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CN-121999162-A - Three-dimensional space-time kernel density estimation method based on self-adaptive bandwidth

CN121999162ACN 121999162 ACN121999162 ACN 121999162ACN-121999162-A

Abstract

The invention discloses a three-dimensional space-time kernel density estimation method based on self-adaptive bandwidth, which comprises the steps of determining the boundary outline of a research area in a geographic space and determining the lower bound and the upper bound of the occurrence time of a target event, and constructing an effective space-time cube, and collecting a target event sample internally to obtain a target event data set. The data set is input to calculate and fit the real background distribution of the target event, namely, the joint probability density model. And then carrying out time slicing treatment on the combined probability density model to obtain a space conditional probability density model. And respectively carrying out qualitative analysis and quantitative analysis on the two models according to requirements, and analyzing the spatial distribution rule and the time evolution characteristic of the high-incidence area (hot area) of the target event. By introducing the self-adaptive bandwidth change into the traditional algorithm, the algorithm has better fitting result, more accurate prediction performance, more centralized hot zone identification capability and more robust capability of absorbing extreme event impact.

Inventors

  • Jiao Longxiao
  • ZHANG BO
  • JIE CHANGLU
  • SUN PENGZHI
  • ZHANG ZHISHANG

Assignees

  • 河南省地质局矿产资源勘查中心

Dates

Publication Date
20260508
Application Date
20260127

Claims (10)

  1. 1. The three-dimensional space-time kernel density estimation method based on the self-adaptive bandwidth is characterized by comprising the following steps of: S1, determining boundary contours of a research area in a geographic space and determining time lower bounds and time upper bounds of occurrence of target events, acquiring target event samples in an effective space-time domain according to the boundary contours, the time upper bounds and the time lower bounds to obtain a target event data set, fitting real background distribution of the target events according to the target event data set to obtain a joint probability density model, wherein a specific joint probability density function is as follows: ; ; ; ; ; ; ; Wherein, the As a joint probability density function, and boundary contours as closed polygons on the XY plane of the geographic space The upper time limit is The upper time limit is From closed polygons And an upper time bound and a lower time bound The enclosed area is an effective time-space domain From closed polygons Minimum bounding rectangle and upper and lower time bounds of (2) The enclosed cubes are space-time cubes In the effective time-space domain Is collected together Individual event samples Each event sample I.e. each event sample contains geospatial coordinates , And time coordinates , Is the first The abscissa of the individual event samples in the geographic space; Is the first The ordinate of the individual event samples in the geographic space; Is the first Coordinates of the individual event samples in time space; Is an indication function, each event sample The kernel density of the contribution falls into the effective time-space domain Taking 1 when the time is, otherwise taking 0; 、 For each event sample The adaptive bandwidth-based kernel function, in particular the gaussian kernel function, In (a) and (b) The representation may be in a general formula May also be The assumption of XY isotropy, i.e. any event, is used here After this has taken place, the effect is uniform in all directions in space, As in the general formula ; Is the first Spatial side adaptive bandwidth of individual event samples, Is the first Time-side adaptive bandwidth for individual event samples; Is that The spatial side of each event sample is optimally fixed in bandwidth; Is that The time side of each event sample is optimally fixed in bandwidth; Is the bandwidth of the global space side; For global time-side bandwidth, where direct order , ; Is that Pilot space-time kernel density estimation model corresponding to each target event sample Is used to determine the geometric mean of the nuclear density values, Is to use fixed optimum bandwidth And Is characterized in that a pilot space-time nuclear density estimation model is arranged at a sample point Nuclear density values at; is an edge correction factor; S2, performing time slicing treatment on the combined probability density model to obtain a space conditional probability density model, wherein a specific space conditional probability density function is as follows: ; Wherein, the Is a space conditional probability density function; and S3, respectively carrying out qualitative and quantitative analysis on the joint probability density model and the space conditional probability density model according to requirements.
  2. 2. The method for estimating three-dimensional space-time kernel density based on adaptive bandwidth as set forth in claim 1, wherein the voxel differentiation rules of the joint probability density model comprise ASTKDE-Larget model and ASTKDE-Base model.
  3. 3. The method of claim 2, wherein the differential voxel parameters corresponding to the ASTKDE-Large model are 695X, 735Y and 365T, the corresponding voxel space-time scale is 50mX100 mX 10 days, and the differential voxel parameters corresponding to the ASTKDE-Base model are 348X, 368Y and 183T, and the corresponding voxel space-time scale is 100deg.mX 100 mX 20 days.
  4. 4. The method for estimating three-dimensional space-time kernel density based on self-adaptive bandwidth as set forth in claim 1, wherein said joint probability density model adopts a mode of "concurrent computation" and "load balancing" in the computation process.
  5. 5. The method for estimating three-dimensional space-time kernel density based on adaptive bandwidth according to claim 1, wherein the step S3 comprises the specific steps of obtaining statistical significance And (3) introducing the combined probability density model into volume rendering software, performing volume rendering gradual change coloring according to the nuclear density value of each voxel, introducing the obtained local density peak points into a scene, and analyzing probability density hot areas in the model through volume rendering and combined display of the peak points.
  6. 6. The method of claim 5, wherein the volume rendering gradient coloring rule is red (significance ) Yellow (significance) ) Blue (significance) ) And (3) completely transparent, and gradually transition coloring according to the significance thresholds corresponding to the red, yellow and blue.
  7. 7. The method for estimating three-dimensional space-time kernel density based on self-adaptive bandwidth according to claim 1, wherein the specific process of carrying out qualitative and quantitative analysis on the joint probability density model in the step S3 is that three-dimensional isosurface is drawn by the joint probability density model in RStudio software and cut according to the degree of year, the annual model segment is projected on an XY plane to form a maximum projection range, local density peak points in the year are also projected on the XY plane together, the area of the maximum projection range is calculated, and the specific result of slicing year by year and the statistical condition of hot area with different saliency corresponding to the specific result of slicing year by year are analyzed.
  8. 8. The method for estimating three-dimensional space-time kernel density based on adaptive bandwidth according to claim 7, wherein the iso-surface coloring rule is: red (significance) ) Yellow (significance) ) Blue (significance) ). Coloring is performed according to the significance threshold values corresponding to red, yellow and blue.
  9. 9. The method for estimating three-dimensional space-time kernel density based on adaptive bandwidth according to claim 1, wherein the step S3 comprises the specific process of qualitative and quantitative analysis of space conditional probability density by calculating statistical significance of each time slice by using space conditional probability density model And connecting local peak points crossing adjacent time slices according to a set minimum distance threshold to form a migration track of the thermal zone moving along with time, and analyzing the migration track of the thermal zone moving along with time.
  10. 10. The method for estimating three-dimensional space-time kernel density based on adaptive bandwidth as set forth in claim 1, wherein said spatial-side optimal fixed bandwidth Optimal fixed bandwidth on time side By leave-one-out cross-validation, interpolation, log-likelihood or rule of thumb.

