Principal Component Analysis Scheme Based on Homomorphic Encryption in a Distributed Environment

Principal component analysis (PCA) is a widely used technique in the field of machine learning and one of the main dimensionality reduction methods. PCA can convert high-dimensional data into lower-dimensional representations, thereby helping to extract important information from data, and is an effective tool for data analysis and pattern recognition. In this paper, we propose a scheme for executing PCA on encrypted data based on homomorphic encryption in a distributed environment. In a distributed setting, computing nodes do not need to perform matrix operations such as matrix multiplication or addition, which reduces the computational burden on the nodes. To ensure the security of the data, we employ the CKKS homomorphic encryption scheme, which allows for approximate calculations on real numbers, meeting the requirements of machine learning. Additionally, we horizontally partition the data to facilitate its application in distributed computing. Furthermore, we optimize the detailed computation of HPCA (Homomorphic PCA), yielding promising results on various datasets.