A personalized location trajectory privacy protection method based on mutual information

Abstract

This invention discloses a personalized location trajectory privacy protection method based on mutual information, belonging to the field of crowdsourced sensing technology. It includes: Step 1: Data preprocessing; Step 2: After generating the Markov matrix in Step 1, the matrix is ​​normalized, and a location privacy protection mechanism is established by setting a distortion threshold and regularization parameters; Step 3: Measuring the effectiveness of location privacy protection. This method generates a Markov transition matrix by merging user location trajectory data, analyzes implicit privacy information and adds distortion perturbations, and uses mutual information to measure the degree of privacy leakage, achieving a trade-off between privacy and usability. It solves the problem that existing technologies cannot effectively overcome the risk of location information privacy leakage.

Description

Technical Field

[0001] This invention belongs to the field of crowd intelligence sensing technology, specifically relating to a personalized location trajectory privacy protection method based on mutual information. Background Technology

[0002] Location-based services (LBS) have gradually become an important part of people's lives and work. They are widely used in areas such as location sharing, map navigation, ride-hailing services, and restaurant recommendations. However, using LBS also means uploading your real-time data to servers, which carries the risk of privacy breaches.

[0003] In recent years, research on privacy protection has yielded numerous results, mainly focusing on innovations in measurement standards, expansion of the privacy concept, and utilization of data structures and transformation techniques, providing diverse ideas and methods for privacy protection. Haonan Yan et al., in their paper "YAN H, LI X, ZHANG W, et al. CODER: Protecting Privacy in ImageRetrieval With Differential Privacy [J]. IEEE Transactions on Dependable and Secure Computing, 2024, 21(6): 5420-30", proposed using MSE (Mean Square Error) and SSIM (Structural Similarity Index Measure) to measure utility and accurately assess the performance of re-identification attacks. Experiments were conducted on a server, and a protection mechanism was proposed. Liyue Fan, in her paper "FAN L. Image Pixelization with Differential Privacy [M]. Data and Applications Security and Privacy XXXII.2018: 148-62", proposed an image pixelation method with differential privacy guarantees, achieving a good balance between utility and privacy protection, and effectively reducing the success rate of re-identification attacks. In the paper “ZHANG W, LI M, TANDON R, et al. Online Location Trace Privacy: An Information Theoretic Approach [J]. IEEE Transactions on Information Forensics and Security, 2019, 14(1): 235-50”, Wenjing Zhang et al. proposed a new location trajectory privacy metric using information theory, derived upper and lower bounds for the privacy-utility tradeoff, generated an optimal algorithm based on the upper bound, and verified the advantages of the proposed method through experiments.In her paper "FAN L. Practical Image Obfuscation with Provable Privacy; proceedings of the 2019 IEEE International Conference on Multimedia and Expo (ICME), F 8-12 July 2019, 2019 [C]", Liyue Fan proposed an image blurring scheme based on metric privacy, utilizing singular value decomposition and random sampling mechanisms to improve utility while protecting provable privacy. Mutual information can be used to measure the balance between privacy and utility. For the binary case, this trade-off is characterized under perfect privacy conditions, and an upper limit is given for allowing a certain degree of privacy leakage. Zhang Wenjing, in her paper "Zhang Wenjing. Research on Location Privacy Problems Based on Information Theory Methods [D], 2021", conducted research on the conditional mutual information minimization problem satisfying availability constraints, performing theoretical and algorithmic experiments. However, none of the above methods can effectively overcome the risk of location information privacy leakage.

[0004] Based on this, the present invention proposes a personalized location trajectory privacy protection method based on mutual information to solve the problems existing in the prior art. Summary of the Invention

[0005] To address the aforementioned technical problems, this invention provides a personalized location trajectory privacy protection method based on mutual information, which solves the problem that existing technologies cannot effectively overcome the risk of location information privacy leakage.

[0006] To achieve the above objectives, the present invention provides the following technical solution:

[0007] A personalized location trajectory privacy protection method based on mutual information includes:

[0008] Step 1: Data preprocessing;

[0009] The trajectory data of the target user is filtered by verifying the latitude and longitude range. The filtered and retained data is then optimized to reduce the complexity of data processing and reduce the interference of noise in the data.

[0010] Step 2: After generating the Markov matrix in Step 1, the matrix is ​​normalized, and a location privacy protection mechanism is established by setting the distortion threshold and regularization parameters.

[0011] Step 3: Measure the effectiveness of location privacy protection;

[0012] Step 3.1: Initialize the parameter space;

[0013] Step 3.2: Traverse the parameter combinations and calculate the overall score;

[0014] Step 3.3: Select the optimal parameter combination.

[0015] In a preferred embodiment of the present invention, the data preprocessing process in step 1 includes:

[0016] Step 1.1: Generate a state sequence—transform the continuous trajectory of the target user into discrete states;

[0017] Step 1.2: Construct the transition matrix—quantify the transition probabilities between states;

[0018] Step 1.3: Calculate steady-state distribution—analyze users' long-term location preferences;

[0019] Step 1.4: Visual Presentation—Intuitively displaying migration patterns and location preferences;

[0020] The abstract transition matrix and steady-state distribution are "visualized" by using heatmaps of the transition matrix and steady-state distribution paths, making it easier to quickly identify key information.

[0021] In a preferred embodiment of the present invention, step 1.1, which involves converting the continuous trajectory of the target user into a discrete state, includes:

[0022] Step 1.1.1: Traverse all input user trajectory points and perform "state matching" for each trajectory point: Based on the latitude and longitude coordinates of the point, determine which geographical region in the state label set S it falls into, and then use the state label corresponding to that region as the "discrete state" of the trajectory point.

[0023] Step 1.1.2: Arrange the discrete states of all trajectory points in chronological order to form a "state sequence".

[0024] In a preferred embodiment of the present invention, the process of quantifying the transition probability between states in step 1.2 involves constructing a Markov transition matrix by statistically analyzing the "jumping pattern between adjacent states" in the state sequence, thereby realizing the transformation from "number of transitions to transition probability". Specifically, this includes:

[0025] Step 1.2.1: Count the number of transfers:

[0026] (1) First, create a two-dimensional matrix, where the rows and columns of the matrix correspond to the discrete states in the state label set S;

[0027] (2) Traverse the state sequence generated in step 1.1. For each pair of adjacent states, increment the count by 1 at the position of the i-th row and j-th column of the matrix. The final matrix element value is the total number of times the state transitions from state S_i to state S_j.

[0028] Step 1.2.2: Perform normalization processing:

[0029] (1) Since the transition matrix needs to satisfy the "Markov chain property", each row of the transition number matrix needs to be "normalized": divide each element of the row by the sum of all elements in the row to obtain the "probability of transitioning from state S_i to state S_j";

[0030] (2) After the above processing, the Markov transition matrix M is finally obtained. The matrix element M[i][j] represents the probability of transitioning from state i to state j.

[0031] In a preferred embodiment of the present invention, the process of analyzing the user's long-term location preferences in step 1.3 includes:

[0032] Step 1.3.1: Solve for the principal eigenvectors:

[0033] According to Markov chain theory, the vector π corresponding to the steady-state distribution must satisfy the mathematical equation "π×M = π", and the solution to this equation is the "left eigenvector" with "eigenvalue 1" corresponding to the transition matrix M.

[0034] Step 1.3.2: Normalization process:

[0035] Since the steady-state distribution must satisfy the condition that "the sum of the probabilities of all states is 1", the initial feature vector π_raw needs to be normalized: each element in the vector is divided by the sum of all elements to obtain the final steady-state distribution π.

[0036] In a preferred embodiment of the present invention, the process of establishing the location privacy protection mechanism in step 2 includes:

[0037] Step 2.1: Generate the perturbation matrix element by element;

[0038] Step 2.2: Normalize the perturbation matrix;

[0039] Step 2.2.1: Traverse each row i of the perturbation matrix M' and calculate the sum of all elements in that row.

