In this study, we present an incremental machine learning framework called Adaptive Decision Forest (ADF), which produces a decision forest to classify new records. Based on our two novel theorems, we introduce a new splitting strategy called iSAT, which allows ADF to classify new records even if they are associated with previously unseen classes. ADF is capable of identifying and handling concept drift; it, however, does not forget previously gained knowledge. Moreover, ADF is capable of handling big data if the data can be divided into batches. We evaluate ADF on nine publicly available natural datasets and one synthetic dataset, and compare the performance of ADF against the performance of eight state-of-the-art techniques. We also examine the effectiveness of ADF in some challenging situations. Our experimental results, including statistical sign test and Nemenyi test analyses, indicate a clear superiority of the proposed framework over the state-of-the-art techniques.