  Multilinear Principal Component Analysis (MPCA) is a widely utilized method
for the dimension reduction of tensor data. However, the integration of MPCA
into federated learning remains unexplored in existing research. To tackle this
gap, this article proposes a Federated Multilinear Principal Component Analysis
(FMPCA) method, which enables multiple users to collaboratively reduce the
dimension of their tensor data while keeping each user's data local and
confidential. The proposed FMPCA method is guaranteed to have the same
performance as traditional MPCA. An application of the proposed FMPCA in
industrial prognostics is also demonstrated. Simulated data and a real-world
data set are used to validate the performance of the proposed method.
