Digital breast tomosynthesis (DBT) with improved lesion conspicuity and characterization has been adopted in screening practice. DBT-based diagnosis strongly depends on physicians' experience, so an automatic lesion malignancy classification model using DBT could improve the consistency of diagnosis among different physicians. Tensor-based approaches that use the original imaging data as input have shown promising results for many classification tasks. However, DBT data are pseudo-3D volumetric imaging as the slice spacing of DBT is much coarser than that of the in-plane resolution. Thus, directly constructing DBT as the third-order tensor in a conventional tensor-based classifier with introducing additional information to the original DBT data along the slice-spacing dimension will lead to inconsistency across all three dimensions. To avoid such inconsistency, we introduce a collection input based support tensor machine (CISTM)-based classifier that uses the tensor collection as input for classifying lesion malignancy in DBT. In CISTM, instead of introducing the third dimension directly into the geometry construction, the third-dimension structural relationship is related by weight parameters in the decision function, which is dynamically and automatically constructed during the classifier training process and is more consistent with the pseudo-3D nature of DBT. We tested our method on a DBT dataset of 926 images among which 262 were malignant and 664 were benign. We compared our method with the latest tensor-based method, KSTM (kernelled support tensor machine), which does not consider the unique non-uniform resolution property of DBT. Experimental results illustrate that the CISTM-based classifier is effective for classifying breast lesion malignancy in DBT and that it outperforms the KSTM-based classifier.