A sparse map construction method based on clustering bayesian optimization

Abstract

The application relates to a sparse map construction method based on clustering Bayesian optimization, which comprises the following steps: 1) constructing an initial data set, and constructing and training an initial agent model; 2) distributing sampling points in a map to initial clustering centers according to a hard clustering algorithm and a self-defined distance judgment standard, and iteratively calculating new clustering centers; 3) calculating a prior probability distribution, and obtaining a Bayesian optimization collection function based on spatial clustering; 4) selecting a spatial point with the maximum collection function value as a new optimal sampling point, obtaining information of the optimal sampling point and minimizing uncertainty; 5) expanding the initial data set, and updating the initial agent model; 6) if the error of the new agent model is greater than a threshold value, step 4) is executed, if the error is less than the threshold value or the maximum iteration number is reached, step 7) is entered; and 7) constructing a complete sparse map according to the new agent model. Compared with the prior art, the application has the advantages of higher precision, stronger robustness and the like.

Description

Technical Field

[0001] This invention relates to a method for constructing a high-precision map from sparse sampling points, and more particularly to a sparse map construction method based on clustering Bayesian optimization. Background Technology

[0002] With the widespread development of automation and artificial intelligence, an increasing number of tedious, repetitive, and dangerous tasks are being delegated to intelligent agents, such as automated guided vehicles (AGVs) and unmanned aerial vehicles (UAVs). Currently, one of the most important tasks of intelligent agents is to collect measurements of a feature of interest in different regions and infer predicted values ​​of that feature in unknown environments, ultimately constructing a "map" for the feature of interest. These features of interest include a variety of categories such as spectral density, seabed height, or crop growth rate.

[0003] High-quality maps are crucial for environmental monitoring, route navigation, and battlefield area exploration, and can further facilitate subsequent analysis and decision-making. Typical examples of high-quality maps include indoor radio maps, planetary exploration maps, and topographic maps.

[0004] Two key issues for intelligent agents to effectively build high-quality maps are data acquisition strategies and inference models.

[0005] The main technical challenges of data acquisition strategies are when, where, and how to measure and collect data. Efficient data acquisition strategies rely on autonomous, proactive, and intelligent exploration strategies. In most current research and applications, the performance of a data acquisition strategy can be measured by the total amount of information acquired, as abundant information is a prerequisite for optimizing subsequent inference models. This type of problem is sometimes referred to as informational path planning. Path selection and planning algorithms for information exploration come in two forms. Methods where the agent decides its next action in the short term and iteratively replans the path are called "myopic" algorithms. "Non-myopic" algorithms, on the other hand, have a global, long-term perspective, operating and optimizing the overall sequence.

[0006] Inference models use limited measurement information collected in the spatial, temporal, or frequency domains to infer numerical values ​​of a feature of interest in an unknown region. Besides models derived from physical characteristics, noteworthy methods in inference models include statistical tests, matrix completion, the recently emerging neural networks, and Gaussian process regression, which is widely used in industry.

[0007] The current sparse map construction methods generally have the following defects: (1) Because the sampling point selection and optimization problem has NP-hard properties, it is difficult to calculate using the "non-myopia" data acquisition strategy in most cases; while the "myopia" algorithm may get stuck in local optima and produce poor long-term results; (2) Inference models based on machine learning and neural networks generally have high prediction accuracy, but require a large amount of data support; while hypothesis testing and other methods generally require physical modeling of the features of interest in the map; (3) Sparse map construction methods need to balance short-term computing speed and long-term accuracy and stability, and existing solutions rarely take into account both the optimization of data acquisition strategy and inference model. Summary of the Invention

[0008] The purpose of this invention is to overcome the shortcomings of the existing technology and provide a sparse map construction method based on clustering Bayesian optimization.

