Estimation method for business leisure space stay duration and walking speed based on zero-inflated gamma model

Abstract

The present application belongs to the technical field of data processing and computer application, and particularly relates to a business leisure space staying time length and walking speed estimation method based on a zero-inflated Gamma model. Sparse positioning data is used to obtain the total activity time length of tourists in a business leisure space set, estimate the sub-space sequence passed by the tourists, estimate the probability distribution of the staying time length of the tourists in each sub-space, and estimate the probability distribution of the walking speed of the pedestrians using a zero-inflated Gamma model. The method uses relatively easily obtained sparse positioning data, and the staying time length result can be used as an evaluation index of the attraction of the business leisure space, and the walking speed result can be used as a basis for the design and construction of the walking environment, thereby supporting business leisure space planning, design, operation, management and the like. The method is suitable for business street blocks, comprehensive shopping malls, parks, amusement parks, scenic spots and the like, and can be used as a module or algorithm in space utilization monitoring and evaluation work, and is feasible.

Description

Technical Field

[0001] This invention belongs to the field of data processing and computer application technology, specifically involving a method for estimating dwell time and walking speed in commercial and leisure spaces based on a zero-inflation Gamma model. This method is based on sparse location data to calculate the dwell time and walking speed of tourists in commercial and leisure spaces, and can be applied to the fields of commercial district development and management, retail, tourism, and urban planning. Background Technology

[0002] Commercial and leisure spaces, including commercial districts, shopping malls, parks, amusement parks, and scenic spots, are important venues for urban life and can be crucial windows into a city's economy. Visitor behavior within these spaces is a core basis for evaluating operational performance and developing planning and management measures. Among these, the duration of visitor stay is a key indicator of space vitality and utilization efficiency, while visitor walking speed is related to visitor experience and the safety and quality of the pedestrian environment. Currently, the mainstream method for evaluating the performance of personnel activities in commercial and leisure spaces is to measure and statistically analyze visitor flow, but the measurement of visitor stay duration remains insufficient, leading to an incomplete evaluation of space utilization; furthermore, insufficient attention is paid to visitor walking speed.

[0003] The lack of data on dwell time and walking speed in commercial and leisure spaces is primarily due to the limitations of existing measurement methods. The most traditional method is visitor questionnaires, which rely on visitors' recollections and accounts of their activities within the space. This data collection process is time-consuming, inefficient, and the accuracy is greatly affected by individual factors. More objective and accurate methods use sensors to locate visitors, such as RFID, Wi-Fi, and Bluetooth; however, these methods have limited practicality, mainly due to three issues: first, sensors require special deployment, resulting in high investment and maintenance costs; second, visitors need to carry signal transmitters or actively turn on Wi-Fi or Bluetooth, making implementation difficult and controllable; and third, high-frequency recording of location data is required to calculate individual dwell time, placing high demands on data processing and storage, leading to high implementation costs. Furthermore, while GPS can also be used for visitor positioning without sensors and is widely used on personal devices, it is not commonly used due to its impact on device battery life and the need for active cooperation from visitors for data feedback. Indoor positioning is also not feasible, thus its practical feasibility is also low.

[0004] To address this issue, existing methods, such as the Chinese invention patent application number CN2022106521399 entitled "Method for Estimating the Duration of Stay in Commercial and Leisure Spaces Based on Sparse Location Data", utilize sparse location data to calculate the duration of stay in commercial and leisure spaces. However, this method has four main problems: First, it assumes that the duration of stay in a space follows a normal distribution, but in reality, the duration of stay is non-negative, and using a normal distribution would result in unreasonable cases of negative stay durations. Second, the shape of a normal distribution is relatively regular, making it difficult to accurately depict the complexity of the actual duration of stay distribution; for example, zero stay duration (no stay) may account for a large proportion. Third, it assumes that the walking speed of pedestrians is a constant value of 1 m / s, estimates the walking time based on this value, and then subtracts it from the total activity time to obtain the total stay duration for model estimation. However, in reality, the walking speed of pedestrians is not constant, and the calculation based on a constant value artificially introduces errors. Fourth, this method fails to effectively handle the correlation of stay behaviors in different subspaces. Tourists are more likely to stay in adjacent subspaces, leading to a correlation in the number of stays in subspaces and causing a bias in the estimation of stay duration. This algorithm lacks effective constraints or regularization processing. Summary of the Invention