[0040] Step 2.2.2: Divide each element M'[i][j] in the row by sum_row_i to obtain the normalized element value, i.e., M'[i][j] = M'[i][j] / sum_row_i.

[0041] Step 2.2.3: After normalization, the sum of each row of elements is restored to 1, ensuring that the perturbed matrix can still accurately reflect the probability distribution of user state transitions.

[0042] In a preferred embodiment of the present invention, the process of generating the perturbation matrix element by element in step 2.1 involves traversing all elements of the original transition matrix M and calculating the perturbation probability value based on the relationship between the physical distance between states and the distortion threshold. The specific rules are as follows:

[0043] Step 2.1.1: Determine the relationship between distance and threshold;

[0044] If D[i][j] > θ: an "exponential decay penalty" needs to be applied to the original transition probability M[i][j]. The penalty coefficient is calculated as follows: penalty = exp (−λ∗ (D[i][j]−θ)).

[0045] Where exp() is the exponential function, and (D[i][j]−θ) represents the "distance portion exceeding the threshold";

[0046] If D[i][j]≤θ: no additional penalty is required, the penalty coefficient is penalty=1.0, and the probability after perturbation M'[i][j]=the original probability M[i][j], directly retaining the transition characteristics of the near state;

[0047] Step 2.1.2: Calculate the probability after the perturbation;

[0048] For each transition pair (i, j), the original probability M[i][j] is multiplied by the corresponding penalty coefficient to obtain the probability value after the initial perturbation, i.e., M'[i][j] = M[i][j] * penalty.

[0049] In a preferred embodiment of the present invention, the process of initializing the parameter space in step 3.1 includes:

[0050] Step 3.1.1: Determine the range of values ​​for λ:

[0051] Set a minimum value λ_min and a maximum value λ_max for λ. The values ​​should reflect the "difference in decay rate"—λ_min corresponds to "weak penalty" and λ_max corresponds to "strong penalty".

[0052] Step 3.1.2: Determine the range of values ​​for θ:

[0053] Set the minimum value θ_min and the maximum value θ_max of θ. The values ​​should reflect the "difference of the perturbation boundary"—θ_min corresponds to the "no exemption distance" and θ_max corresponds to the "wide exemption distance".

[0054] Step 3.1.3: Generate parameter combinations:

[0055] By using a grid search method, the ranges of λ and θ are discretized with a fixed step size, generating all possible parameter combinations {(λ1,θ1), (λ1,θ2), ..., (λ...}. n ,θ m )}, ensuring that every key node in the parameter space is traversed.

[0056] In a preferred embodiment of the present invention, step 3.2, which involves traversing parameter combinations and calculating a comprehensive score, includes:

[0057] Step 3.2.1: Generate the perturbation matrix M';

[0058] Based on the current parameters λ and θ, the privacy-enhanced transition matrix is ​​generated with reference to the perturbation logic in step 2. The core is to calculate the correspondence between the original matrix and the penalty coefficient through the "Hadamard product":

[0059] (1) First, for each element D[i][j] of the distance matrix D, calculate the penalty coefficient matrix P: if D[i][j]>θ, then P[i][j]=exp(−λ*(D[i][j]−θ)); if D[i][j]≤θ, then P[i][j] = 1.0;

[0060] (2) Then, the preliminary perturbation matrix is ​​calculated by the Hadamard product: M'_raw[i][j] = M[i][j]*P[i][j];

[0061] (3) Finally, normalize M'_raw:

[0062] Iterate through each row i, calculate the sum of the elements in that row and sum_row_i, divide each row element by sum_row_i to obtain the final perturbation matrix M';

[0063] Step 3.2.2: Calculate the core evaluation indicators;

[0064] The core evaluation metrics include "Mutual Information (MI)" and "Distortion (Dist)," which need to be calculated and recorded separately:

[0065] (1) Calculate mutual information MI: Referring to the logic of step 3, based on the original matrix M, the perturbation matrix M' and the steady-state distribution π, calculate the original system entropy H(X), the perturbation system entropy H(Y), and the joint entropy H(X,Y) in sequence. Finally, obtain the mutual information value through MI=H(X) +H(Y)−H(X,Y)—the larger the MI, the more original trajectory information the perturbation matrix retains, and the higher the risk of privacy leakage.

[0066] (2) Calculate the distortion Dist:

[0067] The loss of data availability is quantified by the "change in average transfer distance", using the following formula:

[0068] Dist=(1 / N)*Σ|d_ij' −d_ij|;

[0069] Where N is the total number of transfer pairs, d_ij is the geographical distance of the original transfer pair (i,j), and d_ij' is the "probability-weighted distance" of the perturbed transfer pair (i,j);

[0070] Step 3.2.3: Indicator normalization processing;

[0071] Because MI and Dist have different units and ranges of value, direct weighting will lead to one indicator dominating the score. Therefore, normalization is required to map the indicators uniformly to the [0,1] interval:

[0072] (1) Mutual information normalization:

[0073] Calculate the maximum mutual information MI_max among all parameter combinations, and let MI_norm = MI / MI_max — the closer MI_norm is to 1, the more serious the privacy leakage; the closer it is to 0, the better the privacy protection effect.

[0074] (2) Distortion normalization:

[0075] Calculate the maximum distortion value Dist_max among all parameter combinations, and set Dist_norm = Dist / Dist_max — the closer Dist_norm is to 1, the lower the data availability; the closer it is to 0, the higher the data availability.

[0076] Step 3.2.4: Calculate the overall score;

[0077] Based on the normalized indicators and weights α, a linear weighted comprehensive scoring model is constructed, with the formula: Comprehensive score = α * MI_norm + (1 − α) Dist_norm. Model logic: α MI_norm reflects the "cost of privacy leakage", and (1 − α) * Dist_norm reflects the "cost of usability loss". The smaller the sum of the two, the better the "privacy-utility balance effect" of the parameter combination.

[0078] In a preferred embodiment of the present invention, step 3.3, the process of selecting the optimal parameter combination, includes:

[0079] Step 3.3.1: Collect the "parameter pair (λ,θ)−comprehensive score" data corresponding to all parameter combinations to form a score list;

[0080] Step 3.3.2: Find the record with the "smallest overall score" in the score list. The corresponding parameter pair is the optimal parameter pair (λ∗, θ∗).

[0081] Step 3.3.3: Verify the rationality of the optimal parameters:

[0082] It is necessary to ensure that the MI_norm corresponding to (λ∗, θ∗) is small and the Dist_norm is small (availability meets the standard) to avoid the extreme case of "one indicator is optimal and the other indicator is extremely poor";

[0083] Step 3.3.4: The final output (λ∗, θ∗) can be directly used to generate a personalized privacy protection mechanism for users in the future. Substituting this parameter combination into step 2 will yield a perturbation-transition matrix that is "less prone to privacy leaks and more usable", thus achieving a balance between location trajectory privacy protection and data application.

[0084] Compared with existing technologies, this invention provides a personalized location trajectory privacy protection method based on mutual information, which has the following beneficial effects:

[0085] 1. In terms of optimizing user privacy protection strategies, the method described in this invention improves the practicality of user location trajectory by adding the parameters of dwell time and number of visits, further optimizes and upgrades the relevant algorithms, and enhances the effect of user privacy protection, thereby improving the effectiveness of dynamic trajectory protection.

[0086] 2. The method incorporates a dynamic range design with added regularization parameters to dynamically consider the parameters, thereby improving their dynamic optimization characteristics. Furthermore, it uses grid search combined with contour plots to visualize the optimal parameters. This dynamic regularization design effectively enhances the sensitivity of the parameters.

[0087] 3. In the final rendering of the method in the program, this method uses a comparative analysis of linear weighting and nonlinear combination as the basis for empirical selection; and in the visualization process, the optimal solution distribution in the parameter space is displayed through 3D surface plots and contour plots. 3D surface plots and contour plots have the advantage of better intuitive display, which effectively improves the visibility of the system.