[0009] The objective of this invention can be achieved through the following technical solutions:

[0010] A sparse map construction method based on clustering Bayesian optimization, comprising the following steps:

[0011] 1) Construct an initial dataset and train an initial surrogate model based on it using Gaussian process regression;

[0012] 2) Based on the hard clustering algorithm and the custom distance judgment criteria, the sampling points in the entire map space are assigned to the initial cluster centers, and the new cluster centers are iteratively calculated based on the assignment results until the total distance is minimized;

[0013] 3) Calculate the prior probability distribution based on the final clustering results and obtain the Bayesian optimized acquisition function based on spatial clustering;

[0014] 4) Select the spatial point that maximizes the value of the acquisition function as the new optimal sampling point, and perform data observation at the optimal sampling point to obtain information about the optimal sampling point;

[0015] 5) Expand the initial dataset using the information from the optimal sampling points, and update the initial agent model based on the expanded dataset to obtain a new agent model;

[0016] 6) Determine the error effect of the new proxy model. If the error is greater than the threshold, proceed to 4). If the error is less than the threshold or the maximum number of iterations is reached, proceed to 7).

[0017] 7) Based on the new proxy model obtained, construct a complete sparse map using sparse and limited sampling points.

[0018] Furthermore, the initial cluster centers are calculated using the K-means++ algorithm, specifically: the points that are farther away from all current cluster centers have a higher probability of becoming the next initial cluster center.

[0019] Furthermore, the initial dataset is a dataset composed of randomly generated sampling points.

[0020] Furthermore, the initial proxy model is constructed using a radial basis function kernel, expressed as:

[0021]

[0022] Wherein, ∈ and l are scaling hyperparameters, x represents any sampling point in the space, and x′ represents the center of the kernel function; the scaling hyperparameters are estimated using the maximum a posteriori probability estimation method and have been trained and optimized on the initial dataset.

[0023] Furthermore, the distance judgment criterion is as follows:

[0024]

[0025] Where d represents the defined spatial distance, z i Let x represent the input vector. i y represents the position of any sampling point in space. i c represents the signal strength at that point. j Let x represent the j-th initial spatial cluster center obtained after iteration. jc y represents the map cluster center point in the current iteration. jc x represents jc The signal strength at that location, where δ represents the scaling parameter;

[0026] The expression for the hard clustering algorithm is:

[0027]

[0028] Where A represents the entire map space and C represents the set of cluster centers.

[0029] Furthermore, the specific calculation formula for iteratively calculating the new cluster centers is as follows:

[0030]

[0031] The new criterion for determining cluster centers is that the difference between the second moments of the two rounds is less than a pre-set threshold e. At the same time, an upper limit for iteration is set to avoid the hard clustering algorithm from getting stuck in local optima.

[0032] Furthermore, the formula for calculating the prior probability distribution is as follows:

[0033]

[0034] Where x represents the sampling point, n represents the total number of sampling points, and A k Let x represent the k-th space after partitioning. i This represents a sampling point in space.

[0035] Furthermore, the expression for the Bayesian optimized acquisition function based on spatial clustering is as follows:

[0036]

[0037] Where, σ 2 (x) represents the variance of the sampling point x, dx′ represents the derivative of x′, and x′ represents the center of the kernel function.

[0038] An application of the sparse map construction method based on clustering Bayesian optimization, used to predict and construct an electromagnetic spectrum map and predict Wi-Fi signal reception strength, includes the following steps:

[0039] 1) Utilize a small amount of electromagnetic data in space to construct an initial dataset, and then train an initial surrogate model based on Gaussian process regression.

[0040] 2) Based on the hard clustering algorithm and the custom distance judgment criteria, the sampling points in the entire map space are assigned to the initial cluster centers, and the new cluster centers are iteratively calculated based on the assignment results until the total distance is minimized;

[0041] 3) Calculate the prior probability distribution based on the final clustering results and obtain the Bayesian optimized acquisition function based on spatial clustering;

[0042] 4) Select the spatial point that maximizes the value of the acquisition function as the new optimal sampling point, observe the data at the optimal sampling point, and obtain the electromagnetic signal of the optimal sampling point;

[0043] 5) Expand the initial dataset using the electromagnetic signals from the optimal sampling points, and update the initial agent model based on the expanded dataset to obtain a new agent model;

[0044] 6) Determine the error effect of the new proxy model. If the error is greater than the threshold, proceed to 4). If the error is less than the threshold or the maximum number of iterations is reached, proceed to 7).

