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.

翻译：多线性主成分分析（MPCA）是张量数据降维中广泛使用的方法。然而，现有研究尚未探讨MPCA与联邦学习的结合。针对这一空白，本文提出一种联邦多线性主成分分析（FMPCA）方法，使多个用户能够协作降低其张量数据的维度，同时保持各用户数据的本地性与机密性。所提出的FMPCA方法被证明具有与传统MPCA相同的性能。本文还展示了FMPCA在工业故障预测中的应用，并通过仿真数据与真实数据集验证了该方法的有效性。