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）是广泛应用于张量数据降维的方法。然而，现有研究尚未探索将MPCA融入联邦学习的方案。针对这一空白，本文提出联邦多线性主成分分析（FMPCA）方法，使多个用户能够在保持各自数据本地化和机密性的同时，协同完成张量数据降维。所提出的FMPCA方法在性能上与传统MPCA具有同等保证。本文还展示了所提方法在工业预测中的应用实例。通过模拟数据与真实数据集对方法性能进行了验证。