[0045] 7) Based on the new proxy model, a complete electromagnetic spectrum map is constructed using sparse and limited sampling points to accurately predict the Wi-Fi signal reception strength at all locations within a set spatial range.

[0046] A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the method described above.

[0047] Compared with the prior art, the present invention has the following beneficial effects:

[0048] I. This invention constructs sparse maps by using a clustering-based Bayesian optimization method, which can build high-quality maps that are closest to the ideal map while maintaining high accuracy and strong interpretability.

[0049] Second, this invention has good portability and universality, and is suitable for high-quality construction of various maps such as spectrum maps, noise maps and hydrological maps, and has broad application prospects.

[0050] Third, this invention is specifically applied to the field of electromagnetic spectrum maps. By constructing high-quality electromagnetic spectrum maps, it is possible to accurately predict the Wi-Fi signal reception strength at all locations within a set spatial range. Attached Figure Description

[0051] Figure 1 This is a schematic diagram of the method flow of the present invention;

[0052] Figure 2 This is a plan view of the sampling points of the present invention;

[0053] Figure 3 This is the ideal wireless signal strength diagram of the present invention;

[0054] Figure 4 This is a schematic diagram of the results of the random search algorithm;

[0055] Figure 5 This is a schematic diagram of the results of the grid search algorithm;

[0056] Figure 6 A schematic diagram of the results of the Maximum Prediction Error (MPE) sampling algorithm;

[0057] Figure 7 This is a schematic diagram of the results of the clustering-based Bayesian optimization of the present invention. Detailed Implementation

[0058] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. These embodiments are based on the technical solution of the present invention and provide detailed implementation methods and specific operating procedures. However, the scope of protection of the present invention is not limited to the following embodiments.

[0059] Example

[0060] Bayesian optimization is primarily used to solve computationally expensive black-box optimization problems, which have two main characteristics: the objective function f(x) and its derivative are unknown; and the objective function has high computational complexity. In each iteration, Bayesian optimization utilizes previously observed historical information (prior knowledge) for the next optimization. The optimization process mainly consists of two important components: a surrogate model and a data collection function. The surrogate model is a computationally simple and fast proxy function. To fit the true objective function f(x), common surrogate models include Gaussian Processes (GP) and Probabilistic Random Forests (PRF). The acquisition function determines the next sampling point, utilizing more observational information to optimize the surrogate model and make it approximate the true objective function. The acquisition function generally considers two properties: utilizing the currently observed area, i.e., continuing the search near the previous sampling point; and exploring unexplored areas, i.e., searching for possible global optima in areas not yet searched. Commonly used acquisition functions include Improved Probability (PI), Expected Improvement (EI), and Upper and Lower Confidence Boundaries (LCB, UCB). In map construction, Bayesian optimization methods can be used to treat the complex mapping relationship between coordinates and values ​​in a real-world map as the objective function f(x), where the x vector represents sparse sampling points in space. Based on the acquisition function, the most informative sampling points are selected to optimize the surrogate model and predict the value of a feature of interest. This invention will use a spectrum map as an example to demonstrate the process of constructing a high-quality spectrum map from sparse sampling points. The coordinates in the map are two-dimensional spatial points, and the feature value is the received signal strength of Wi-Fi.

[0061] like Figure 1 As shown, a sparse map construction method based on clustering Bayesian optimization is described, and the method includes the following steps:

[0062] 1) Determine the type of sparse map according to actual needs. In this invention, electromagnetic spectrum map is used as an example. The sensing data is the Wi-Fi signal reception strength. Using a comprehensive variance reduction scheme, a small amount of electromagnetic data is sensed in space to construct an initial dataset. Based on this data, Gaussian process regression is used to construct and train an initial agent model. The initial dataset is a dataset composed of randomly generated sampling points.