[0005] To address the problems of existing technologies, the purpose of this invention is to calculate the dwell time of tourists and the walking speed of pedestrians in commercial and leisure spaces based on sparse location data and a specific algorithm. Using sparse location data, the total activity time of tourists in a set of commercial and leisure spaces is obtained, and the sequence of subspaces traversed by tourists is estimated. A zero-inflation Gamma model is used to estimate the probability distribution of tourist dwell time and pedestrian walking speed in each subspace. This method utilizes relatively easily obtainable sparse location data. The dwell time results can be used as an evaluation index of the attractiveness of commercial and leisure spaces, and the walking speed results can serve as a basis for the design and construction of pedestrian environments, supporting the planning, design, operation, and management of commercial and leisure spaces. The method is applicable to commercial districts, shopping malls, parks, amusement parks, scenic spots, and similar commercial and leisure spaces, and can be used as a module or algorithm in space utilization monitoring and evaluation, demonstrating good feasibility.

[0006] The technical solution of this invention is:

[0007] A method for estimating dwell time and walking speed in commercial leisure spaces based on a zero-inflation Gamma model includes the following steps:

[0008] Step 1. Setting conditions and acquiring data;

[0009] The commercial space is divided into several sub-spaces. ,in The number of subspaces; collecting sparse location trajectories of tourists;

[0010] Step 2. Data processing;

[0011] Extract location point pairs ,in The number of location pairs; calculate the total activity time between location pairs. and distance Based on the specific form of the commercial and leisure space, determine the number of times tourists pass through each sub-space. ;

[0012] Step 3. Estimation of dwell time and walking speed;

[0013] Assuming the tourist's walking time per unit distance Follows Gamma distribution ,in For shape parameters, For scale parameters;

[0014] Assuming the tourist is in the subspace The random variable of dwell time For all journeys through this subspace All point pairs are independent and identical zero-inflated Gamma distributions. ,in, Let's say it's the probability of not stopping. Let Gamma be the shape parameter of the distribution. is the scale parameter, and it is consistent across all subspaces;

[0015] Solve for the distribution parameters to obtain estimates of dwell time and walking speed.

[0016] Specifically,

[0017] Step 1. Setting conditions and acquiring data

[0018]

Step 1.1

[0019]

Step 1.2

[0020] Step 2. Data Processing

[0021]

Step 2.1

[0022]

Step 2.2

[0023]

Step 2.3

[0024]

Step 2.4

[0025]

Step 2.5

[0026] Step 3. Estimation of dwell time and walking speed

[0027]

Step 3.1

[0028]

[0029] in,

[0030] It is the walking time per unit distance (1m) for tourists. That is, walking speed; assuming Follows Gamma distribution ,in For shape parameters, For scale parameters;

[0031] Tourists in subspace The random variable of dwell time in the subspace is assumed to be for all passes through the subspace. All point pairs are independent and identical zero-inflated Gamma distributions. Its probability density function is:

[0032]

[0033] in, Let's say it's the probability of not stopping. Let Gamma be the shape parameter of the distribution. Let be the scale parameter, and let be consistent across all subspaces. This is the Gamma function.

[0034]

Step 3.2

[0035] Duration of stay It is also a random variable, and its probability distribution is derived as follows:

[0036] For the The trajectory between a pair of location points, allowing a certain trip The subspaces traversed are used Indicates (where) The set of subspaces traversed is Visitors may stop in a transit subspace ( ), or it may not stay ( Therefore, the total number of combinations of activities that either stay or do not stay in each of the pathway subspaces is . .use This represents a combination of activities, where the set of non-stop trips is... The set of stops is The probability of a combination of activities occurring is:

[0037]

[0038] in, This represents the probability of not staying in the dwell subspace. This represents the probability of staying in the non-staying subspace.

[0039] When the set of stops is not empty ( The sum of the dwell times in the corresponding subspace is a random variable. According to the summation rule of the independent and identically scaled Gamma distribution, the distribution of this duration sum is still a Gamma distribution. Its shape parameters are:

[0040]

[0041] Therefore, within an activity combination, the duration of stay The probability density function is:

[0042]

[0043] Due to walking time Scale parameters and dwell time They are different; neither is the sum of zero. The distribution requires the Welch-Satterthwaite formula to obtain an approximate Gamma distribution. Among them, shape parameters and scale parameters The calculation formula is as follows:

[0044]

[0045] Based on this, the total activity duration The probability density function is:

[0046]

[0047]

Step 3.3

[0048]

[0049] in, It is a constant, and uses parameters This is used to correct the non-stop probability of non-complete path subspaces.

