Research On Functional Data Analysis Algorithm Under Differential Privacy

In the era of big data,with the development of science and technology and the improvement of storage technology,functional data has been more and more applied in many fields such as healthcare,social media,sensor networks,etc.processing needs.Functional data analysis is a data processing and analysis method for functional data,which can be used to reduce data dimensions and effectively extract key information.Functional data regression is a special regression analysis in which the response or covariates contain functional data.It uses principal component analysis to project the original high-dimensional data into a low-dimensional principal component space to obtain simplified data,making the data easier to use and reducing computational cost of the algorithm.However,functional data usually contains sensitive information.In the process of regression analysis,the unprotected algorithm output has the risk of leaking private information,which will pose a potential threat to individuals and enterprises.As one of the most effective privacy protection mechanisms at present,differential privacy provides a new idea for the privacy protection of functional data.Combining differential privacy and functional data regression algorithms,by adding noise to disturb the process or results of data analysis,the protection of private data can be achieved.The main idea of functional data regression for differential privacy protection is to smooth discrete functional data and transform it into the product of basis functions and their coefficients.Then use the method of function principal component analysis to calculate the smoothing coefficient,therefore the model of function regression is obtained.Based on the regression model,noise perturbation is performed on the coefficients of the model according to certain rules,and noise conforming to the Laplace distribution is added to it.The output of this algorithm can protect data privacy while the function is regressing.To solve the privacy protection problem in functional data analysis,this thesis has done the following innovative work:1.Aiming at the privacy protection problem in functional principal component analysis,a functional data regression algorithm DP-in-FR that provides differential privacy protection through Laplacian mechanism is designed and implemented.The security of the algorithm is proved in theory,and the usability of the algorithm is verified by two indexes of root mean square prediction error and average coverage probability.2.Based on the privacy issues in clustering differential privacy and functional fuzzy systems,an algorithm DP-in-FFS is proposed to protect data privacy based on differential privacy Laplacian mechanism.The privacy and algorithm complexity of the algorithm are analyzed theoretically,and compared with similar algorithms experimentally,it is proved that the algorithm has high availability and is better than the DP-in-FR algorithm in terms of mean square prediction error.3.Aiming at the allocation of privacy budget in the algorithm DP-in-FFS,the algorithm DPBAin-FFS is proposed.This algorithm allocates more privacy budget to sensitive data in proportion,and allocates less privacy budget to ordinary data,which improves privacy.protection efficiency.Through theoretical analysis and logical proof,the algorithm DPBA-in-FFS meets the definition requirements of differential privacy and has a certain level of privacy protection.