  Tensor decompositions are powerful tools for dimensionality reduction and
feature interpretation of multidimensional data such as signals. Existing
tensor decomposition objectives (e.g., Frobenius norm) are designed for fitting
raw data under statistical assumptions, which may not align with downstream
classification tasks. In practice, raw input tensors can contain irrelevant
information while data augmentation techniques may be used to smooth out
class-irrelevant noise in samples. This paper addresses the above challenges by
proposing augmented tensor decomposition (ATD), which effectively incorporates
data augmentations and self-supervised learning (SSL) to boost downstream
classification. To address the non-convexity of the new augmented objective, we
develop an iterative method that enables the optimization to follow an
alternating least squares (ALS) fashion. We evaluate our proposed ATD on
multiple datasets. It can achieve 0.8% - 2.5% accuracy gain over tensor-based
baselines. Also, our ATD model shows comparable or better performance (e.g., up
to 15% in accuracy) over self-supervised and autoencoder baselines while using
less than 5% of learnable parameters of these baseline models