[0050] On the other hand, in the case of a pause, the duration of the pause may be reduced, which is achieved by adjusting the shape parameters:

[0051]

[0052] in, To correct the parameters. Based on this, [the following is done]: Make corrections.

[0053]

Step 3.4

[0054]

[0055] Assuming that the generation processes of all position pairs are independent, the sample likelihood is the joint probability of the likelihoods of all position pairs:

[0056]

[0057]

Step 3.5

[0058]

[0059] in, It is the cumulative density function of the Gamma distribution. All constraints must be satisfied simultaneously, therefore the constraint likelihood is:

[0060]

[0061] The sample population constraint likelihood is:

[0062]

[0063] The sample population likelihood is corrected using the geometric mean of the sample population constraint likelihood:

[0064]

[0065] The model parameters are solved using the maximum likelihood method. Since maximizing the likelihood number is equivalent to maximizing the log-likelihood number, taking the natural logarithm of the likelihood number yields:

[0066]

[0067] The first term is a constant and can be omitted:

[0068]

[0069] The parameters obtained include: , , , , , , .

[0070] Based on these parameters, the probability that a tourist will not stop in any subspace, assuming the tourist has traversed the entire subspace, is:

[0071]

[0072] Substituting into Equation 2, we obtain the dwell time of each subspace ( The zero-inflation Gamma distribution .

[0073] Get the walking time per unit distance ( Gamma distribution Its reciprocal ( (i.e., walking speed)

[0074] Beneficial effects

[0075] Compared with the prior art, the advantages of the present invention are:

[0076] (1) The feasibility and sustainability of the implementation of the method of using easily accessible sparse positioning data to measure the dwell time and pedestrian walking speed in commercial and leisure spaces are good; it has a wide range of applicable scenarios.

[0077] (2) By introducing the zero-inflation Gamma model to estimate the probability distribution of the length of stay of tourists in each subspace, we can obtain the length of stay and walking speed distribution estimates that conform to the actual properties, and provide more accurate and reliable information support for the estimation of length of stay and walking speed. Attached Figure Description

[0078] Figure 1 This is a flowchart illustrating the implementation of the method of the present invention;

[0079] Figure 2 This is a schematic diagram illustrating the division of commercial street plots according to an embodiment of the present invention;

[0080] Figure 3 This is a sample table of sparse positioning trajectory data in an embodiment of the present invention;

[0081] Figure 4 This is a sample table of location point pairs in an embodiment of the present invention;

[0082] Figure 5 This is a table showing the inference of land parcel transit information based on location points in an embodiment of the present invention (1: transited, 0: not transited).

[0083] Figure 6 This is a table showing incomplete route information for land parcels in an embodiment of the present invention;

[0084] Figure 7 This is a table showing the model parameter estimation results of an embodiment of the present invention;

[0085] Figure 8 Table of average dwell time for land parcels estimated using the method in CN2022106521399;

[0086] Figure 9 This is a schematic diagram illustrating the distribution of walking time per unit distance according to an embodiment of the present invention;

[0087] Figure 10 This is a schematic diagram showing the distribution of dwell time on land parcels according to an embodiment of the present invention. Detailed Implementation

[0088] The technical solution provided in this application will be further described below with reference to specific embodiments and accompanying drawings. The advantages and features of this application will become clearer from the following description.

[0089] For example Figure 2 Taking a commercial street as an example, this paper presents a method for estimating dwell time and walking speed in commercial and leisure spaces based on a zero-inflation Gamma model, including the following steps: Figure 1 )

[0090] Step 1. Setting conditions and acquiring data;

[0091]

Step 1.1

[0092]

Step 1.2

[0093] Step 2. Data processing;

[0094]

Step 2.1

[0095]

Step 2.2

[0096]

Step 2.3

[0097]

Step 2.4

[0098] This embodiment provides an example of how to estimate the number of times a tourist passes through each plot of land: for example, if the starting plot is 2 and the ending plot is 4, then the plots passed through are 2, 3, and 4; or if the starting plot is 7 and the ending plot is 4, then the plots passed through are 7, 6, 5, and 4.

