Selective ensemble of uncertain extreme learning machine for pattern classification with missing features

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 missing-value data classifications.