Business leisure space staying duration and walking speed estimation method based on zero expansion Gamma model

Abstract

The invention belongs to the technical field of data processing and computer application, and particularly relates to a commercial leisure space staying duration and walking speed estimation method based on a zero-expansion Gamma model. The method comprises the following steps: acquiring the total activity duration of tourists in a commercial leisure space set by using sparse positioning data, estimating a subspace sequence through which the tourists pass, and estimating the probability distribution of the residence duration of the tourists in each subspace and the probability distribution of the walking speed of the pedestrians by using a zero-expansion Gamma model. According to the method, sparse positioning data which are relatively easy to obtain are utilized, a stay duration result can be used as an evaluation index of the attraction of the commercial leisure space, a walking speed result can be used as a basis for design and construction of a walking environment, and works such as planning, design, operation and management of the commercial leisure space are supported. The method is suitable for commercial leisure spaces such as commercial street areas, comprehensive shopping malls, parks, amusement parks and scenic spots, can be used as a module or algorithm in space utilization monitoring and evaluation work, and is good in feasibility.

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: A method for estimating dwell time and walking speed in commercial leisure spaces based on a zero-inflation Gamma model 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; collecting 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.

[0007] Specifically, Step 1. Setting conditions and acquiring data

Step 1.1

[0008]

Step 1.2

[0009] Step 2. Data Processing

Step 2.1

[0010]

Step 2.2

[0011]

Step 2.3

[0012]

Step 2.4

[0013]

Step 2.5

[0014] Step 3. Estimation of dwell time and walking speed

Step 3.1

[0015]

Step 3.2

[0016] 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, making 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: in, This represents the probability of not staying in the dwell subspace. This represents the probability of staying in the non-staying subspace.

[0017] 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: Therefore, within an activity combination, the duration of stay The probability density function is: 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: Based on this, the total activity duration The probability density function is:

Step 3.3

[0018] 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: in, To correct the parameters. Based on this, [the following is done]: Make corrections.

[0019]

Step 3.4

Step 3.5

[0020] 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 ( The zero-inflation Gamma distribution .

[0021] Get the walking time per unit distance ( Gamma distribution Its reciprocal ( (i.e., walking speed)

[0022] Beneficial effects Compared with the prior art, the advantages of the present invention are: (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.

[0023] (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 estimated length of stay and walking speed that are consistent with the actual properties, and provide more accurate and reliable information support for the estimation of length of stay and walking speed. Attached Figure Description

[0024] Figure 1 This is a flowchart illustrating the implementation of the method of the present invention; Figure 2 This is a schematic diagram illustrating the division of commercial street plots according to an embodiment of the present invention; Figure 3 This is a sample table of sparse positioning trajectory data in an embodiment of the present invention; Figure 4 This is a sample table of location point pairs in an embodiment of the present invention; 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). Figure 6 This is a table showing incomplete route information for land parcels in an embodiment of the present invention; Figure 7 This is a table showing the model parameter estimation results of an embodiment of the present invention; Figure 8 Table of average dwell time for land parcels estimated using the method in CN2022106521399; Figure 9 This is a schematic diagram illustrating the distribution of walking time per unit distance according to an embodiment of the present invention; 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

[0025] 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.

[0026] 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 ) Step 1. Setting conditions and acquiring data;

Step 1.1

[0027]

Step 1.2

[0028] Step 2. Data processing;

Step 2.1

[0029]

Step 2.2

[0030]

Step 2.3

[0031]

Step 2.4

[0032] 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.

[0033]

Step 2.5

[0034] Step 3. Estimation of dwell time and walking speed;

Step 3.1

[0035]

Step 3.2

[0036] 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.

[0037] 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 the length of stay and walking speed in commercial leisure space based on zero-inflated Gamma model, characterized in that, Comprising the following steps: Step 1. Condition setting and data acquisition; Divide a commercial space into several subspaces wherein is the number of subspaces; Collecting sparse positioning trajectories of tourists; Step 2. Data processing; Extracting position point pairs Wherein is the number of position point pairs; calculating the total activity duration between position point pairs and distance ; according to the specific form of commercial leisure space, determining the number of times that tourists pass through each sub-space ; Step 3. Estimation of stay duration and walking speed; Assuming the length of time a tourist walks per unit distance Subject to a Gamma distribution where is a shape parameter, is a scale parameter; Assume that the length of stay of a visitor in a subspace is a random variable that is independent and identically distributed zero inflated Gamma for all visits to that subspace and for all pairs of locations where is the probability of not staying, is the shape parameter of the Gamma distribution, is the scale parameter, and is uniform across all subspaces; Solving distribution parameters to obtain the estimation of stay duration and walking speed.

