A method for releasing a line chart based on differential privacy

Abstract

The application discloses a line chart desensitization information publishing method based on differential privacy, inputs all the turning points of an original line chart, determines the starting point and the ending point as characteristic turning points, obtains the total number of the characteristic turning points, the available privacy budget in the characteristic turning point selection stage and the available privacy budget in the numerical value noise adding stage specified by a user, calculates the probability of each unselected turning point in the utility score region being selected as a characteristic turning point based on an exponential mechanism, randomly selects a turning point from the utility score region as the next characteristic turning point according to the probability, adds random noise conforming to a Laplace distribution to the numerical value of each characteristic turning point, connects the turning points with noise added in sequence into a line, and obtains the line chart of the desensitization information. The application can more stably reproduce the trend of the line chart under the same privacy budget, and greatly optimizes the time complexity in the characteristic turning point determination link.

Description

Technical Field

[0001] This invention relates to the field of data privacy protection technology, and in particular to a method for de-sensitive information publishing using line graphs based on differential privacy. Background Technology

[0002] Differential privacy technology protects sensitive information by perturbing numerical values. Generally, the larger the perturbation, the lower the privacy budget ε, the more severe the data distortion, and the better the privacy protection effect.

[0003] The differential privacy-based line graph generation method, DPLCP, provides privacy protection for monotonically increasing line graphs starting from 0 through two stages. The first stage is the time segmentation stage. Based on the user-given number n, dynamic programming is used to divide the line graph into n-1 intervals, with the overall slope of each interval approximating the slope of each line segment within that interval as closely as possible. The two endpoints of each interval are selected as feature vertices, for a total of n. To ensure privacy, a differential privacy exponential mechanism is used to perturb the selection of feature vertices by proximity. Each feature vertices has a certain probability of being switched to its nearest neighbor. The total privacy budget ε1 consumed by the perturbation process is given by the user, and the budget consumed by each perturbation is expressed as... The second stage is the numerical noise-adding stage, which perturbs the values ​​of the feature inflection points so that each point in the polyline satisfies the differential privacy budget ε2. Specifically, the perturbation of the i-th (i>1) feature point follows a Laplace distribution. Among them l i Let be the length of the (i-1)th interval. Since the left endpoint of the first interval is fixed at 0, it does not need to be perturbed. Finally, connect the perturbed feature vertices to form a line, which is then published as the final line chart. This method has two drawbacks: First, after perturbing the selection of feature points using an exponential mechanism, key feature points have a certain probability of not participating in the drawing of the line chart, making it impossible to reconstruct the trend of the line chart. Second, this method is only applicable to monotonically increasing curves starting from 0, meaning the value of the first vertices must be 0, and the value of each subsequent vertices cannot be higher than the values ​​of subsequent vertices. In the first stage, when the curve has undulations, the dynamic programming method will ignore important trend features of the line chart, such as vertices and troughs. In the second stage, the DPLCP method cannot provide comprehensive privacy protection for line charts where the first vertices are not 0. Summary of the Invention

[0004] The purpose of this invention is to propose a method for desensitizing information in line graphs based on differential privacy. The method identifies feature points based on the trend characteristics of the line graph itself, adds random noise conforming to a Laplace distribution to the value of each feature point, and connects the noise-added points sequentially to form a line graph, thereby obtaining a desensitized line graph.

[0005] This invention is achieved using the following technical solution:

[0006] A method for de-sensitive information publishing using line charts based on differential privacy, specifically including the following process:

[0007] Step 1: Input all the vertices R0, R1, ..., R of the original line chart. m Calculate the coordinates of each inflection point based on the drawing space of the line chart;

[0008] Step 2: Determine the starting point R0 and the ending point R m For feature vertices, obtain the total number of feature vertices n specified by the user, the privacy budget ε1 available during the feature vertices selection stage, and the privacy budget ε2 available during the numerical noise addition stage;

[0009] Step 3: Based on the trend of the line chart, select the next feature inflection point. The selection strategy is described in detail below:

[0010] For each vertex R that was not selected as a feature vertex i Determine the nearest historical feature inflection points R on its left and right sides. l and R r The utility score region R is formed. i R l R r The utility fraction region R is calculated using the coordinates of the inflection points described in step 1. i R l R r The area is S i,l,r ,based on The exponential mechanism calculates the probability that each unselected inflection point in the utility score region will be selected as a feature inflection point, and randomly selects one inflection point from among them according to the probability as the next feature inflection point; where u(R) i ) is the selection of the inflection point R. i The utility score generated at the feature inflection point is quantified as S. i,l,r ,Δu i The utility score u(R) is the value generated when one of the data records in the line chart changes. i The maximum change value;

[0011] Step 4: Repeat steps 2 to 3 until the total number of selected feature vertices equals n;

[0012] Step 5: Based on the Laplace mechanism, add random noise conforming to a Laplace distribution to the values ​​of each feature inflection point. Wherein, Δh is the maximum difference that can be caused by any change in a data record when drawing a line chart, that is, the maximum value in the data record is mapped to the height of the drawing space;

[0013] Step 6: Connect the noise-added break points in sequence to form a polyline, and obtain the desensitized polyline graph.

