Geometric Active Learning via Enclosing Ball Boundary

Active Learning (AL) requires learners to retrain the classifier with the minimum human supervisions or labeling in the unlabeled data pool when the current training set is not enough. However, general AL sampling strategies with a few label support inevitably suffer from performance decrease. To identify which samples determine the performance of the classification hyperplane, Core Vector Machine (CVM) and Ball Vector Machine (BVM) use the geometry boundary points of each Minimum Enclosing Ball (MEB) to train the classification hypothesis. Their theoretical analysis and experimental results show that the improved classifiers not only converge faster but also obtain higher accuracies compared with Support Vector Machine (SVM). Inspired by this, we formulate the cluster boundary point detection issue as the MEB boundary problem after presenting a convincing proof of this observation. Because the enclosing ball boundary may have a high fitting ratio when it can not enclose the class tightly, we split the global ball problem into two kinds of small Local Minimum Enclosing Ball (LMEB): Boundary ball (B-ball) and Core ball (C-ball) to tackle its over-fitting problem. Through calculating the update of radius and center when extending the local ball space, we adopt the minimum update ball to obtain the geometric update optimization scheme of B-ball and C-ball. After proving their update relationship, we design the LEB (Local Enclosing Ball) algorithm using centers of B-ball of each class to detect the enclosing ball boundary points for AL sampling. Experimental and theoretical studies have shown that the classification accuracy, time, and space performance of our proposed method significantly are superior than the state-of-the-art algorithms.