Most feature-weighted fuzzy support vector machines only calculate the weight of each feature without considering inter-feature correlations, leading to redundant features that significantly impact final classification results. Additionally, designing fuzzy affiliation based on Euclidean distance overlooks the overall sample distribution and inter-feature coupling. To address these issues, we propose a fuzzy support vector machine incorporating intra-feature correlation and weighted Mahalanobis distance. First, ReliefF is employed to calculate feature weights, while the Pearson algorithm introduces a penalty factor based on the Pearson coefficient between features, updating the weights to mitigate the impact of redundant features on classification performance. Second, Mahalanobis distance replaces Euclidean distance, and a feature-weighted subordinate function based on Mahalanobis distance is constructed using the covariance matrix to eliminate variance differences between dimensions, ensuring feature independence and uniform distribution. Finally, a feature-weighted kernel function is integrated to prevent weakly correlated or uncorrelated features from dominating kernel function calculations. Accuracy and F1 value are chosen as evaluation metrics and compared with existing algorithms on the UCI dataset. Experimental results demonstrate that this algorithm effectively reduces the interference of weakly correlated, irrelevant, and redundant features while considering sample distribution, leading to superior classification performance.

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Feature Intracorrelation and Weighted Mahalanobis Distance for Fuzzy Support Vector Machine

  • Lan Jiang,
  • Li Lv,
  • Siwei Peng,
  • Haihua Xie

摘要

Most feature-weighted fuzzy support vector machines only calculate the weight of each feature without considering inter-feature correlations, leading to redundant features that significantly impact final classification results. Additionally, designing fuzzy affiliation based on Euclidean distance overlooks the overall sample distribution and inter-feature coupling. To address these issues, we propose a fuzzy support vector machine incorporating intra-feature correlation and weighted Mahalanobis distance. First, ReliefF is employed to calculate feature weights, while the Pearson algorithm introduces a penalty factor based on the Pearson coefficient between features, updating the weights to mitigate the impact of redundant features on classification performance. Second, Mahalanobis distance replaces Euclidean distance, and a feature-weighted subordinate function based on Mahalanobis distance is constructed using the covariance matrix to eliminate variance differences between dimensions, ensuring feature independence and uniform distribution. Finally, a feature-weighted kernel function is integrated to prevent weakly correlated or uncorrelated features from dominating kernel function calculations. Accuracy and F1 value are chosen as evaluation metrics and compared with existing algorithms on the UCI dataset. Experimental results demonstrate that this algorithm effectively reduces the interference of weakly correlated, irrelevant, and redundant features while considering sample distribution, leading to superior classification performance.