[0014] Compared with the prior art, the beneficial effects and advantages of the present invention are as follows:

[0015] 1) Under the same privacy budget, the trend of the polyline graph can be reproduced more stably, thereby achieving the same privacy protection effect;

[0016] 2) The time complexity is greatly optimized in the step of determining the feature break points. Brief Description of the Drawings

[0017] Figure 1 is an overall flowchart of the desensitized information publishing method for polyline graphs based on differential privacy of the present invention;

[0018] Figure 2 is a schematic diagram of a feature break point selection example;

[0019] Figure 3 is an effect diagram of the embodiment. Detailed Description of the Embodiments

[0020] The present invention will be further described in detail below with reference to the accompanying drawings.

[0021] As shown Figure 1 , the desensitized information publishing method for polyline graphs based on differential privacy of the present invention specifically includes the following processes:

[0022] Step 1: Input all break points R0, R1, ..., R of the original polyline graph m , calculate the coordinates of each break point according to the final drawing space of the polyline graph; the original polyline graph to be processed supports the release of various types of polyline graphs;

[0023] Step 2: Determine the start point R0 and the end point R m as feature break points, and obtain the total number n of feature break points specified by the user (2≤n≤m), the available privacy budget ε1 in the feature break point selection stage and the available privacy budget ε2 in the value noising stage;

[0024] Step 3: Select the next feature break point, and the selection strategy is specifically described as follows:

[0025] As shown Figure 2 , for each break point R that has not been selected as a feature break point i (0<i<m), determine the nearest historical feature break points R on its left and right sides l and R r , forming a utility score region R i R l R, and calculate the triangle R i R l Rr The area is S i,l,r ,based on The exponential mechanism calculates the probability that each unselected inflection point in the utility score region will be selected as a feature inflection point, and randomly selects one inflection point from among them according to the probability as the next feature inflection point; where u(R) i ) is the selection of the inflection point R. i The utility score generated at the feature inflection point is quantified as S. i,l,r ,Δu i The utility score u(R) is the value generated when one of the data records in the line chart changes. i The maximum change value;

[0026] Step 4: Repeat steps 2 to 3 until the total number of selected feature vertices equals n;

[0027] Step 5: Based on the Laplace mechanism, add random noise conforming to a Laplace distribution to the values ​​of each feature inflection point. Wherein, Δh is the maximum difference that can be caused by any change in a data record when drawing a line chart, that is, the maximum value in the data record is mapped to the height of the drawing space;

[0028] Step 6: Connect the inflection points after adding noise to form a broken line to obtain a broken line graph with desensitized information.

[0029] Furthermore, when perturbing the zigzag line, try to preserve important trend characteristics, such as peaks, troughs, and inflection points.

[0030] This invention significantly optimizes the time complexity in the feature inflection point determination stage, specifically reducing the time complexity from O(m·n) 2 The time complexity is optimized to O(m·nlogn), where O is the symbol used to represent time complexity.

[0031] It should be noted that although the present invention has been shown and described with reference to specific exemplary embodiments thereof, those skilled in the art should understand that the present invention is not limited to the above embodiments, and all modifications to the present invention fall within the scope of protection of the present invention.

Claims

1. A method for desensitizing information in line graphs based on differential privacy, characterized in that, Specifically, the process includes the following steps: Step 1: Input all the vertices R0, R1, ..., R of the original line chart. m Calculate the coordinates of each inflection point based on the drawing space of the line chart; Step 2: Determine the starting point R0 and the ending point R m For feature vertices, obtain the total number of feature vertices n specified by the user, the privacy budget ε1 available during the feature vertices selection stage, and the privacy budget ε2 available during the numerical noise addition stage; Step 3: Based on the trend of the line chart, select the next feature inflection point. The selection strategy is described in detail below: For each vertex R that was not selected as a feature vertex i Determine the nearest historical feature inflection points R on its left and right sides. l and R r The utility score region R is formed. i R l R r The utility fraction region R is calculated using the coordinates of the inflection points described in step 1. i R l R r The area is S i,l,r ,based on The exponential mechanism calculates the probability that each unselected vertex will be selected as a feature vertex, and randomly selects one vertex from these probabilities as the next feature vertex; where u(R) i ) is the selection of the inflection point R. i The utility score generated at the feature inflection point is quantified as S. i,l,r ,Δu i The utility score u(R) is the value generated when one of the data records in the line chart changes. i The maximum change value; Step 4: Repeat steps 2 to 3 until the total number of selected feature vertices equals n; Step 5: Based on the Laplace mechanism, add random noise conforming to a Laplace distribution to the values ​​of each feature inflection point. Wherein, Δh is the maximum difference that can be caused by any change in a data record when drawing a line chart, that is, the maximum value in the data record is mapped to the height of the drawing space; Step 6: Connect the inflection points after adding noise to form a broken line to obtain a broken line graph with desensitized information.

2. The method for desensitizing information in line charts based on differential privacy as described in claim 1, characterized in that, When perturbing the fold line, priority should be given to retaining important trend features, including at least peaks, troughs, and inflection points.

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