[0088] 4. This method avoids interference from extreme values ​​by setting the distortion threshold through quantile normalization, thereby increasing the robustness of parameter evaluation.

[0089] 5. By employing a quadtree subdivision granularity control method, this method can significantly improve the accuracy of data processing, meet the accuracy requirements of users' daily location trajectory, reduce the impact of infrequently occurring data on the redundancy of the overall dataset, and effectively improve the utility of the data. Attached Figure Description

[0090] Figure 1This is a flowchart of the personalized location trajectory privacy protection method based on mutual information according to the present invention.

[0091] Figure 2 This is a Markov matrix diagram for different users of this invention.

[0092] Figure 3 The graph shows the results of the mutual information matrix algorithm in Embodiment 2 of the present invention.

[0093] Figure 4 The graph shows the results of the distortion matrix algorithm in Embodiment 2 of the present invention.

[0094] Figure 5 This is a graph showing the running results of the comprehensive index matrix algorithm in Embodiment 2 of the present invention.

[0095] Figure 6 This is a comparison diagram of mutual information leakage in Embodiment 2 of the present invention.

[0096] Figure 7 This is a comparison chart of POI recall rates in Embodiment 2 of the present invention.

[0097] Figure 8 This is a comparison chart of average geographical errors in Embodiment 2 of the present invention. Detailed Implementation

[0098] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0099] Example 1:

[0100] Please see Figures 1-8 This invention provides a technical solution: a personalized location trajectory privacy protection method based on mutual information. This method first verifies the legitimacy of the user-input dataset and obtains a directory. After selecting a user, it dynamically adjusts the grid granularity. High-density areas are subdivided using quadtrees to generate a finer grid, forming a unique geographic state identifier. For each state, the algorithm statistically analyzes the access frequency and dwell time, and calculates a weighted sensitivity score. Then, it traverses the combination of regularization parameters and distortion thresholds through grid search to construct a state transition matrix and calculate physical distance. A comprehensive evaluation curve is generated by combining mutual information and distortion indicators. Finally, the optimal parameter point is located, and the results are visualized through a 3D surface map and contour lines, with key parameter values ​​annotated. Specifically, it includes:

[0101] Step 1: Data preprocessing;

[0102] The algorithm filters the trajectory data of target users by verifying the latitude and longitude range. Due to the characteristics of the dataset, most users' location trajectories are located within Beijing. Therefore, special points outside the territory of the People's Republic of China are filtered and discarded, with a focus on the privacy protection requirements of location trajectories within Beijing. The remaining filtered data is then optimized to reduce processing complexity and minimize noise interference.

[0103] First, the grid size is adjusted based on trajectory density to perform dynamic grid partitioning, thereby improving the rationality of data granularity. For high-density data regions, a finer network is established to more meticulously perturb these areas with high privacy leakage risks, ensuring adequate privacy protection. Finally, low-frequency states are merged, effectively reducing the interference of invalid data on algorithm complexity.

[0104] After initial assessment and filtering of the data, the next step is to extract usable information from the dataset.

[0105] First, the trajectory information of a specified user is extracted from the geographic trajectory dataset, converted into a state sequence, the original transition matrix is ​​calculated and normalized, and the steady-state distribution is calculated through eigenvalue decomposition.

[0106] Subsequently, a Markov transition matrix is ​​constructed based on the state sequence, and the matrix is ​​visualized using a heatmap. Finally, a thermodynamic matrix is ​​generated, visually displaying the probability of transitioning from the initial state to the target state in the trajectory data. Schematic diagrams of the Markov matrices for different users are shown below. Figure 2 As shown.

[0107] pass Figure 2 It can be seen that the Markov transition matrices of different users have different characteristics, which is consistent with the personalization design goal at the beginning of the algorithm design, and can personalize the location trajectory of individual users through the algorithm.

[0108] The heatmap of the Markov transition matrix shows that users generally follow routes with a probability close to 1, which is consistent with the straightness of travel routes. This demonstrates the reliability and realism of the model and verifies the credibility of the experimental results.

[0109] Observing some of these trajectory points reveals a significant change in probability, shifting to any value between 0 and 1. This indicates that some "abnormal behaviors" of users were discovered during data processing. The higher probability values ​​among these "abnormal behaviors" can reflect users' lifestyle habits and implicit personal privacy, such as their home and work addresses. More detailed analysis can reveal users' preferred milk tea shops, etc. These "abnormal behaviors" represent privacy breaches and become key data points requiring protection.

[0110] The core objective of data preprocessing is to discretize user location trajectory data, model state transition patterns, and analyze long-term location preferences. The results are ultimately presented visually to provide data support for subsequent privacy protection strategy design. The specific process consists of four key steps. Before starting the algorithm, two core input data points must be clearly defined to ensure that the data format and content meet the requirements of subsequent processing:

[0111] User trajectory point set: contains the location data of users at different time points. Each trajectory point must record both the geographic coordinates (such as latitude and longitude) and the corresponding timestamp (such as "2024-05-20 08:30:00"). This data is the original basis for analyzing user movement patterns, such as the set of continuous location points of a user from home to the company during the morning rush hour.

[0112] State label set S: A predefined geographic region classification rule used to "map" continuous geographic coordinates to discrete "states". A common implementation is to subdivide the geographic space using a quadtree to generate dynamic grids (e.g., dividing Beijing into several equally sized or adjustable grids). Each grid corresponds to a unique state label (e.g., "S1", "S2"), and different grids (states) do not overlap and cover the entire study area, ensuring that each trajectory point can be matched with a unique state. The specific data preprocessing process in this embodiment includes:

[0113] Step 1.1: Generate a state sequence—transform the continuous trajectory of the target user into discrete states;

[0114] The core of this step is to eliminate the "continuity" of the trajectory data and transform it into a "discrete state sequence" that meets the requirements of the Markov model. The specific operations are as follows:

[0115] Step 1.1.1: Traverse all input user trajectory points and perform "state matching" for each trajectory point: Based on the latitude and longitude coordinates of the point, determine which geographical region (such as a grid) in the state label set S it falls into, and then use the state label (such as "S3") corresponding to that region as the "discrete state" of the trajectory point.

[0116] Step 1.1.2: Arrange the discrete states of all trajectory points in chronological order to form a "state sequence". For example, a user starts from home (corresponding to state S1), passes through a subway station (S5), near an office building (S8), and finally arrives at the company (S10). The state sequence may be "[S1, S1, S5, S5, S8, S10, S10]" (chronological order from left to right), and the sequence length is the same as the total number of trajectory points.

[0117] Step 1.2: Construct the transition matrix—quantify the transition probabilities between states;

[0118] By statistically analyzing the "transition patterns between adjacent states" in the state sequence, a Markov transition matrix is ​​constructed to achieve the transformation from "number of transitions to transition probability." This process involves two steps:

[0119] Step 1.2.1: Count the number of transitions: (1) First, create a two-dimensional matrix (initially all elements are 0). The rows and columns of the matrix correspond to the discrete states in the state label set S (e.g., the row represents the "current state" and the column represents the "next state"). (2) Traverse the state sequence generated in step 1.1. For each pair of adjacent states (e.g., the t-th state is S_i and the (t+1)-th state is S_j), increment the count by 1 at the position of the i-th row and j-th column of the matrix. The final matrix element value is the "total number of transitions from state S_i to state S_j". For example, if "S1→S5" appears 12 times in the state sequence, then the value of the first row and fifth column of the matrix is ​​12.

