A classification algorithm is separated into one or more input-invariant parts and one or more input-dependent classification parts. The input-invariant parts of the classification algorithm capture the underlying and unchanging relationships between the plurality of data elements being operated upon by the classification algorithm, whereas the one or more classification parts embody the probabilistic labeling of the data elements according to the various classifications. For any given iteration, a user's input is used to modify at least one classification part of the algorithm. Recalculated classification parts (i.e., updated classification results) are determined based on computationally simple combinations of the one or more modified classification parts and the one or more input-invariant parts. Preferably, a graphical user interface is used to solicit user input. In this manner, wait times between user feedback iterations can be dramatically reduced, thereby making application of active learning to classification tasks a practical reality.