With the widespread application of big data, privacy-preserving data analysis has become a topic of increasing significance. The current research studies mainly focus on privacy-preserving classification and regression. However, principal component analysis (PCA) is also an effective data analysis method which can be used to reduce the data dimensionality, commonly used in data processing, machine learning, and data mining. In order to implement approximate PCA while preserving data privacy, we apply the Laplace mechanism to propose two differential privacy principal component analysis algorithms: Laplace input perturbation (LIP) and Laplace output perturbation (LOP). We evaluate the performance of LIP and LOP in terms of noise magnitude and approximation error theoretically and experimentally. In addition, we explore the variation of performance of the two algorithms with different parameters such as number of samples, target dimension, and privacy parameter. Theoretical and experimental results show that algorithm LIP adds less noise and has lower approximation error than LOP. To verify the effectiveness of algorithm LIP, we compare our LIP with other algorithms. The experimental results show that algorithm LIP can provide strong privacy guarantee and good data utility.

In big data era, massive and high-dimensional data is produced at all times, increasing the difficulty of analyzing and protecting data. In this paper, in order to realize dimensionality reduction and privacy protection of data, principal component analysis (PCA) and differential privacy (DP) are combined to handle these data. Moreover, support vector machine (SVM) is used to measure the availability of processed data in our paper. Specifically, we introduced differential privacy mechanisms at different stages of the algorithm PCA-SVM and obtained the algorithms DPPCA-SVM and PCADP-SVM. Both algorithms satisfy ε , 0 -DP while achieving fast classification. In addition, we evaluate the performance of two algorithms in terms of noise expectation and classification accuracy from the perspective of theoretical proof and experimental verification. To verify the performance of DPPCA-SVM, we also compare our DPPCA-SVM with other algorithms. Results show that DPPCA-SVM provides excellent utility for different data sets despite guaranteeing stricter privacy.

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