  This paper proposes a supervised dimension reduction methodology for tensor
data which has two advantages over most image-based prognostic models. First,
the model does not require tensor data to be complete which expands its
application to incomplete data. Second, it utilizes time-to-failure (TTF) to
supervise the extraction of low-dimensional features which makes the extracted
features more effective for the subsequent prognostic. Besides, an optimization
algorithm is proposed for parameter estimation and closed-form solutions are
derived under certain distributions.
