Inductive learning refers to machine learning algorithms that learn a model from a set of training data instances. Any test instance is then classified by comparing it to the learned model. When the set of training instances lend themselves well to modeling, the use of a model substantially reduces the computation cost of classification. However, some training data sets are complex, and do not lend themselves well to modeling. Transductive learning refers to machine learning algorithms that classify test instances by comparing them to all of the training instances, without creating an explicit model. This can produce better classification performance, but at a much higher computational cost. Medical images vary greatly across human populations, constituting a data set that does not lend itself well to modeling. Our previous work showed that the wide variations seen across training sets of normal chest radiographs make it difficult to successfully classify test radiographs with an inductive (modeling) approach, and that a transductive approach leads to much better performance in detecting atypical regions. The problem with the transductive approach is its high computational cost. This paper develops and demonstrates a novel semi-transductive framework that can address the unique challenges of atypicality detection in chest radiographs. The proposed framework combines the superior performance of transductive methods with the reduced computational cost of inductive methods. Our results show that the proposed semitransductive approach provides both effective and efficient detection of atypical regions within a set of chest radiographs previously labeled by Mayo Clinic expert thoracic radiologists.