[0099]

Step 2.5

[0100] Step 3. Estimation of dwell time and walking speed;

[0101]

Step 3.1

[0102] : The constant term of the probability function for each plot of land not staying;

[0103] : Correction parameters for the non-stop probability function of incomplete route parcels;

[0104] : A constant term for the shape parameter of the distribution of dwell time in each plot;

[0105] Scale parameters for the distribution of dwell time on land parcels;

[0106] Shape correction parameters for the distribution of dwell time of incomplete transit sites;

[0107] Shape parameters of the walking time distribution per unit distance;

[0108] : Scale parameter of walking time distribution per unit distance.

[0109]

Step 3.2

[0110] Compare the results of applying the CN2022106521399 method (the old method) Figure 8 The method of this invention additionally estimates the pedestrian walking speed distribution. Figure 9 The calculated mean is 1.31 s / m (0.76 m / s), indicating a relaxed and leisurely pace, which is more in line with reality. The old method showed significant fluctuations in the estimated average dwell time for each plot; for example, the dwell time for plots 2, 4, and 6 was significantly shorter than other plots, and plot 2 even had a negative dwell time, which is illogical. This is mainly due to the correlation of passing behavior between adjacent plots. The method of this invention estimates a dwell time distribution that is more in line with reality and estimates the probability of not dwelling based on a zero-inflation structure, providing richer information, such as... Figure 10 The red dashed line represents the average dwell time including non-dwelling (duration = 0) behavior, and the blue dashed line represents the average dwell time excluding non-dwelling behavior.

[0111] The above description is merely a description of preferred embodiments of this application and is not intended to limit the scope of this application in any way. Any changes or modifications made by those skilled in the art based on the above-disclosed technical content should be considered as equivalent and valid embodiments and fall within the scope of protection of the technical solution of this application.

Claims

1. A method for estimating dwell time and walking speed in commercial leisure spaces based on a zero-inflation Gamma model, characterized in that, Includes the following steps: Step 1. Setting conditions and acquiring data; The commercial space is divided into several sub-spaces. ,in The number of subspaces; Collect sparse location trajectories of tourists; Step 2. Data processing; Extract location point pairs ,in The number of location pairs; calculate the total activity time between location pairs. and distance Based on the specific form of the commercial and leisure space, determine the number of times tourists pass through each sub-space. ; Step 3. Estimation of dwell time and walking speed; Assuming the tourist's walking time per unit distance Follows Gamma distribution ,in For shape parameters, For scale parameters; Assuming the tourist is in the subspace The random variable of dwell time For all journeys through this subspace All point pairs are independent and identical zero-inflated Gamma distributions. ,in, Let's say it's the probability of not stopping. Let Gamma be the shape parameter of the distribution. is the scale parameter, and it is consistent across all subspaces; Solve for the distribution parameters to obtain estimates of dwell time and walking speed.

2. The method for estimating dwell time and walking speed in commercial leisure spaces based on a zero-inflation Gamma model according to claim 1, characterized in that, Step 1 specifically involves: 【Step 1.1】Divide a commercial and leisure space into several sub-spaces, each sub-space consisting of… It means that among them The number of subspaces; 【Step 1.2】Collect sparse location trajectory samples of tourists in the commercial and leisure space. Each trajectory records several location points of a tourist and the time of occurrence.

3. The method for estimating dwell time and walking speed in commercial leisure spaces based on a zero-inflation Gamma model according to claim 1, characterized in that, Step 2 specifically involves: 【Step 2.1】Extract several pairs of adjacent position points from each trajectory; all position point pairs extracted from the trajectory sample constitute a position point pair sample, and the position point pairs are numbered as follows. ,in This represents the number of location pairs; 【Step 2.2】For the first For each pair of location points, the starting position is indicated by the chronological order of the tourist's actions. The termination position is indicated as The corresponding recording time is and ,satisfy Calculate the total time the tourist spends moving between this pair of locations. ; 【Step 2.3】Place the tourists at the first Activities between location pairs are divided into two categories: (1) walking activities, which refer to the movement of tourists between subspaces; and (2) staying activities, which refer to all activities other than walking activities, such as shopping, sightseeing, and resting. The time spent on walking activities is denoted by _____. This indicates the distance it traveled. Calculated based on the starting and ending locations and the form of the commercial space; the duration of the stay is calculated using... express( ); 【Step 2.4】For the first Based on the specific form of the commercial and leisure space, the number of times tourists pass through each sub-space is estimated using these location points. express( Then the total number of subspace traversals is: ; 【Step 2.5】For each pair of locations, in its subspace with non-zero traversal counts, distinguish between complete traversal spaces and incomplete traversal spaces; a complete traversal space refers to a subspace in which it can be assured that all activities of the visitor within that type of subspace are completely contained. and Within; rather than a complete transit space, refers to a subspace in which some of the activities of tourists may occur earlier than [the previous time period]. or later ; Use dummy variables Indicates the first Each pair of locations represents a non-complete path subspace. This indicates a complete path through the subspace.

