Most commonly used classification algorithms process data in the form of vectors. At the same time, mod- ern datasets often comprise multimodal measurements that are naturally modeled as multi-way arrays, also known as tensors. Processing multi-way data in their tensor form can enable enhanced inference and classification accuracy. Tucker decomposition is a standard method for tensor data processing, which however has demonstrated severe sensitivity to corrupted measurements due to its L2-norm formulation. In this work, we present a selection of classification methods that employ an L1-norm-based, corruption-resistant reformulation of Tucker (L1-Tucker). Our experimental studies on multiple real datasets corroborate the corruption-resistance and classification accuracy afforded by L1-Tucker.