A structured perspective of volumes on active learning

•We theoretically divide the earlier AL strategies into two kinds: Outer Volume Sampling and Inner Volume Sampling.•We design a theoretical AL framework termed “Volume-based AL Model” in version space.•We generalize our theoretical model into an easy-to-implement algorithm called VAL (Volume-based Active Learning) in Euclidean space.•VAL is independent of classifier and prior labels but declines the error rate of prediction fast.