[0120] Step 1.2.2: Normalization: (1) Since the transition matrix needs to satisfy the "Markov chain property" (the sum of probabilities of transitioning from a certain state to all other states is 1), each row of the transition number matrix needs to be "normalized": divide each element (transition number) of the row by the sum of all elements in the row (the total number of transitions of the state) to obtain the "probability of transitioning from state S_i to state S_j". For example, the total number of transitions of state S1 is 60, of which the number of "S1→S5" is 12. Then the probability value of the 1st row and 5th column after normalization is 12 / 60=0.2, that is, the probability of transitioning from S1 to S5 is 20%. After the above processing, the "Markov transition matrix M" is finally obtained, and the matrix element M[i][j] represents the "probability of transitioning from state i to state j".

[0121] Step 1.3: Calculate steady-state distribution—analyze users' long-term location preferences;

[0122] The steady-state distribution is the "long-term probability distribution" of the system's various states after the Markov chain has run for a "sufficiently long time." It reflects the user's core location preferences (such as high-frequency dwell states like home and workplace) in their long-term trajectory. The specific calculation is as follows:

[0123] Step 1.3.1: Solving for the principal eigenvector: According to Markov chain theory, the vector π corresponding to the steady-state distribution must satisfy the mathematical equation "π×M = π" (the result of multiplying the vector π by the transition matrix M is still equal to π). The solution to this equation is the "left eigenvector" (principal eigenvector) of the transition matrix M with an eigenvalue of 1. In actual calculations, this vector can be solved using mathematical methods such as matrix eigenvalue decomposition. For example, the initial vector π_raw = [0.35, 0.05, 0.12, ..., 0.28] (the number of elements is consistent with the total number of states).

[0124] Step 1.3.2: Normalization: Since the steady-state distribution needs to satisfy "the sum of the probabilities of all states is 1", the initial feature vector π_raw needs to be normalized: divide each element in the vector by the sum of all elements to obtain the final steady-state distribution π. For example, if the sum of π_raw is 1.02, after normalization π = [0.34, 0.05, 0.12, ..., 0.27], where π[i] represents "the probability that the user is in state i in the long run". The larger the value of π, the more likely that the state is the user's core area of ​​residence (e.g., the π value of the state corresponding to the home may be as high as 0.34, that is, 34% of the time is spent in this state).

[0125] Step 1.4: Visual Presentation—Intuitively displaying migration patterns and location preferences;

[0126] The abstract transition matrix and steady-state distribution are "visualized" through charts, facilitating the rapid identification of key information. Two types of charts are included:

[0127] Step 1.4.1: Transition Matrix Heatmap: Based on the transition matrix M, the matrix element values ​​(transition probabilities) are mapped using "color depth"—the darker the color (e.g., dark red), the higher the transition probability between corresponding states; the lighter the color (e.g., light yellow), the lower the transition probability. The horizontal axis of the chart represents the "next state," and the vertical axis represents the "current state." For example, in the heatmap, the cell for "current state S1 → next state S5" is dark blue, which visually shows that this is a user's high-frequency transition path (such as the daily route from home to the subway station).

[0128] Step 1.4.2: Steady-state distribution path diagram: Combining the steady-state distribution π and the transition matrix M, draw the "path network" of user state transitions: Each node in the diagram represents a discrete state, and the "size" of the node is positively correlated with the steady-state probability π[i] of that state (the larger π[i] is, the larger the node is), which can quickly locate the user's core dwell state (such as the state with the largest node being home or work); the connection between nodes represents the transition between states, and the "width" of the connection is positively correlated with the probability M[i][j] in the transition matrix (the larger M[i][j] is, the thicker the connection is), which can intuitively identify high-frequency transition paths (such as the thickest connection from home to subway station).

[0129] Step 2: After generating the Markov matrix in Step 1, normalize the matrix and establish a location privacy protection mechanism;

[0130] After the Markov matrix is ​​generated, key privacy-preserving points exposed need to be protected. This embodiment chooses to add perturbations for protection. By setting distortion thresholds and regularization parameters, the intensity of data perturbation can be controlled.

[0131] The regularization parameter controls the decay rate of the disturbance intensity. A larger regularization parameter value results in a faster decay of the exponential penalty term, allowing only very short-distance transfers (high privacy protection, low availability). Conversely, a smaller value results in a slower decay of the penalty term, allowing more long-distance transfers (low privacy protection, high availability). By dynamically adjusting the regularization parameter, the most suitable parameter for the user can be selected.

[0132] The choice of threshold determines the size of the perturbation unit, which directly determines the performance of the perturbation in terms of user privacy and usability. The perturbation strength is set by dynamically examining the threshold.

[0133] The core objective of location privacy protection mechanisms is to protect user privacy while preserving the availability of trajectory data as much as possible by adding targeted perturbations to the Markov transition matrix of the original location trajectory.

[0134] First, clarify the input and output data for this part. The input data is the original transition matrix M: a Markov transition matrix generated based on the user's historical trajectory. The matrix element M[i][j] represents the probability of the user transitioning from state i (such as a geographic grid) to state j, and satisfies that the sum of the probabilities of each row is 1 (which conforms to the Markov chain property).

[0135] The physical distance matrix D between states: Matrix element D[i][j] represents the "physical distance between the geographic regions corresponding to state i and state j". The distance is calculated using the Haversine formula (applicable to the spherical distance calculation of latitude and longitude coordinates) and is used to determine the degree of spatial correlation between different states.

[0136] The output data is the perturbation matrix M': a new transition matrix after adding perturbation and normalization to the original matrix M, which both masks the sensitive transition patterns of the user's real trajectory (protecting privacy) and retains a reasonable transition probability distribution (ensuring availability), and also satisfies that the sum of the probabilities of each row is 1.

[0137] Two key parameters need to be predefined to control the strength and granularity of the perturbation. The parameter values ​​need to be adjusted based on actual privacy requirements and data availability goals:

[0138] The regularization parameter λ plays a crucial role in controlling the rate at which geographical distance diminishes the intensity of disturbances. A larger λ value results in a stronger penalty (compression) on the probability of transitions between distant states, leading to higher privacy protection, but may reduce data availability. A smaller λ value results in a weaker penalty, retains more original transition information, and increases availability, but also increases the risk of privacy breaches.

[0139] The distortion threshold θ: Its core function is to define the spatial boundary of "whether additional perturbation is applied". The value of θ represents the "maximum geographical distance allowed without additional perturbation". When the physical distance D[i][j] ≤ θ between two states, they are considered to be spatially closely related and no additional compression is needed (preserving the original transfer characteristics); when D[i][j] > θ, they are considered to be spatially weakly related and their transfer probability needs to be weakened through exponential penalty (reducing privacy leakage). The specific process of establishing the location privacy protection mechanism described above in this embodiment includes:

[0140] Step 2.1: Generate the perturbation matrix element by element;

[0141] Iterate through all elements of the original transition matrix M (i.e., all state transition pairs (i, j)), and calculate the perturbation probability value based on the relationship between the physical distance between states and the distortion threshold, as follows:

[0142] Step 2.1.1: Determine the relationship between distance and threshold;

[0143] If D[i][j] > θ (states i and j are far apart): an "exponential decay penalty" needs to be applied to the original transition probability M[i][j]. The penalty coefficient is calculated as: penalty=exp (−λ∗ (D[i][j]−θ)).

[0144] Here, exp() is an exponential function, (D[i][j]−θ) represents the "distance part exceeding the threshold", and λ controls the degree of influence of this distance on the penalty coefficient - the larger the distance exceeding the threshold, the larger λ is, the closer the penalty is to 0, the smaller the probability M'[i][j] after perturbation, and the stronger the privacy protection.

[0145] If D[i][j]≤θ (states i and j are close): no additional penalty is required, the penalty coefficient is penalty=1.0, and the probability after perturbation M'[i][j]=the original probability M[i][j], directly retaining the transition characteristics of close states (avoiding excessive compression leading to loss of availability).

[0146] Step 2.1.2: Calculate the probability after the perturbation;

[0147] For each transition pair (i, j), the original probability M[i][j] is multiplied by the corresponding penalty coefficient to obtain the probability value after the initial perturbation, i.e., M'[i][j] = M[i][j] * penalty.

