Differential Privacy Protection Of PCA Algorithm In Federated Learning

With the development of the Internet,big data and artificial intelligence technologies have been applied in all walks of life.However,in the application process,the problem of data islands appeared.When data is distributed horizontally or vertically in different institutions,each institution is unwilling to share its own data with others due to data privacy considerations.Therefore,the data among institutions forms isolated islands.This problem also exists in the field of big data dimensionality reduction algorithms.Principal Component Analysis(PCA)is a data dimensionality reduction method widely used in the field of big data.It projects high-dimensional original data into a low-dimensional space composed of part of the eigenvectors of the data covariance matrix through linear transformation.The dimension of the data is reduced,and the features that contribute the most to the variance in the data are retained.However,the low-dimensional data output by the PCA algorithm has the risk of leaking user privacy information,causing security risks.The differential privacy protection method proposed by Dwork provides a new way for data privacy protection,and the combination of differential privacy and PCA can provide privacy protection for data processing.The integrated differential privacy PCA algorithm realizes the protection of private data by adding noise to the covariance matrix data of the PCA algorithm for disturbance.Most of the existing differential privacy PCA algorithms are designed for data centralization scenarios.However,for scenarios where data is distributed horizontally or vertically in different institutions,that is,horizontal federated learning and vertical federated learning,how to design an effective differential privacy PCA algorithm to ensure the privacy of local data is an urgent problem to be solved.In order to solve the privacy protection problem of PCA algorithm in horizontal and vertical federated learning scenarios,the thesis made the following innovations:1.Aiming at the privacy protection problem of PCA algorithm in the horizontal federated earning scenario,a horizontal federated PCA differential privacy protection algorithm HFedPCA is proposed to protect the privacy of local data and dimensionality reduction data. The privacy,communication cost and algorithm complexity of the algorithm are analyzed theoretically.Compared with similar algorithms in experiments,it is proved that the algorithm is more usable.2.Aimig at the privacy protection problem of PCA algorithm in the vertical federated learning scenario,a vertical federated PCA differential privacy protection algorithm VFedPCA is proposed to protect the privacy of local data and dimensionality reduction data.And theoretically analyze the algorithm’s privacy,communication cost,and algorithm complexity. Experimental comparison with the original PCA algorithm proves that the algorithm has high usability.3.From the perspective of usability(including noise addition,communication cost,and algorithm complexity),the existing PCA privacy protection algorithm in federated learning is theoretically analyzed,and compared with the usability of the two algorithms HFedPCA and VFedPCA proposed in the thesis,it proves that the two algorithms are more usable.