[0063] The initial surrogate model is constructed using a radial basis function (RBF) because the RBF is relatively easy to compute numerically and has strong adaptability, meeting the real-time and accuracy requirements of most map reconstructions. The expression is:

[0064]

[0065] Here, ∈ and l are scaling hyperparameters, whose values ​​need to be selected specifically according to the characteristics of the map reconstruction scene; x represents any sampling point in space, and x′ represents the center of the kernel function; the scaling hyperparameters are estimated using the maximum a posteriori probability method, and were trained and optimized on the initial dataset. Because noise is ignored during sampling, the mean μ of the surrogate model after inferring unknown points on the map is... n (x) and variance σ 2 (x) are respectively:

[0066]

[0067]

[0068] Where μ0(X) is the dataset The mean of the upsampled points, X = {x1, ..., x n} represents n sampling points x (two-dimensional vectors) in space, Y = {y1,…,y2} n} represents the signal strength of the corresponding sampling point, and n is the total number of sampling points. This represents the radial basis kernel function.

[0069] This invention selects Gaussian process regression to train the initial agent model, which also serves as an inference model for predicting Wi-Fi signal strength in unknown areas of a map. In the field of two-dimensional input geographic interpolation and map building, Gaussian process regression is often referred to as Kriging interpolation. Gaussian process regression does not rely on black-box details and prior knowledge of the environment, making it suitable for most "myopic" algorithm optimizations, i.e., considering the short-term optimal solution under the current state. It also provides a method for quantifying observation noise and uncertainty. Gaussian process regression uses a Gaussian process as a prior, assuming that the learning samples are samples of a Gaussian process; therefore, its estimation results are closely related to the covariance function (also known as the kernel function) describing the correlation between samples. From the mathematical Gaussian process, the prior mean function... and positive semidefinite kernel function Fully defined.

[0070] 2) Based on the hard clustering algorithm and the custom distance judgment criteria, the sampling points in the entire map space are assigned to the initial cluster centers, and the new cluster centers are iteratively calculated based on the assignment results until the total distance is minimized.

[0071] The initial cluster centers are calculated using the K-means++ algorithm, specifically: the farther away a point is from all current cluster centers, the higher its probability of becoming the next initial cluster center.

[0072] The distance judgment criteria are as follows:

[0073]

[0074] Where d represents the defined spatial distance, z i Let x represent the input vector. i y represents the position of any sampling point in space. i c represents the signal strength at that point. j Let x represent the j-th initial spatial cluster center obtained after iteration. jc y represents the map cluster center point in the current iteration. jc x represents jc The signal strength at the point, where δ represents the scaling parameter, used to control the relative weights of the two parts;

[0075] The expression for the hard clustering algorithm is:

[0076]

[0077] Where A represents the entire map space, such as in a two-dimensional map. C represents the set of cluster centers.

[0078] The specific calculation formula for iteratively calculating the new cluster centers is as follows:

[0079]

[0080] The new criterion for determining cluster centers is that the difference between the second moments of the two rounds is less than a pre-set threshold e. At the same time, an upper limit for iteration is set to avoid the hard clustering algorithm from getting stuck in local optima.

[0081] 3) Calculate the prior probability distribution based on the final clustering results and obtain the Bayesian optimized acquisition function based on spatial clustering.

[0082] The formula for calculating the prior probability distribution is as follows:

[0083]

[0084] Where x represents the sampling point, n represents the total number of sampling points, and A k Let x represent the k-th space after partitioning. i This represents a sampling point in space.

[0085] The Bayesian optimized acquisition function expression based on spatial clustering is as follows:

[0086]

[0087] Where, σ 2 (x) represents the variance of the sampling point x, dx′ represents the derivative of x′, and x′ represents the center of the kernel function.

[0088] 4) Select the spatial point that maximizes the value of the acquisition function as the new optimal sampling point, observe the data at the optimal sampling point, obtain information about the optimal sampling point and minimize uncertainty, thereby reducing global variance and uncertainty.

[0089] 5) Expand the initial dataset using the information from the best sampling points, and update the initial proxy model based on the expanded dataset to obtain a new proxy model that is closer to the real distribution.