[0148] Step 2.2: Normalize the perturbation matrix;

[0149] Since the sum of elements in each row of the perturbation matrix M' may no longer be equal to 1 after adding the penalty (violating the probability distribution property of the Markov transition matrix), each row needs to be "row normalized" to ensure that the final matrix satisfies the probabilistic logic:

[0150] Step 2.2.1: Traverse each row i of the perturbation matrix M' and calculate the sum of all elements in that row (denoted as sum_row_i).

[0151] Step 2.2.2: Divide each element M'[i][j] in the row by sum_row_i to obtain the normalized element value, i.e., M'[i][j] = M'[i][j] / sum_row_i.

[0152] Step 2.2.3: After normalization, the sum of each row of elements is restored to 1, ensuring that the perturbed matrix can still accurately reflect the probability distribution of user state transitions, and can be used for subsequent trajectory analysis or LBS service calls.

[0153] Step 3: Measure the effectiveness of location privacy protection;

[0154] Mutual information, as a metric for measuring the interdependence between two random variables, can be understood as the degree of information sharing, used to measure the ability of two random variables to transfer information. This embodiment mainly uses mutual information as a criterion for evaluating the privacy protection effect before and after perturbation. The mutual information of the original and perturbed transition matrices is calculated using a formula. The formula for mutual information is as follows:

[0155] ;

[0156] In the formula, Let P be the steady-state distribution of state i (obtained through the eigenvalue decomposition of the transition matrix P). Let be the probability of transitioning from state i to state j in the original transition matrix. Let be the probability of transitioning from state i to state j in the compressed transition matrix.

[0157] Calculations show that the larger the mutual information value, the worse the privacy protection effect. Thus, mutual information is used to quantify the risk of privacy leakage and ensure that the disturbed data is difficult to trace back to the original trajectory.

[0158] The core objective of measuring the effectiveness of location privacy protection is to quantify the degree of privacy leakage and evaluate the effectiveness of privacy protection mechanisms by calculating the mutual information value between the original transition matrix and the perturbated transition matrix. At the same time, by combining the calculation of entropy and joint entropy, a complete privacy-information correlation analysis framework is constructed.

[0159] Specify input and output data: Input data

[0160] The original transition matrix M is an initial Markov transition matrix generated based on the user's trajectory. The matrix element M[i][j] represents the "original probability of transitioning from state i to state j", and the sum of the probabilities in each row is 1. It is the "benchmark data" for measuring privacy leakage.

[0161] Perturbation matrix M': The privacy-enhanced transition matrix obtained after step 2. The matrix element M'[i][j] represents the probability of transitioning from state i to state j after adding perturbation. It also satisfies that the sum of the probabilities of each row is 1, which is the "target data" after the privacy protection mechanism is applied.

[0162] Steady-state distribution π: The vector obtained by performing eigenvalue decomposition and normalization on the original transition matrix M in step 1. The vector element π[i] represents the "probability of the user being in state i in the long run", which is used to calculate the system entropy by weighting and reflects the weight of the impact of different states on overall privacy (such as higher weight for high-frequency stay states).

[0163] Minimum value ε: A pre-defined small constant (e.g., 10⁻) 8 The core function is to avoid the mathematical anomaly of "log(0)" in logarithmic calculations and ensure that the algorithm can still run normally in the scenario of matrix elements with a probability of 0.

[0164] Output data

[0165] Mutual Information Value (MI): An indicator that quantifies the degree of "information sharing" between the original matrix M and the perturbation matrix M'. The larger the MI value, the more original trajectory information is retained by the perturbation matrix, and the higher the risk of privacy leakage; the smaller the MI value, the better the privacy protection mechanism covers the original information, and the higher the privacy security.

[0166] Entropy is an indicator of the uncertainty of a random variable. In this embodiment, system entropy reflects the degree of disorder in the probability distribution of the transition matrix. A higher entropy value indicates a more dispersed transition probability distribution, stronger uncertainty, and greater difficulty for attackers to deduce the original trajectory through probability; a lower entropy value indicates a more concentrated transition probability distribution, stronger certainty, and a higher risk of privacy leakage. The algorithm needs to calculate the system entropy corresponding to the original and perturbation matrices separately. The specific steps are as follows:

[0167] Step 3.1: Initialize the parameter space;

[0168] The parameter space is the set of values ​​for the regularization parameter λ and the distortion threshold θ. It needs to be predefined in conjunction with actual privacy requirements and data characteristics (such as trajectory density and geographical range) to ensure coverage of the entire scenario from "weak perturbation-strong privacy" to "strong perturbation-weak privacy". The specific operation is as follows:

[0169] Step 3.1.1: Determine the range of values ​​for λ: Set the minimum value of λ_min (e.g., 0.001) and the maximum value of λ_max (e.g., 10). The values ​​should reflect the "difference in decay rate"—λ_min corresponds to "weak penalty (weak compression of long-distance transfer probability, weak privacy protection, strong usability)", and λ_max corresponds to "strong penalty (strong compression of long-distance transfer probability, strong privacy protection, weak usability)".

[0170] Step 3.1.2: Determine the range of θ values: Set the minimum value θ_min (e.g., 0) and the maximum value θ_max (e.g., 0.5) of θ. The values ​​should reflect the "difference of perturbation boundaries"—θ_min corresponds to "no exemption distance (all state transitions require perturbation, strong privacy protection)", and θ_max corresponds to "wide exemption distance (most short-distance transitions do not require perturbation, strong usability)".

[0171] Step 3.1.3: Generate parameter combinations: Using the "grid search" method, discretize the ranges of λ and θ with a fixed step size (e.g., λ step size 0.01, θ step size 0.05) to generate all possible parameter combinations {(λ1,θ1), (λ1,θ2), ...,(λ1,θ2)}. n ,θ m )}, ensuring that every key node in the parameter space is traversed.

[0172] Step 3.2: Traverse the parameter combinations and calculate the overall score;

[0173] For each parameter combination (λ, θ), the process of "generating the perturbation matrix → calculating the evaluation index → ​​normalization → calculating the comprehensive score" is executed sequentially to quantify the privacy-utility balance effect under this combination. The specific steps are as follows:

[0174] Step 3.2.1: Generate the perturbation matrix M';

[0175] Based on the current parameters λ and θ, the privacy-enhanced transition matrix is ​​generated with reference to the perturbation logic in step 2. The core is to calculate the correspondence between the original matrix and the penalty coefficient through the "Hadamard product (element-wise multiplication)".

[0176] (1) First, for each element D[i][j] of the distance matrix D, calculate the penalty coefficient matrix P: if D[i][j]>θ, then P[i][j]=exp(−λ*(D[i][j]−θ)) (exponential decay penalty); if D[i][j]≤θ, then P[i][j] = 1.0 (no additional penalty).

[0177] (2) Then, the initial perturbation matrix is ​​calculated by the Hadamard product: M'_raw[i][j] = M[i][j]*P[i][j] (that is, the original probability is multiplied element by element by the corresponding penalty coefficient).

[0178] (3) Finally, normalize M'_raw: traverse each row i, calculate the sum of the elements in that row and sum_row_i, divide each row element by sum_row_i, and obtain the final perturbation matrix M' (satisfying that the sum of the probabilities of each row is 1, which conforms to the Markov chain property).

[0179] Step 3.2.2: Calculate the core evaluation indicators;

[0180] The core evaluation metrics include "Mutual Information (MI)" (measuring privacy breaches) and "Distortion (Dist)" (measuring usability loss), which need to be calculated and recorded separately:

[0181] (1) Calculate mutual information MI: Referring to the logic of step 3, based on the original matrix M, the perturbation matrix M' and the steady-state distribution π (obtained from step 1), calculate the original system entropy H(X), the perturbation system entropy H(Y), and the joint entropy H(X,Y) in sequence. Finally, obtain the mutual information value through MI=H(X) +H(Y)−H(X,Y). The larger the MI, the more original trajectory information is retained by the perturbation matrix, and the higher the risk of privacy leakage.

