基于相对熵和K-means的形状相似差分隐私轨迹保护机制

doi:10.11959/j.issn.1000-436x.2021008

摘要/Abstract

摘要：

为解决绝大多数研究未充分考虑位置对隐私预算的敏感程度以及轨迹形状带来的影响，使发布的轨迹可用性较差的问题，提出了基于相对熵和K-means的形状相似差分隐私轨迹保护机制。首先，根据地理空间的拓扑关系，利用相对熵计算真实位置对隐私预算的敏感程度，设计了位置敏感的隐私级别实时计算算法，并与差分隐私预算结合建立了一个新的隐私模型。其次，通过K-means算法对发布位置进行聚类，得到与真实位置方向最相似的发布位置集合，并引入 Fréchet 距离衡量发布轨迹与真实轨迹的相似性，提升发布轨迹的可用性。通过对真实数据集的实验表明，所提轨迹保护机制与其他方法相比在轨迹可用性方面有明显的优势。

关键词: 轨迹隐私, 差分隐私, 相对熵, K-means, 形状相似性

Abstract:

To solve the problem that most studies had not fully considered the sensitivity of location to privacy budget and the influence of trajectory shape, which made the usability of published trajectory poor, a shape similarity differential privacy trajectory protection mechanism based on relative entropy and K-means was proposed.Firstly, according to the topological relationship of geographic space, relative entropy was used to calculate the sensitivity of real location to privacy budget, a real-time calculation method of location sensitive privacy level was designed, and a new privacy model was built in combination with differential privacy budget.Secondly, K-means algorithm was used to cluster the release position to obtain the release position set that was most similar to the real position direction, and Fréchet distance was introduced to measure the similarity between the release track and the real track, so as to improve the availability of the release track.Experiments on real data sets show that the proposed trajectory protection mechanism has obvious advantages in trajectory availability compared with others.

Key words: trajectory privacy, differential privacy, relative entropy, K-means, shape similarity

中图分类号:

TP391

朱素霞, 刘抒伦, 孙广路. 基于相对熵和K-means的形状相似差分隐私轨迹保护机制[J]. 通信学报, 2021, 42(2): 113-123.

Suxia ZHU, Shulun LIU, Guanglu SUN. Shape similarity differential privacy trajectory protection mechanism based on relative entropy and K-means[J]. Journal on Communications, 2021, 42(2): 113-123.

图/表 9

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常用符号"

符号表示	符号含义
p^(t)-	t时刻的先验概率
p^(t)+	t时刻的后验概率
TL	整条轨迹的真实位置区域的集合
DL	整条轨迹的干扰位置区域的集合
PL^t	t时刻真实位置可能存在的集合
PRN^t	根据状态转移矩阵得到的t时刻可能存在位置的集合
PRNN^t	t时刻可能发布位置的集合
$R^{t}$	t时刻真实区域到扰乱区域的概率转移矩阵
$M$	真实区域状态转移概率矩阵
ep^t	t时刻隐私预算的集合
fr^t	t时刻Fréchet距离的集合

表1

图2

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图5

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图8

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