Research On Negative Surveys Model With Personalized Options And Its Reconstruction Algorithm

In recent years,the popularity and rapid development of the mobile Internet has brought great convenience to users' work and life,but at the same time it has also threatened the privacy of users.The negative survey is a novel method for collecting sensitive information,which can protect the privacy of respondents to some extent while collecting data to meet the needs of investigators.The negative survey reconstruction algorithm can reconstruct the collected negative survey results into the positive survey results that are ultimately required by the investigators.In the surveys with personalized options that exist in reality,investigators will set up personalized option groups in one question,according to different characteristics of the participants.The participants whose characteristics are same will have the same option groups.This form often appears in online surveys.For example,when conducting a teacher satisfaction survey,the investigators will set the corresponding teachers as their options according to the class.However,the traditional negative surveys didn't take this situation into account,and the existing reconstruction algorithm can't reconstruct positive results from negative results on the whole.If we use the existing negative surveys model,to carry out negative surveys in some people,who belong to the same option groups,the accuracy may be a little low due to the small number of participants,and the results may even be unavailable.Therefore,this thesis proposes a model,called Negative Surveys with Personalized Options,and uses existing algorithms for reconstruction.Through comparing and analyzing the reconstruction results,we find that,in the negative surveys with personalized options,the reconstruction results may exist unreasonable positive values,which are much bigger than original positive results.And none of the existing algorithms take this problem into account.Based on this,this thesis proposes two algorithms,which work for the negative surveys with personalized options.The main work in this thesis includes the following three aspects:1)A model for negative surveys with personalized options is established,and its definition and formal representation are given.Combining the survey form with personalized options and negative surveys,this thesis establishes a model for negative surveys with personalized options.In this model,investigators will set up personalized option groups for the participants to choose according to their characteristics,such as gender,age and subordinate units.2)The effect of four existing reconstruction algorithms in the negative surveys with personalized options is analyzed and verified.In this thesis,four main algorithms including NSto PS,NSto PS-I,NSto PS-II and NSto PS-MLE,are applied into the negative surveys with personalized options.This thesis finds that the four algorithms have their own flaws.For example,for a group of participants with the same options to choose,if their number is less than 3,NSto PS-II algorithm will reconstruct the number of participants to 0,and the reconstruction accuracy of NSto PS-I algorithm is low,even the results are almost unusable.Compared to the situation when the positive data meets the uniform distribution,when the positive data of one or several options is significantly less than the other options,the reconstruction accuracy,of NSto PS-I algorithm,NSto PS-II algorithm and NSto PS-MLE algorithm,will decrease,even it will be lower than the accuracy of NSto PS algorithm whose results may contain negative values.It is worth noting that,none of the existing algorithms consider the situation of unreasonable positive values during the reconstruction process.As a result,the accuracy of the algorithms in the negative surveys with personalized options is lower than that in the traditional negative surveys.3)Two improved algorithms are proposed based on maximum likelihood estimation for the negative surveys with personalized options.According to the problems existing in NSto PS-MLE algorithm,this thesis proposes two improved algorithms: NSto PS-PO algorithm and NSto PS-PO2 algorithm.Both algorithms have advantages and disadvantages.NSto PS-PO algorithm can get more accurate results,but the algorithm complexity is high;NSto PS-PO2 algorithm uses greedy strategy to improve computing efficiency,but it may get an approximate solution.The two proposed algorithms will not get unreasonable results containing negative values,and they will adjust some unreasonable results of positive values accordingly.Simulation results show that,the reconstruction error of NSto PS-PO2 algorithm is reduced by an average of 7.38% compared to the NSto PS-MLE algorithm,and the reconstruction error of NSto PS-PO algorithm is lower than that of NSto PS-PO2 algorithm by 2.72%.