[0090] 6) Determine the error effect of the new proxy model. If the error is greater than the threshold, proceed to step 4). If the error is less than the threshold or the maximum number of iterations is reached, proceed to step 7).

[0091] 7) Based on the new agent model, a complete sparse map is constructed using sparse and limited sampling points to accurately predict the Wi-Fi signal reception strength at all locations within a certain spatial range.

[0092] In this embodiment, Wi-Fi received signal strength is selected as the feature of interest in the map to draw a two-dimensional wireless signal strength map. Using NetSpot (Wi-Fi signal scanning, detection, and evaluation software), Wi-Fi signal strength data from the lobby on the first floor of Hualou Building at Tongji University's Jiading Campus was independently collected, and an initial dataset was constructed based on this data. Relevant parameters are shown in Table 1.

[0093] Table 1 Initial Dataset Parameters

[0094]

[0095] like Figure 2 The image shows a floor plan of the lobby on the first floor of the building, including obstacles that hinder signal propagation, such as elevators, staircases, and movable display stands. The image was drawn based on 90 densely sampled points. Figure 3 The diagram shows the ideal wireless signal strength.

[0096] To evaluate the model's performance, this invention proposes two evaluation methods. One is to calculate the root mean square error (RMSE) of each point in the inferred wireless signal strength map and the ideal map, using the following formula:

[0097]

[0098] Where f(x) i ) represents the dense sampling obtained in x i The true signal strength at point μ n (x i ) represents the inference result of fitting the optimal surrogate model under the condition of a finite number of n sampling points.

[0099] Another more intuitive method is to compare maps generated by inference from fewer sampling points (10, 20, 30, 40 sampling points) with ideal wireless signal strength maps generated by dense sampling (90 sampling points). Based on the differences between the different maps, it is determined whether the acquisition function successfully selected the optimal sampling points. This invention compares a clustering-based Bayesian optimization method with random search algorithms, grid search algorithms, and maximum prediction error (MPE) sampling algorithms. Since the minimum number of sampling points is 10, it is assumed that... The capacity is 5, and 5 points are randomly selected from A. Simultaneously, k=5, and the K-means++ algorithm is used to select 5 high-quality initial cluster centers. The final experimental comparison results are obtained, as follows: Figures 4-7 As shown.

[0100] Furthermore, this invention also calculated the root mean square error between the constructed wireless signal strength map and the ideal map under four sampling modes, based on 20 or 40 data points respectively. The results are shown in Table 2.

[0101] Table 2 Root Mean Square Error Table

[0102]

[0103] Experimental results show that the random search algorithm performs poorly, and using this method to select the next sampling point provides little or no information for the inference model. As the number of sampling points increases, the grid search algorithm and the maximum prediction error sampling algorithm gradually achieve better results, but their construction efficiency is relatively low, and they may miss some weak signal areas in the map. In contrast, the sparse map construction method based on clustering Bayesian optimization can construct a high-quality map that most closely resembles the ideal map while maintaining high accuracy, efficiency, and interpretability.

[0104] The present invention also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the method described above.

[0105] The preferred embodiments of the present invention have been described in detail above. It should be understood that those skilled in the art can make numerous modifications and variations based on the concept of the present invention without creative effort. Therefore, all technical solutions that can be obtained by those skilled in the art based on the concept of the present invention through logical analysis, reasoning, or limited experimentation on the basis of existing technology should be within the scope of protection defined by the claims.