Description

Three-dimensional space-time kernel density estimation method based on self-adaptive bandwidth Technical Field The invention belongs to the technical field of three-dimensional space-time kernel density estimation, and particularly relates to a three-dimensional space-time kernel density estimation method based on self-adaptive bandwidth. Background In the prior art, a conventional space-time kernel density Estimation method (Traditional Spatiotemporal KERNEL DENSITY Estimation, TSTKDE) is a common and mature method in the analysis and evaluation method of geographic information events (or points of interest). The method obtains the optimal fixed bandwidth on the space side and the optimal fixed bandwidth on the time side through limited event records, and then fits the actual probability density distribution behind the events through a kernel method, thereby helping expert students or institution departments to explore and analyze the historical development change rules of the events, dividing risk class regions, providing key decision basis for downstream tasks and predicting future development change trend. However, this conventional algorithm has the disadvantage that it always uses a fixed bandwidth for model fitting, which results in unavoidable over-smooth estimates in data-densely distributed areas, loss of detail, blurred hot-zones, under-smooth estimates in data-sparsely distributed areas, noise, and finally unreliable fitting results when processing unevenly distributed data. Such shortboards are the result of conventional algorithms that select a fixed bandwidth, and necessarily result when dealing with non-uniform data, whether in one-dimensional, two-dimensional, or three-dimensional application scenarios, and whether the selected fixed bandwidth is the "optimal bandwidth". For events in the real world, the distribution in space and time tends to be non-uniform, and some expert scholars have recognized this internationally, and three-dimensional TSTKDE is proposed to innovate in the direction of adaptive bandwidth so as to better solve the deviation caused by the non-uniform problem of the traditional algorithm treatment. However, the research on the space-time kernel density estimation method for the self-adaptive bandwidth is very little in China and internationally, and the space-time kernel density estimation method is difficult to realize in a floor mode because of huge calculation amount under a three-dimensional application field, lacks engineering, and is not proved by specific real data application cases. Therefore, a new three-dimensional space-time kernel density estimation method is needed to solve the above technical problems. Disclosure of Invention The invention aims to provide a three-dimensional space-time kernel density estimation method (STKDE WITH ADAPTIVE bandwidths, which is abbreviated as ASTKDE below) based on self-adaptive bandwidth, which is used for solving the problem that the traditional space-time kernel density estimation method in the prior art generates unreliable fitting results when processing non-uniformly distributed data. The technical scheme for solving the technical problems is as follows: A three-dimensional space-time kernel density estimation method based on self-adaptive bandwidth comprises the following steps: S1, determining boundary contours of a research area in a geographic space and determining time lower bounds and time upper bounds of occurrence of target events, acquiring target event samples in an effective space-time domain according to the boundary contours, the time upper bounds and the time lower bounds to obtain a target event data set, fitting real background distribution of the target events according to the target event data set to obtain a joint probability density model, wherein a specific joint probability density function is as follows: ; ; ; ; ; ; ; Wherein, the As a joint probability density function, and boundary contours as closed polygons on the XY plane of the geographic space. The upper time limit isThe upper time limit is. From closed polygonsAnd an upper time bound and a lower time boundThe enclosed area is an effective time-space domainFrom closed polygonsMinimum bounding rectangle and upper and lower time bounds of (2)The enclosed cubes are space-time cubesIn the effective time-space domainIs collected togetherIndividual event samplesEach event sampleI.e. each event sample contains geospatial coordinates,And time coordinates,Is the firstThe abscissa of the individual event samples in the geographic space; Is the first The ordinate of the individual event samples in the geographic space; Is the first Coordinates of the individual event samples in time space; Is an indication function, each event sample The kernel density of the contribution falls into the effective time-space domainTaking 1 when the time is, otherwise taking 0;、 For each event sample The adaptive bandwidth-based kernel function, in particular the gaus