Outlier robust fuzzy active learning method (ALM)

Active Learning Method (ALM) is a fuzzy learning method and is inspired by the approach of human's brain toward understanding complicated problems. In this algorithm, a Multi-Input Single-Output system is modeled by some Single-Input Single-Output sub-systems. Each sub-model tries to capture the input-output relationship of each sub-system on a plane called IDS plane. The output of the original system is then approximated by fuzzy aggregation of the output of all submodels. The most important step in ALM, though, is to choose an appropriate radius for ink drop spread, to achieve desirable result. In this paper, a novel method, based on the idea of K-Nearest Neighbor (KNN) algorithm, is proposed to locally choose appropriate radius for ink drop spread according to the density of the data points in each region of the IDS plane. It will be shown that by this criterion, not only the sparsity of data points in different regions of the dataset is taken into account, but also the algorithm will be equipped with the capability to identify and filter out the outliers. The mathematical analysis of this method is provided to confirm its validity and simulations were conducted on various datasets in order to evaluate its efficiency.