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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<jats:inline-formula><a:math xmlns:a=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><a:mfenced open=\"(\" close=\")\" separators=\"|\"><a:mrow><a:mi>\u03b5<\/a:mi><a:mo>,<\/a:mo><a:mn>0<\/a:mn><\/a:mrow><\/a:mfenced><\/a:math><\/jats:inline-formula>-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. 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