2. The method of claim 1, wherein the method is based on a zero-inflated Gamma model. Step 1 is specifically, [Step 1.1] Divide a commercial leisure space into several subspaces, each of which is represented by wherein is the number of subspaces; 【Step 1.2】Collecting sparse positioning trajectory samples of tourists in the commercial leisure space, each trajectory recording a number of position points of a tourist and the time of recording. 3.The method of claim 1, wherein, Step 2 is specifically, 【Step 2.1】Extract several pairs of adjacent position points from each trajectory; all the pairs of position points extracted from the trajectory samples constitute a sample of pairs of position points, and the pairs of position points are numbered as wherein is the number of pairs of position points. 【Step 2.2】For the first location point pair, according to the time sequence of the occurrence of the tourist behavior, the starting location is represented as , the ending location is represented as , the corresponding recording time is and , and the following is satisfied . The total duration of the activity of the tourist between the location point pair is calculated as ; 【Step 2.3】The activities between pairs of visitor's position points are classified into two categories: (1) walking activity, which refers to the movement behavior between subspaces; (2) staying activity, which refers to all activities other than walking activity, such as shopping, visiting, resting, etc. The duration of walking activity is denoted by , which is calculated according to the start position, end position and the shape of the commercial space; the duration of staying activity is denoted by . ​​ 【Step 2.4】For the pair of the first and the second location points, the number of times that a tourist passes through each sub-space is denoted by according to the specific form of the commercial leisure space; then the total number of times that a tourist passes through each sub-space is . [Step 2.5] For each location pair, in its non-zero visit frequency subspace, distinguish between the complete visit subspace and the incomplete visit subspace; the complete visit subspace refers to the subspace in which all activities that can be confidently attributed to the visitor are contained within and ; while the incomplete visit subspace refers to the subspace in which some activities that can be attributed to the visitor are likely to be prior to or subsequent to ; with dummy variables denotes the pair of non-complete pass subspaces, denotes the complete pass subspace.

4. The method of claim 3, wherein the method is based on a zero-inflated Gamma model. Step 3 is specifically, [Step 3.1] The total activity duration between pairs of location points for a tourist is decomposed into walking duration and dwell duration in the transit subspace , expressed as: ​ Wherein, is the length of time a tourist walks for a unit distance (1 m), i.e. walking speed; it is assumed obeys a Gamma distribution where is the shape parameter, is the scale parameter; is a random variable of the length of stay of a visitor in a subspace , assuming that for all passing visits in this subspace and for all pairs of location points is an independent and identically distributed zero-inflated Gamma distribution with probability density function wherein is the probability of not staying, is the shape parameter of the Gamma distribution, is the scale parameter, and uniform across all subspaces, is the Gamma function; [Step 3.2] Walking duration For random variable, according to multiplication rule, its probability distribution is also Gamma distribution with the same shape parameter as and scale parameter ; Residence time Also a random variable, whose probability distribution is derived as follows: For the The trajectory between a pair of location points, making 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: wherein, denotes the non-residence probability of the residence subspace, denotes the residence probability of the non-residence subspace; When the set of dwell times is non-empty, the sum of dwell times in the corresponding subspace is a random variable ; the distribution is Gamma with shape parameter ​ Accordingly, under one activity combination, the probability density function of the length of stay is: ​ Duration of walk Scale parameter of the distribution of the duration of stay Sum of the two non-zero values The distribution of the duration of stay is approximated by a Gamma distribution using the Welch-Satterthwaite formula Where the shape parameter And the scale parameter The formula for the calculation is as follows: Accordingly, the probability density function of the total activity duration is 【Step 3.3】Correcting the stay duration distribution of the subspace; on the one hand, the probability of not staying may increase, which is corrected to by a logistic function: wherein is a constant and the non-habiting probability of the incomplete passage subspace is corrected by the parameter ; On the other hand, in the case of staying, the duration of staying may decrease, which is realized by correcting the shape parameter: wherein is a correction parameter; based on this, the is corrected; [Step 3.4] For each position pair, define a likelihood number The probability of occurrence of the total activity length observed; due to the uncertainty of the occurrence of the activity combination, the probability of occurrence of the total activity length is synthesized from the probabilities of occurrence under all activity combinations: Assuming that the generation process between all position pairs is independent, the sample likelihood number is the joint probability of all position pair likelihood numbers: 【Step 3.5】For each position pair, the constraint condition is: the stay duration and walking duration in the subspace each time do not exceed the total activity duration; its occurrence probability is equivalent to the probability density of the total activity duration under the stay duration or walking duration distribution: wherein is the cumulative density function of the Gamma distribution; all constraints need to be satisfied simultaneously, so the constraint likelihood is: The sample population constraint likelihood number is: The sample population likelihood number is corrected by the geometric mean of the sample population constraint likelihood number: The model parameters are solved by the maximum likelihood method; the natural logarithm of the likelihood number is taken: After omitting the first term, we get: Parameters sought include: , , , , , , ; According to these parameters, in the case of a complete journey of the tourist through the subspace, the probability of not staying in each subspace is: Substituting equation 2, we get the length of stay of each subspace a zero-inflated Gamma distribution ; The length of time taken to walk a unit distance The Gamma distribution The inverse of this The walking speed.

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