A robust band selection method for hyperspectral images based on maximum entropy fuzzy clustering

Abstract

The present invention relates to a method for robust band selection of hyperspectral images based on maximum entropy fuzzy clustering, which belongs to the technical field of pattern recognition. A dynamic information entropy graph Y is constructed to reduce the sensitivity of the algorithm to the initialization of cluster centers. On this basis, the "sample-cluster centroid" least squares term metric function is modified to be based on l 2,1 The global robustness metric of the norm is used to further improve the algorithm's robustness to noisy data. The designed method can strictly guarantee convergence to the optimal solution while improving computational efficiency and thus having stronger generalization performance, thereby improving the robustness of the selection of bands for noisy hyperspectral images.

Description

Technical Field

[0001] The present invention belongs to the technical field of pattern recognition and relates to a method for robust band selection of hyperspectral images based on maximum entropy fuzzy clustering. Background Art

[0002] Benefiting from innovations and advancements in satellite and remote sensing sensor technology, and the rapid development of hyperspectral imaging technology both domestically and internationally, hyperspectral remote sensing image processing and analysis have become a research focus in many fields. However, hyperspectral remote sensing image processing and analysis techniques are characterized by large data volumes, high inter-band correlation, and a high level of redundant information, making them difficult to process. Furthermore, using high-dimensional features for classification is unsuitable both in terms of computational complexity and classification effectiveness. As hyperspectral image information becomes increasingly complex and labels become increasingly difficult to obtain, clustering-based band selection methods have attracted widespread attention because they do not require any prior supervision. The idea is to treat each band as an object and, through clustering, divide all bands into several clusters, maximizing the differences between clusters and ensuring that objects within a cluster are as similar as possible. A representative band from each cluster is then selected to form a subset. This effectively reduces the similarity between extracted bands and is one of the main methods for hyperspectral image band selection. Furthermore, hyperspectral image information is susceptible to noise contamination, such as water vapor, which can lead to a certain degree of image quality loss and hinder the subsequent effective recognition of hyperspectral images. Therefore, it is of great significance to efficiently and automatically obtain pure and high-quality hyperspectral bands and achieve robust hyperspectral band selection.

[0003] Chen Jing et al. ("Greedy Unsupervised Hyperspectral Image Band Selection Method Based on Variable Precision Rough Sets," Acta Photonica Sinica, 2021, 50(02): 111-122.) proposed a greedy unsupervised hyperspectral band selection method based on variable precision rough sets. The main idea is to use variable precision rough sets to define a new dependency metric, making it insensitive to the misclassification parameters in the variable precision rough sets, thereby fully utilizing the similarity between bands. However, this method does not correct the cluster center deviation caused by noise contamination of hyperspectral bands. In addition, the greedy search algorithm is prone to falling into local optimal solutions, affecting computational efficiency and failing to guarantee the global convergence of the algorithm. Therefore, its robustness is limited by noise, affecting the subsequent accurate recognition of hyperspectral image information. Summary of the Invention

[0004] Technical problems to be solved

[0005] Aiming at the lack of label information in the current hyperspectral image band selection algorithm and the inability to effectively solve the impact of noise on the hyperspectral image band selection performance, the robustness is poor. In this paper, a hyperspectral image robust band selection method based on maximum entropy fuzzy clustering is adopted.

[0006] Technical Solution

[0007] A method for robust band selection of hyperspectral images based on maximum entropy fuzzy clustering is characterized by the following steps:

[0008] Step 1: Obtain image data information to construct a data matrix

[0009] For hyperspectral image data with a spectral band feature dimension of d, the number of pixel samples in a single band is n. The image data of each band is stretched into a row vector of 1×n, where u and v are the length and width of the single band hyperspectral image, respectively, so n=u×v; the hyperspectral image data with a total number of bands of d is converted into the target data matrix Each row of the matrix represents the hyperspectral image of the i-th band; the image of each band represents a data sample; if the number of selected band features is c, the cluster centers of c clusters can be randomly initialized, that is, the initial is the centroid of the jth cluster;

[0010] Step 2: Establish a robust band selection framework for hyperspectral images based on maximum entropy fuzzy clustering

[0011] When processing hyperspectral image data containing noise, the cluster centers are initialized to the noise data; inspired by the entropy metric, a dynamic information entropy graph Y is constructed to reduce the sensitivity of the algorithm to the initialized cluster centers in low signal-to-noise ratio data, and the "sample-cluster centroid" metric function is modified to be based on l 2,1 The global robustness measurement method of norm sparse learning is used to further improve the robustness of the algorithm to noisy data; the optimization goal is

[0012]

[0013] stY≥0,Y1=1,s T 1=k,0≤s≤1

[0014] in is the fuzzy membership, and the centroid matrix of the cluster is The matrix Y represents each element y ij Indicates the membership of the i-th sample to the j-th cluster; Used to filter nk noise data, s i is the value of the i-th element of s;

[0015] Step 3: Alternate iterative optimization of the objective function

[0016] The alternating iterative optimization method is used to solve the three variables m, Y, and s in the objective function. First, m and Y are initialized, and s is calculated according to the formula; then s and m are fixed, and different optimizations are performed on real samples and noise data to obtain Y; then s and Y are fixed, and m is solved according to the formula, and the cycle is repeated until convergence.

