A New $k$-Nearest Neighbors Algorithm for Learning from Multiple Experts' Uncertain Decisions

$k$-nearest neighbors algorithm ($k$-NN) is a simple yet powerful method that can predict an unlabeled object using the $k$ closest samples whose labels are already known. However, in some cases such as medical treatment decision making, multiple experts can provide their individual decisions and there is no single ground truth for the labels of samples. As a result, the accuracy of the predictions can be affected by the uncertainties of historical decisions. In order to learn from uncertain decisions from multiple experts, we propose a new $k$-NN algorithm. This algorithm firstly measures the uncertainties of labels. Then, the prediction is made based on the uncertain labels of the $k$ closest samples based on the Dempster-Shafer theory. We also introduce two methods to compute the optimal $k$ value. Experiments on a real-world medical treatment dataset prove that our algorithm has better performance compared with other algorithms.