Claims

1. A sparse map construction method based on clustered Bayesian optimization, characterized in that, The method comprises the following steps: 1) constructing an initial data set and training an initial surrogate model based on Gaussian process regression; 2) distributing sampling points in the whole space of the map to initial clustering centers according to a hard clustering algorithm and a self-defined distance judgment standard, and iteratively calculating new clustering centers according to the distribution result until the total distance is minimized; 3) calculating a prior probability distribution according to the final clustering result, and obtaining a Bayesian optimization acquisition function based on spatial clustering; 4) selecting a spatial point with the maximum value of the acquisition function as a new optimal sampling point, observing data at the optimal sampling point, and obtaining information of the optimal sampling point and minimizing uncertainty; 5) expanding the initial data set by using the information of the optimal sampling point, updating the initial surrogate model according to the expanded data set, and obtaining a new surrogate model; 6) judging the error effect of the new surrogate model, if the error is greater than a threshold, executing 4), if the error is less than the threshold or the maximum iteration number is reached, entering 7); 7) constructing a complete sparse map by using the sparse limited sampling points according to the obtained new surrogate model. The self-defined distance judgment standard is: wherein, denotes a defined spatial distance, denotes an input vector, denotes the position of an arbitrary sampling point in space, denotes the signal strength of this point, denotes the jthinitial spatial cluster center resulting after iteration, denotes the map cluster center point under the current iteration, denotes the signal strength at the point, denotes a scaling parameter; The expression of the hard clustering algorithm is: wherein, represents the set of all map spaces, represents the set of cluster centers.

2. The sparse map construction method based on cluster Bayesian optimization according to claim 1, characterized in that, The initial clustering centers are calculated by using a K-mean++ algorithm, specifically, the farther the point is from the current all clustering centers, the higher the probability of becoming the next initial clustering center.

3. The sparse map construction method based on cluster Bayesian optimization according to claim 1, characterized in that, The initial data set is a data set composed of randomly generated sampling points.

4. The sparse map construction method based on cluster Bayesian optimization according to claim 1, characterized in that, The initial surrogate model is constructed by using a radial basis kernel function, and the expression is: wherein, is a scaling hyperparameter, represents an arbitrary sampling point in the space, represents a kernel function center; the scaling hyperparameter is trained and optimized on an initial data set using a maximum a posteriori estimation method.

5. The sparse map construction method based on cluster Bayesian optimization according to claim 1, characterized in that, The specific calculation formula of the iterative calculation of the new clustering centers is as follows: The judgment standard of the new cluster center is that the difference between the second moments of the two rounds is less than a preset threshold value At the same time, the upper limit of iteration is set to avoid the hard clustering algorithm falling into local optimum.

6. The sparse map construction method based on clustered Bayesian optimization of claim 1, wherein, The calculation formula of the prior probability distribution is as follows: wherein, denotes a sampling point, denotes the total number of sampling points, denotes the kth partitioned space, denotes a sampling point in the space.

7. The sparse map construction method based on cluster Bayesian optimization according to claim 6, characterized in that, The expression of the Bayesian optimization acquisition function based on spatial clustering is: wherein, denotes the variance of the sampling points , denotes the derivative of , denotes the center of the kernel function.

8. An application of the sparse map construction method based on cluster Bayesian optimization of claim 1, for predicting the construction of an electromagnetic spectrum map, predicting Wi-Fi signal reception strength, characterized in that, The method comprises the following steps: 1) constructing an initial data set by using a small amount of electromagnetic data in the space, and training an initial surrogate model based on Gaussian process regression; 2) distributing sampling points in the whole space of the map to initial clustering centers according to a hard clustering algorithm and a distance judgment standard, and iteratively calculating new clustering centers according to the distribution result until the total distance is minimized; 3) calculating a prior probability distribution according to the final clustering result, and obtaining a Bayesian optimization acquisition function based on spatial clustering; 4) selecting a spatial point with the maximum value of the acquisition function as a new optimal sampling point, observing data at the optimal sampling point, and obtaining information of the optimal sampling point and minimizing uncertainty; 5) expanding the initial data set by using the information of the optimal sampling point, updating the initial surrogate model according to the expanded data set, and obtaining a new surrogate model; 6) judging the error effect of the new surrogate model, if the error is greater than a threshold, executing 4), if the error is less than the threshold or the maximum iteration number is reached, entering 7); 7) constructing a complete electromagnetic spectrum map by using the sparse limited sampling points according to the obtained new surrogate model, and accurately predicting Wi-Fi signal receiving strength at all positions in a set space range.

9. A computer readable storage medium having stored thereon a computer program, characterized in that, The program is executed by a processor to realize the method in any one of claims 1-7.

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