[0017] Further technical solution of the present invention: Step 3 is as follows:

[0018] Step 3.1: Introduce auxiliary variable q ij =12x i -m j 2 2The first item of the conversion optimization goal is the smoothing item:

[0019]

[0020] stY≥0,Y1=1,s T 1=k,0≤s≤1

[0021] According to the random initialization of c cluster centers, the initial Initialize all elements in Y to y ij =1 / c; Considering that the initial probability of the sample distribution in each class is equal, define To classify the sample x with a certain membership degree i The value obtained by weighting and summing the distances to all cluster centers; Arrange in order from smallest to largest The corresponding s can be calculated i :

[0022]

[0023] Step 3.2: Optimize the real sample and noise data to get Y

[0024] In step 3.1, we get the s corresponding to the first k samples closest to all cluster centers. i =1, the s corresponding to the remaining samples i =0; e i Sort them in ascending order and place the corresponding samples x i Sorting can get the sorted data matrix Its corresponding sorted membership matrix

[0025] Step 3.2.1: For real samples, when the sample corresponding to s i = 1, the problem can be equivalently transformed into

[0026]

[0027] The optimal membership degree corresponding to the selected real sample is obtained by optimizing the Lagerrange multiplier method

[0028]

[0029] Step 3.2.2: For the noise data in the optimization process, when the sample corresponding to s i = 0, the optimal membership value corresponding to the noise data in the optimization process is

[0030]

[0031] The optimal solution of the membership of all sample points can be obtained for

[0032]

[0033] Step 3.3: Take the partial derivative of the objective function with respect to m and get it equal to 0.

[0034]

[0035] At this point, m, Y, and s are updated, and the next iteration is performed again until m no longer changes.

[0036] Step 4: Optimize the It is used to filter the image bands polluted by noise, and finally obtain c purer clusters, from which the cluster centroid m in each cluster represents the band in the cluster, thereby obtaining the representative band subset

[0037] A computer system, characterized in that it includes: one or more processors, and a computer-readable storage medium for storing one or more programs, wherein when the one or more programs are executed by the one or more processors, the one or more processors implement the above-mentioned method.

[0038] A computer-readable storage medium is characterized by storing computer-executable instructions, which are used to implement the above method when executed.

[0039] Beneficial effects

[0040] This paper proposes a robust band selection method for hyperspectral images based on maximum entropy fuzzy clustering. This method robustly filters noise-contaminated hyperspectral image information during application, thereby improving the robustness and accuracy of the fuzzy clustering band selection algorithm for hyperspectral images. Furthermore, sparsification of the membership matrix improves data processing speed. To enhance the robustness of the clustering algorithm to noisy and abnormal data, a weighted loss function term incorporating fuzzy information is designed to adaptively correct for noise-induced deviations, thereby obtaining a more accurate data topology partitioning.

[0041] The beneficial effects of the method of the present invention mainly include:

[0042] (1) A robust sparse clustering method based on maximum entropy is proposed. In this algorithm, the objective function consists of a robust noise suppression term and an entropy regularization term. By iteratively optimizing the objective function, an adaptive weight is added to each sample point, thereby screening pure samples and noise-contaminated samples, thereby enhancing the robustness of the algorithm.

[0043] (2) Inspired by the entropy metric, the maximum entropy principle is an important tool for representing the probability distribution of collected data when label information is limited. It is generally considered to be the most conservative and stable estimate. This paper proposes to construct a dynamic information entropy graph to effectively reduce the algorithm's sensitivity to the initialization of cluster centers, which can improve the stability of the algorithm's clustering performance in low signal-to-noise ratio data.

[0044] (3) The present invention modifies the least squares metric function of "sample-cluster centroid" into a function based on l 2,1 A global robustness measure for norm sparsity learning is introduced, along with a noise constraint vector to determine if data points are noise points, adaptively correcting for noise deviations. Sparsification results in a more effective sample and feature distribution structure, preventing noise contamination from clustering image data while reducing data storage and computational complexity, thereby improving computational efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] The accompanying drawings are only for the purpose of illustrating particular embodiments and are not to be considered limiting of the present invention. Like reference symbols denote like parts throughout the drawings.

