Big, multidimensional data such as brain/heart MRI is expected to transform healthcare. However, such data poses great challenges, particularly the need for interpretation and very high dimensionality accompanied by a relatively small sample size. Deep learning models are powerful but inadequate to address these problems, due to their opaque and data-hungry nature. This talk will present tensor-based machine learning models for extracting/selecting compact, interpretable features directly from tensor representations of multidimensional data. I will show their applications in prediction and interpretation of brain fMRI for neural decoding and cardiac MRI for disease diagnosis. Finally, I will discuss some ongoing and future research works on interpretable machine learning, transfer learning, and network embedding.