Dost Muhammad Khan

Amjad Ali, Muhammad Hamraz, Naz Gul et al.

kNN based ensemble methods minimise the effect of outliers by identifying a set of data points in the given feature space that are nearest to an unseen observation in order to predict its response by using majority voting. The ordinary ensembles based on kNN find out the k nearest observations in a region (bounded by a sphere) based on a predefined value of k. This scenario, however, might not work in situations when the test observation follows the pattern of the closest data points with the same class that lie on a certain path not contained in the given sphere. This paper proposes a k nearest neighbour ensemble where the neighbours are determined in k steps. Starting from the first nearest observation of the test point, the algorithm identifies a single observation that is closest to the observation at the previous step. At each base learner in the ensemble, this search is extended to k steps on a random bootstrap sample with a random subset of features selected from the feature space. The final predicted class of the test point is determined by using a majority vote in the predicted classes given by all base models. This new ensemble method is applied on 17 benchmark datasets and compared with other classical methods, including kNN based models, in terms of classification accuracy, kappa and Brier score as performance metrics. Boxplots are also utilised to illustrate the difference in the results given by the proposed and other state-of-the-art methods. The proposed method outperformed the rest of the classical methods in the majority of cases. The paper gives a detailed simulation study for further assessment.

Amjad Ali, Muhammad Hamraz, Dost Muhammad Khan et al.

Ensembles based on k nearest neighbours (kNN) combine a large number of base learners, each constructed on a sample taken from a given training data. Typical kNN based ensembles determine the k closest observations in the training data bounded to a test sample point by a spherical region to predict its class. In this paper, a novel random projection extended neighbourhood rule (RPExNRule) ensemble is proposed where bootstrap samples from the given training data are randomly projected into lower dimensions for additional randomness in the base models and to preserve features information. It uses the extended neighbourhood rule (ExNRule) to fit kNN as base learners on randomly projected bootstrap samples.

Amjad Ali, Zardad Khan, Dost Muhammad Khan et al.

The traditional k nearest neighbor (kNN) approach uses a distance formula within a spherical region to determine the k closest training observations to a test sample point. However, this approach may not work well when test point is located outside this region. Moreover, aggregating many base kNN learners can result in poor ensemble performance due to high classification errors. To address these issues, a new optimal extended neighborhood rule based ensemble method is proposed in this paper. This rule determines neighbors in k steps starting from the closest sample point to the unseen observation and selecting subsequent nearest data points until the required number of observations is reached. Each base model is constructed on a bootstrap sample with a random subset of features, and optimal models are selected based on out-of-bag performance after building a sufficient number of models. The proposed ensemble is compared with state-of-the-art methods on 17 benchmark datasets using accuracy, Cohen's kappa, and Brier score (BS). The performance of the proposed method is also assessed by adding contrived features in the original data.