[0182] (2) Calculate the distortion degree Dist: The loss of data availability is quantified by the "average change in transfer distance". The formula is Dist=(1 / N)*Σ|d_ij' −d_ij| (where N is the total number of transfer pairs, d_ij is the geographical distance of the original transfer pair (i,j), and d_ij' is the "probability-weighted distance" of the transfer pair (i,j) after perturbation). The larger Dist is, the greater the spatial difference between the perturbation trajectory and the original trajectory, and the lower the data availability.

[0183] Step 3.2.3: Indicator normalization processing;

[0184] Because MI and Dist have different units and ranges of value (e.g., MI may be [0,2], and Dist may be [0,1000]), direct weighting can lead to one indicator dominating the score. Therefore, normalization is required to map the indicators uniformly to the [0,1] interval.

[0185] (1) Mutual information normalization (MI_norm): Calculate the maximum value of mutual information MI_max among all parameter combinations, and let MI_norm=MI / MI_max. The closer MI_norm is to 1, the more serious the privacy leakage; the closer it is to 0, the better the privacy protection effect.

[0186] (2) Distortion normalization (Dist_norm): Calculate the maximum value of distortion Dist_max among all parameter combinations, and let Dist_norm = Dist / Dist_max. The closer Dist_norm is to 1, the lower the data availability; the closer it is to 0, the higher the data availability.

[0187] Step 3.2.4: Calculate the overall score;

[0188] Based on the normalized indicators and weights α, a linear weighted comprehensive scoring model is constructed, with the formula: Comprehensive Score = α * MI_norm + (1 − α)Dist_norm. Model logic: α * MI_norm reflects the "cost of privacy leakage," and (1 − α) * Dist_norm reflects the "cost of usability loss." The smaller the sum of the two, the better the "privacy-utility balance" of this parameter combination. For example, when α = 0.8, the weight of privacy leakage is 4 times that of usability loss, placing greater emphasis on privacy protection.

[0189] Step 3.3: Select the optimal parameter combination;

[0190] After iterating through all parameter combinations and calculating the overall score, the optimal parameter pair is selected by "minimizing the overall score". The specific operation is as follows:

[0191] Step 3.3.1: Collect the "parameter pair (λ,θ)−comprehensive score" data corresponding to all parameter combinations to form a score list.

[0192] Step 3.3.2: Find the record with the "smallest overall score" in the score list. The corresponding parameter pair is the optimal parameter pair (λ∗, θ∗).

[0193] Step 3.3.3: Verify the rationality of the optimal parameters: It is necessary to ensure that the MI_norm corresponding to (λ∗, θ∗) is small (privacy protection meets the standard) and the Dist_norm is small (availability meets the standard), to avoid the extreme case of "one indicator is optimal, the other indicator is extremely poor" (such as pursuing a low MI and causing Dist to be too large, making the trajectory data unusable).

[0194] Step 3.3.4: The final output (λ∗, θ∗) can be directly used to generate a personalized privacy protection mechanism for users in the future. Substituting this parameter combination into step 2 will yield a perturbation-transition matrix that is "less prone to privacy leaks and more usable", thus achieving a balance between location trajectory privacy protection and data application.

[0195] Example 2:

[0196] Unlike Embodiment 1 above, this embodiment uses simulation experiments to verify the effectiveness of the personalized location trajectory privacy protection method based on mutual information described in Embodiment 1.

[0197] 1. Development environment;

[0198] This experiment was implemented using personal computer programming and MATLAB software version R2024a. It verified relevant data on privacy protection parameters and performed operations such as 3D plotting. The main development environment is shown in Table 1.

[0199] Table 1: Development Environment Configuration

[0200] Development Environment Configuration operating system Windows 11 processor 11th Gen Intel(R) Core(TM) i7-11390H @ 3.40GHz 3.42 GHz Memory 16.0 GB language MATLAB Development tools MATLAB, Notepad++

[0201] 2. Data source;

[0202] The GPS dataset used in this embodiment was collected from 182 users in the Geolife project, spanning over five years (from April 2007 to August 2012). The GPS tracks in this dataset are represented by a series of timestamped points, each including latitude, longitude, and altitude information. The dataset contains 17,621 tracks, with a total distance of 1,292,951 kilometers and a total duration of 50,176 hours. These tracks were recorded by different GPS recorders and GPS-enabled mobile phones at varying sampling rates. 91.5% of the tracks were recorded in a dense representation, for example, every 1 to 5 seconds or every 5 to 10 meters per point.

[0203] 3. Algorithm implementation results;

[0204] The algorithm's results are mainly displayed in two modules. The first module constructs the Markov transition matrix, and the second module displays the mutual information surface plot, distortion surface plot, and comprehensive index matrix, such as... Figure 3 , Figure 5 , Figure 5 show.

[0205] like Figure 3The mutual information matrix shows that the horizontal axis (X-axis) represents the hyperparameter λ, the vertical axis (Y-axis) represents the distortion threshold values, and the Z-axis (surface height / color) represents the mutual information value. Analysis of the overall trend reveals that the mutual information value decreases as the hyperparameter λ increases. This is because the hyperparameter λ controls the compression intensity. When the threshold increases, greater geographic distortion is allowed, and the mutual information value increases slightly. The extreme point occurs when the hyperparameter λ reaches its minimum value (0.001) and the threshold reaches its maximum value (0.5), at which point the mutual information is close to its maximum, indicating the most lenient compression and the most information retention. When the hyperparameter λ reaches its maximum value (10) and the threshold reaches its minimum value (0), the mutual information is close to its minimum, indicating the most stringent compression and the greatest information loss.

[0206] like Figure 4 The distortion matrix shows that the horizontal axis (X-axis) represents the hyperparameter λ, the vertical axis (Y-axis) represents the distortion threshold, and the Z-axis (surface height / color) represents the distortion value (used to measure the geographical difference between the compressed trajectory and the original trajectory; the smaller the value, the closer the compressed trajectory is to the original trajectory). Analysis of the overall trend reveals that the distortion value decreases significantly as the hyperparameter λ increases. This is because a larger hyperparameter λ results in a stronger penalty for geographical distance during compression, forcing the compressed trajectory to be closer to the spatial distribution of the original trajectory. When the threshold increases, the distortion value increases slightly (allowing for greater geographical differences, resulting in a looser spatial distribution of the compressed trajectory). The extreme point is when the hyperparameter λ reaches its maximum value (10) and the threshold reaches its minimum value (0), resulting in the smallest distortion value, indicating that the spatial difference between the compressed trajectory and the original trajectory is minimal at this point. When the hyperparameter λ reaches its minimum value (0.001) and the threshold reaches its maximum value (0.5), the distortion value is maximum, indicating that the spatial distribution of the compressed trajectory is the loosest at this point.

[0207] like Figure 5 The comprehensive indicator matrix chart shows the hyperparameter λ on the horizontal axis (X-axis) and the distortion threshold on the vertical axis (Y-axis). The color / contour lines represent the comprehensive indicator values ​​(a weighted indicator balancing mutual information and distortion). Red solid dots mark the optimal parameter combination (the hyperparameter λ and threshold that maximize the comprehensive indicator). Key analytical indicator logic: Mutual information (weight 0.8) dominates the comprehensive indicator, emphasizing the importance of information retention; distortion (weight 0.2) is converted to "fidelity" through 1-distortion, avoiding over-compression that renders the trajectory unusable.

[0208] The optimal parameters emerge when the optimal hyperparameter λ and the threshold are positioned at a trade-off point between mutual information and distortion. For example, if the optimal hyperparameter λ is small and the threshold is large, the system tends towards loose compression to preserve information. If the optimal hyperparameter λ is large and the threshold is small, the system tends towards strict compression to control spatial distortion. Contour distribution: Dense contour areas indicate high parameter sensitivity (small parameter changes significantly affect overall performance). Sparse contour areas indicate strong parameter robustness (allowing for some parameter fluctuations without affecting performance).