4. The method for estimating dwell time and walking speed in commercial leisure spaces based on the zero-inflation Gamma model according to claim 3, characterized in that, Step 3 specifically involves: 【Step 3.1】Place the tourists at the first The total activity time between each pair of locations is broken down into walking time. and the duration of stay in the transit subspace , expressed as: in, It is the walking time per unit distance (1m) for tourists. That is, walking speed; assuming Follows Gamma distribution ,in For shape parameters, For scale parameters; Tourists in subspace The random variable of dwell time in the subspace is assumed to be for all passes through the subspace. All point pairs are independent and identical zero-inflated Gamma distributions. Its probability density function is: in, Let's say it's the probability of not stopping. Let Gamma be the shape parameter of the distribution. Let be the scale parameter, and let be consistent across all subspaces. It is the Gamma function; 【Step 3.2】Walking Time Since they are random variables, according to the multiplication rule, their probability distributions are all Gamma distributions. Its shape parameters are similar to Consistency, scale parameter is ; Duration of stay It is also a random variable, and its probability distribution is derived as follows: For the The trajectory between a pair of location points, allowing a certain trip The subspaces traversed are used To indicate, among which The set of subspaces traversed is Visitors may or may not stop in a transit subspace; therefore, the total number of activity combinations involving stopping or not stopping in each transit subspace is: ;use This represents a combination of activities, where the set of non-stop trips is... The set of stops is The probability of a combination of activities occurring is: in, This represents the probability of not staying in the dwell subspace. This represents the probability of staying in the non-staying subspace; When the set of dwell times is non-empty, the sum of the dwell times in the corresponding subspaces is a random variable. The distribution follows a Gamma distribution. Its shape parameters are: Therefore, within an activity combination, the duration of stay The probability density function is: walking time Scale parameters and dwell time They are different; neither is the sum of zero. The distribution of Gamma is approximated by the Welch-Satterthwaite formula. Among them, shape parameters and scale parameters The calculation formula is as follows: Based on this, the total activity duration The probability density function is: 【Step 3.3】Correct the dwell time distribution of the subspace; on the one hand, the probability of not dwelling may increase, which is corrected by the logistic function as follows: in, It is a constant, and uses parameters To correct the non-stop probability of non-complete path subspaces; On the other hand, in the case of a pause, the duration of the pause may be reduced, which can be achieved by adjusting the shape parameters: in, To correct the parameters; based on this, [the following is done]: Make corrections; 【Step 3.4】For each pair of locations, define the likelihood number. The probability of the observed total activity duration is given; due to the uncertainty of activity combinations, the probability of the total activity duration is synthesized from the probabilities of occurrence for all activity combinations: Assuming that the generation processes of all position pairs are independent, the sample likelihood is the joint probability of the likelihoods of all position pairs: 【Step 3.5】For each location pair, the constraint is: the dwell time and walking time in the subspace each time do not exceed the total activity time; the probability of this occurring is equivalent to the cumulative probability density of the total activity time under the dwell time or walking time distribution: in, It is the cumulative density function of the Gamma distribution; all constraints must be satisfied simultaneously, therefore the constraint likelihood is: The sample population constraint likelihood is: The sample population likelihood is corrected using the geometric mean of the sample population constraint likelihood: The model parameters are solved using the maximum likelihood method; taking the natural logarithm of the likelihood number yields: After omitting the first term, we get: The parameters obtained include: , , , , , , ; Based on these parameters, the probability that a tourist will not stop in any subspace, assuming the tourist has traversed the entire subspace, is: Substituting into Equation 2, we obtain the dwell time of each subspace. Zero-inflation Gamma distribution ; Get walking time per unit distance Gamma distribution Its reciprocal ( (i.e., walking speed)

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