A k-Nearest Neighbours Based Ensemble via Optimal Model Selection for Regression

Ensemble methods based on <tex-math notation="LaTeX">k </tex-math> -NN models minimise the effect of outliers in a training dataset by searching groups of the <tex-math notation="LaTeX">k </tex-math> closest data points to estimate the response of an unseen observation. However, traditional <tex-math notation="LaTeX">k </tex-math> -NN based ensemble methods use the arithmetic mean of the training points’ responses for estimation which has several weaknesses. Traditional <tex-math notation="LaTeX">k </tex-math> -NN based models are also adversely affected by the presence of non-informative features in the data. This paper suggests a novel ensemble procedure consisting of a class of base <tex-math notation="LaTeX">k </tex-math> -NN models each constructed on a bootstrap sample drawn from the training dataset with a random subset of features. In the <tex-math notation="LaTeX">k </tex-math> nearest neighbours determined by each <tex-math notation="LaTeX">k </tex-math> -NN model, stepwise regression is fitted to predict the test point. The final estimate of the target observation is then obtained by averaging the estimates from all the models in the ensemble. The proposed method is compared with some other state-of-the-art procedures on 16 benchmark datasets in terms of coefficient of determination ( <tex-math notation="LaTeX">R² </tex-math> ), Pearson’s product-moment correlation coefficient ( <tex-math notation="LaTeX">r </tex-math> ), mean square predicted error ( <tex-math notation="LaTeX">$MSPE$ </tex-math> ), root mean squared error ( <tex-math notation="LaTeX">$RMSE$ </tex-math> ) and mean absolute error ( <tex-math notation="LaTeX">$MAE$ </tex-math> ) as performance metrics. Furthermore, boxplots of the results are also constructed. The suggested ensemble procedure has outperformed the other procedures on almost all the datasets. The efficacy of the method has also been verified by assessing the proposed method in comparison with the other methods by adding non-informative features to the datasets considered. The results reveal that the proposed method is more robust to the issue of non-informative features in the data as compared to the rest of the methods.