[0209] Analysis of the three images above reveals that in this scheme, a Markov transition matrix is ​​formed based on the dynamic trajectories of different users over a period of time. This matrix is ​​then analyzed to identify the user's unique trajectory points, which are then specially marked. Weights are added based on the user's dwell time and frequency over a period of time, and key privacy protection points are specially protected, thereby increasing the algorithm's practical usability.

[0210] After processing the Markov transition matrix, perturbations are added for protection. This involves setting a distortion threshold, which determines the increase or decrease in privacy and usability. Mutual information plays a role in measuring privacy leakage in the algorithm. The algorithm compromises between privacy and usability requirements for different distortion thresholds, setting different weights to display comprehensive index data. By analyzing the data, the optimal result is obtained, achieving the optimization of privacy protection mechanisms for different users. This allows for the implementation of personalized privacy protection mechanisms for different users, thereby achieving the best balance between privacy and usability. It maximizes usability while ensuring the privacy of user location trajectory usage, thus optimizing the user experience.

[0211] In summary, the method described in Embodiment 1 of this invention incorporates the parameters of dwell time and number of visits in its research on optimizing user privacy protection strategies. This improves the practicality of the method for analyzing user location trajectories, further optimizes and upgrades the relevant algorithms, and enhances the effectiveness of user privacy protection, thereby improving the dynamic trajectory protection of users.

[0212] 4. Method performance analysis;

[0213] In the research on privacy protection strategies based on mutual information, due to the large volume of data and significant data noise interference, data processing requires a certain degree of data filtering and sensitivity design to optimize data processing complexity and improve the speed of running code. The method described in Embodiment 1 of this invention employs the following data processing approach and possesses the following characteristics:

[0214] (1) Adding dynamic regularization parameters

[0215] In the method design, a dynamic range design for the regularization parameter (Lambda) is added to dynamically consider the parameters, improve their dynamic optimization characteristics, and use grid search combined with contour plots to visualize the optimal parameters. The dynamic regularization design effectively improves the sensitivity of the parameters.

[0216] (2) Multi-objective optimization and comprehensive index design

[0217] In the final rendered image, the weighting coefficients in the comprehensive index referenced the Pareto front method proposed by NAGHIZADE E et al. in their paper to optimize the trade-off between mutual information and distortion. A comparative analysis of linear weighting and nonlinear combinations was proposed as the empirical basis for selection. Furthermore, during visualization, 3D surface plots and contour plots were used to display the optimal solution distribution in the parameter space. These methods offer better intuitive visualization, effectively improving the system's visibility.

[0218] (3) Distortion threshold and geographic distance standardization

[0219] Regarding the setting of the distortion threshold, quantile normalization is applied to the distortion threshold to avoid interference from extreme values, increase the robustness of parameter evaluation, and perform weighted processing on the distortion calculation.

[0220] (4) Trajectory data processing and quadtree subdivision

[0221] Since the dataset is based on actual latitude trajectories, and the proportion of data in the dataset is relatively large for individuals, more precise granular control is required. Granular control through quadtree subdivision can significantly improve the accuracy of data processing, meeting the accuracy needs of users for daily location trajectory tracking. Furthermore, state encoding and merging of low-frequency states (those occurring less than 10 times) greatly reduces the redundancy of infrequently occurring data in the overall dataset, effectively improving data utility.

[0222] 4.1: Performance comparison with conventional differential privacy methods;

[0223] The Markov algorithm described in Embodiment 1 of this invention is compared with two representative parameter designs in conventional differential privacy protection algorithms. Since the actual location data requires a large amount of computation, the computation time is too long, and it is difficult to run the algorithm in practice, a simulated dataset is used for performance comparison and analysis.

[0224] The simulated dataset has the following characteristics: Data runs from 08:00:00 on May 28, 2025 to 14:00:00 on the same day, for a total duration of 6 hours. Trajectory points are recorded every 5 minutes, with a fixed sampling interval. To simplify the evaluation algorithm, the range of longitude and latitude variations is set to be small, concentrating the trajectory analysis on a specific local area to reduce the workload of the algorithm in data processing. Dwell time fluctuates periodically between 180 and 420 seconds to simulate user dwell habits in different locations, allowing for the setting of the sensitivity of the Markov privacy protection algorithm.

[0225] 4.2: Performance Comparison Results;

[0226] The algorithm performance was compared in three aspects: mutual information leakage (MI Leakage), point-of-inquiry (POI) recall, and average geographic error (Avg Error). These aspects specifically examined the algorithm's ability to infer original data from anonymized data, its ability to retain key location points in anonymized data, and the average spatial deviation between anonymized and original points. Visualization charts comparing the algorithm described in Embodiment 1 of this invention with differential privacy protection algorithms under two parameter settings are shown below. Figure 6 , Figure 7 and 8 As shown.

[0227] pass Figure 6 As can be seen from the comparison of mutual information leakage, the method described in Embodiment 1 of this invention has less mutual information leakage compared with conventional differential privacy protection algorithms, indicating that it has better performance in privacy protection and stronger ability to resist attackers from inferring original data from anonymous data.

[0228] pass Figure 7 It can be seen that, in terms of POI recall, the method described in Embodiment 1 of this invention has a certain advantage over differential privacy under the two algorithms in terms of the ability to retain key location points in anonymized data, which shows that the method described in Embodiment 1 of this invention has strong usability.

[0229] pass Figure 8 As can be seen, the method described in Embodiment 1 of the present invention has a smaller average geographic error, which can better serve the user's location-related services and improve the accuracy of the user's use of application services.

[0230] The results comparison above show that, compared with the differential privacy method, the Markov method proposed in Embodiment 1 of this invention can effectively guarantee usability while maintaining POI recall, and reduce privacy leakage, thus greatly protecting user privacy. Furthermore, the Markov method significantly outperforms traditional privacy-preserving algorithms in terms of average geographic error, exhibiting greater accuracy. Therefore, the method described in Embodiment 1 of this invention offers a significant improvement in both usability and privacy compared to traditional methods.

[0231] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A personalized location trajectory privacy protection method based on mutual information, characterized in that, include: Step 1: Data preprocessing; The trajectory data of target users is filtered by verifying the latitude and longitude range, and the filtered and retained data is then optimized. Step 2: After generating the Markov matrix in Step 1, the matrix is ​​normalized, and a location privacy protection mechanism is established by setting the distortion threshold and regularization parameters. Step 3: Measure the effectiveness of location privacy protection; Step 3.1: Initialize the parameter space; Step 3.2: Traverse the parameter combinations and calculate the overall score; Step 3.3: Select the optimal parameter combination.

2. The personalized location trajectory privacy protection method based on mutual information as described in claim 1, characterized in that, The data preprocessing process described in step 1 includes: Step 1.1: Generate a state sequence—transform the continuous trajectory of the target user into discrete states; Step 1.2: Construct the transition matrix—quantify the transition probabilities between states; Step 1.3: Calculate steady-state distribution—analyze users' long-term location preferences; Step 1.4: Visual Presentation—Intuitively displaying migration patterns and location preferences; The abstract transition matrix and steady-state distribution are "visualized" through a heatmap of the transition matrix and a pathmap of the steady-state distribution.

3. The personalized location trajectory privacy protection method based on mutual information as described in claim 2, characterized in that, Step 1.1, which describes the process of converting the continuous trajectory of the target user into a discrete state, includes: Step 1.1.1: Traverse all input user trajectory points and perform "state matching" for each trajectory point: Based on the latitude and longitude coordinates of the point, determine which geographical region in the state label set S it falls into, and then use the state label corresponding to that region as the "discrete state" of the trajectory point. Step 1.1.2: Arrange the discrete states of all trajectory points in chronological order to form a "state sequence".

