Selective ensemble of uncertain extreme learning machine for pattern classification with missing features
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Selective ensemble of uncertain extreme learning machine for pattern classification with missing features Shibo Jing1 · Yidan Wang1 · Liming Yang1
© Springer Nature B.V. 2020
Abstract Ensemble learning is an effective technique to improve performance and stability compared to single classifiers. This work proposes a selective ensemble classification strategy to handle missing data classification, where an uncertain extreme learning machine with probability constraints is used as individual (or base) classifiers. Then, three selective ensemble frameworks are developed to optimize ensemble margin distributions and aggregate individual classifiers. The first two are robust ensemble frameworks with the proposed loss functions. The third is a sparse ensemble classification framework with the zero-norm regularization, to automatically select the required individual classifiers. Moreover, the majority voting method is applied to produce ensemble classifier for missing data classification. We demonstrate some important properties of the proposed loss functions such as robustness, convexity and Fisher consistency. To verify the validity of the proposed methods for missing data, numerical experiments are implemented on benchmark datasets with missing feature values. In experiments, missing features are first imputed by using expectation maximization algorithm. Numerical experiments are simulated in filled datasets. With different probability lower bounds of classification accuracy, experimental results under different proportion of missing values show that the proposed ensemble methods have better or comparable generalization compared to the traditional methods in handling missingvalue data classifications. Keywords Ensemble classification · Missing data · uncertainty · Robustness · Extreme learning machine · DC programming
1 Introduction Ensemble learning has been paid considerable attention and applied successfully in big data analysis (Bi et al. 2008; Martin et al. 2018). Studies (Huang et al. 2015; Han et al. 2015) show that ensemble classifier can improve generalization by combining different individual classifiers. Ensemble classifier overcomes the limitations of individual classifier, particularly when the hypothetical function does not contain real function. Generally, * Liming Yang [email protected] 1
College of Science, China Agricultural University, Beijing 100083, China
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ensemble classifier mainly consists of two parts: (1) producing multiple individual classifiers; (2) integrating individual classifiers. The combination is by choosing the suitable rules. The individual classifiers are homogeneous and generated by different runs of the training algorithms. The choice of individual classifiers plays an important role in ensemble learning systems. Classification with missing values is common to see in practical application, especially in big dada analysis, where missing values are often accompanied in the process of data acquisition. Classification with missing
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