to superior overall classification accuracy.

Conclusions:

  • The novel weighted p-norm distance t kernel SVM algorithm offers enhanced classification prediction capabilities.
  • The proposed method effectively addresses the limitations of traditional kernel functions for linearly inseparable data.
  • This approach provides a robust framework for improving SVM performance in diverse application areas.