4. The personalized location trajectory privacy protection method based on mutual information as described in claim 2, characterized in that, Step 1.2 describes the process of quantifying the transition probabilities between states by constructing a Markov transition matrix through statistical analysis of the "jumping patterns between adjacent states" in the state sequence, thereby achieving the transformation from "number of transitions to transition probability." Specifically, this includes: Step 1.2.1: Count the number of transfers; (1) First, create a two-dimensional matrix, where the rows and columns of the matrix correspond to the discrete states in the state label set S; (2) Traverse the state sequence generated in step 1.

1. For each pair of adjacent states, increment the count by 1 at the position of the i-th row and j-th column of the matrix. The final matrix element value is the total number of times the state transitions from state S_i to state S_j. Step 1.2.2: Row normalization processing; (1) Since the transition matrix needs to satisfy the "Markov chain property", each row of the transition number matrix needs to be "normalized" by dividing each element of the row by the sum of all elements in the row to obtain the "probability of transitioning from state S_i to state S_j". (2) After the above processing, the "Markov transition matrix M" is finally obtained. The matrix element M[i][j] represents the "probability of transitioning from state i to state j".

5. A personalized location trajectory privacy protection method based on mutual information as described in claim 2, characterized in that, Step 1.3 describes the process of analyzing users' long-term location preferences, which includes: Step 1.3.1: Solve for the principal eigenvectors; According to Markov chain theory, the vector π corresponding to the steady-state distribution must satisfy the mathematical equation "π×M = π", and the solution to this equation is the "left eigenvector" with "eigenvalue 1" corresponding to the transition matrix M. Step 1.3.2: Normalization process; Since the steady-state distribution must satisfy "the sum of the probabilities of all states is 1", the initial feature vector π_raw needs to be normalized: divide each element in the vector by the sum of all elements to obtain the final steady-state distribution π.

6. The personalized location trajectory privacy protection method based on mutual information as described in claim 1, characterized in that, The process of establishing the location privacy protection mechanism described in step 2 includes: Step 2.1: Generate the perturbation matrix element by element; Step 2.2: Normalize the perturbation matrix; Step 2.2.1: Traverse each row i of the perturbation matrix M' and calculate the sum of all elements in that row; Step 2.2.2: Divide each element M'[i][j] in this row by sum_row_i to obtain the normalized element value, i.e., M'[i][j] = M'[i][j] / sum_row_i; Step 2.2.3: After normalization, the sum of each row of elements is restored to 1.

7. The personalized location trajectory privacy protection method based on mutual information as described in claim 1, characterized in that, Step 2.1 describes the process of generating the perturbation matrix element by element. This involves traversing all elements of the original transition matrix M and calculating the perturbation probability values ​​based on the relationship between the physical distance between states and the distortion threshold. The specific rules are as follows: Step 2.1.1: Determine the relationship between distance and threshold; If D[i][j] > θ: an "exponential decay penalty" needs to be applied to the original transition probability M[i][j]. The penalty coefficient is calculated as follows: penalty = exp (−λ∗ (D[i][j]−θ)). Where exp() is the exponential function, and (D[i][j]−θ) represents "the distance portion exceeding the threshold"; If D[i][j]≤θ: no additional penalty is required, the penalty coefficient is penalty=1.0, and the probability after perturbation M'[i][j]=the original probability M[i][j], directly retaining the transition characteristics of the near state; Step 2.1.2: Calculate the probability after the perturbation; For each transition pair (i, j), the original probability M[i][j] is multiplied by the corresponding penalty coefficient to obtain the probability value after the initial perturbation, i.e., M'[i][j] = M[i][j] * penalty.

8. The personalized location trajectory privacy protection method based on mutual information as described in claim 1, characterized in that, Step 3.1, the process of initializing the parameter space, includes: Step 3.1.1: Determine the range of values ​​for λ; Set a minimum value λ_min and a maximum value λ_max for λ. The values ​​should reflect the "difference in decay rate"—λ_min corresponds to "weak penalty" and λ_max corresponds to "strong penalty". Step 3.1.2: Determine the range of values ​​for θ; Set the minimum value θ_min and the maximum value θ_max of θ. The values ​​should reflect the "difference of the perturbation boundary"—θ_min corresponds to the "no exemption distance" and θ_max corresponds to the "wide exemption distance". Step 3.1.3: Generate parameter combinations; By using a "grid search" method, the ranges of λ and θ are discretized with a fixed step size, generating all possible parameter combinations {(λ1,θ1), (λ1,θ2), ..., (λ...}. n ,θ m )}, ensuring that every key node in the parameter space is traversed.

9. A personalized location trajectory privacy protection method based on mutual information as described in claim 8, characterized in that, Step 3.2, which describes the process of traversing parameter combinations and calculating the comprehensive score, includes: Step 3.2.1: Generate the perturbation matrix M'; (1) First, for each element D[i][j] of the distance matrix D, calculate the penalty coefficient matrix P: if D[i][j]>θ, then P[i][j]=exp(−λ*(D[i][j]−θ)); if D[i][j]≤θ, then P[i][j] = 1.0; (2) Then, the preliminary perturbation matrix is ​​calculated by the Hadamard product: M'_raw[i][j] = M[i][j]*P[i][j]; (3) Finally, normalize M'_raw: Iterate through each row i, calculate the sum of the elements in that row and sum_row_i, divide each row element by sum_row_i to obtain the final perturbation matrix M'; Step 3.2.2: Calculate the core evaluation indicators; The core evaluation metrics include "Mutual Information (MI)" and "Distortion (Dist)," which need to be calculated and recorded separately: (1) Calculate mutual information MI; MI = H(X) + H(Y) − H(X,Y) yields the mutual information value MI; (2) Calculate the distortion Dist; The loss of data availability is quantified by the "change in average transfer distance", using the following formula: Dist=(1 / N)*Σ|d_ij' −d_ij|; Where N is the total number of transfer pairs, d_ij is the geographical distance of the original transfer pair (i,j), and d_ij' is the "probability-weighted distance" of the perturbed transfer pair (i,j); Step 3.2.3: Indicator normalization processing; (1) Mutual information normalization; Calculate the maximum mutual information MI_max among all parameter combinations, and let MI_norm = MI / MI_max — the closer MI_norm is to 1, the more serious the privacy leakage; the closer it is to 0, the better the privacy protection effect. (2) Distortion normalization; Calculate the maximum distortion value Dist_max among all parameter combinations, and set Dist_norm = Dist / Dist_max — the closer Dist_norm is to 1, the lower the data availability; the closer it is to 0, the higher the data availability. Step 3.2.4: Calculate the overall score; Based on the normalized indicators and weights α, a linear weighted comprehensive scoring model is constructed, with the formula: Comprehensive score = α * MI_norm + (1 − α)Dist_norm.

10. A personalized location trajectory privacy protection method based on mutual information as described in claim 9, characterized in that, Step 3.3 describes the process of selecting the optimal parameter combination, which includes: Step 3.3.1: Collect the "parameter pair (λ,θ)−comprehensive score" data corresponding to all parameter combinations to form a score list; Step 3.3.2: Find the record with the "smallest overall score" in the score list. The corresponding parameter pair is the optimal parameter pair (λ∗, θ∗). Step 3.3.3: Verify the rationality of the optimal parameters: It is necessary to ensure that the MI_norm corresponding to (λ∗, θ∗) is small and the Dist_norm is small (availability meets the standard) to avoid the extreme case of "one indicator is optimal and the other indicator is extremely poor"; Step 3.3.4: The final output (λ∗, θ∗) can be directly used to generate a personalized privacy protection mechanism for users in the future. Substituting this parameter combination into step 2 will yield a perturbation-transition matrix that is "less prone to privacy leaks and more usable", thus achieving a balance between location trajectory privacy protection and data application.

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