[0046] Figure 1 It is a flow chart of the method of the present invention.

[0047] Figure 2 This is an example of a hyperspectral image partially contaminated by water vapor noise.

[0048] Figure 3 It is the result map of the ground object classification of the algorithm on a specific hyperspectral image dataset. DETAILED DESCRIPTION

[0049] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below with reference to the accompanying drawings and examples. It should be understood that the specific embodiments described herein are only intended to illustrate the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.

[0050] The present invention adopts a robust band selection method for hyperspectral images based on maximum entropy fuzzy clustering. No prior label information is required. This method is inspired by entropy measurement. When label information is limited, the maximum entropy principle is an important tool for representing the probability distribution of collected data. It is generally considered to represent the most conservative and stable estimate. For this reason, entropy regularization is introduced to maximize the retention of useful information of the original hyperspectral image. In addition, a dynamic information entropy map Y is constructed to reduce the algorithm's sensitivity to the initialization of cluster centers. On this basis, the "sample-cluster centroid" least squares term metric function is modified to be based on l 2,1 The global robustness metric of the norm is used to further improve the algorithm's robustness to noisy data. The designed method does not use a greedy search method, which strictly guarantees convergence to the optimal solution. It also improves computational efficiency and thus has stronger generalization performance, thereby improving the robustness of the selection of bands for noisy hyperspectral images.

[0051] The comprehensive model solution process of the hyperspectral image robust band selection based on maximum entropy fuzzy clustering in this invention is as follows: Figure 1 As shown in the figure, an example of clustering-based band selection is used for the Indian Pines hyperspectral image dataset. The Indian Pines dataset was collected by the AVIRIS sensor at the Indian Pine Experimental Site in northwestern Indiana. It consists of 145×145 pixels and 220 spectral reflectance bands with a wavelength range of 0.4–2.5 10^(-6) meters. The data contains the category label of each pixel in 16 ground instances. It can be used to classify and verify the performance of the algorithm band selection. To test the algorithm, the empirical water vapor noise pollution band of the data is set to 20 as an example, and the number of hyperspectral image samples polluted by water vapor and other noise is p = 20. The specific implementation method includes the following steps:

[0052] Step 1: Input the Indian Pines data matrix The number of band features c, the number of noise-contaminated image samples p = 20 and the regularization parameter λ, where each row of the matrix is a sample, n = 145 × 145 is the number of pixel samples in a single band, d = 220 is the dimension of the data matrix, and c = 1:200 is the number of pure band features after filtering out the water vapor noise pollution band.

[0053] Randomly initialize the cluster centers of c clusters, that is, obtain the initial m. Initialize all elements in Y to y ij =1 / c, k=dp=200. Consider making the initial probability of the sample distribution in each class equal. That is, we can fix m and Y and calculate s. Introduce auxiliary variables The first item of the conversion optimization goal is the smoothing item.

[0054]

[0055] stY≥0,Y1=1,s T 1=k,0≤s≤1

[0056] Fixed m and Y, the optimization problem is transformed into

[0057]

[0058] definition To classify the sample x with a certain membership degree i The value obtained by weighting the distances to all cluster centers and summing them.

[0059]

[0060] Will Sort by order The corresponding s can be calculated i

[0061]

[0062] Based on this, we can filter out sample data that is not contaminated by noise and samples that are contaminated by noise, and continuously optimize them in the subsequent iterative process.

[0063] Step 2: Perform different optimizations on real samples and noise data to obtain Y.

[0064] In step 1, we get the s corresponding to the first k samples closest to all cluster centers i =1, the s corresponding to the remaining samples i = 0. Sort them in ascending order and place the corresponding samples x i Sorting can get the sorted data matrix Its corresponding sorted membership matrix

[0065] Step 2.1: For real samples, define is the sorted data matrix The vector consisting of the elements in row i. ij is the sorted membership matrix The jth element in the i-th row. When the sample corresponding to s i =1, the sub-problem of the objective function is

[0066]

[0067] The Lagrangian function of the above problem is

[0068]

[0069] Among them, β i is an equality-constrained Lagrange multiplier. The above equation is for y ij and β i The derivative of should be equal to zero, as shown below

[0070]

[0071]

[0072] The second term of the original objective function is a regularization term that constructs a dynamic information entropy graph, which can effectively reduce the robustness of the algorithm to the initialization of cluster centers.

[0073] By the Lagrange multiplier method, the above equations and constraints The unknown Lagrange multiplier β can be eliminated i , optimize and obtain the optimal membership degree corresponding to the selected real sample

[0074]

[0075] Step 2.2: For the noise data in the optimization process. When the sample corresponding to s i = 0, the optimal membership value corresponding to the noise data in the optimization process is obtained by solving the Cauchy inequality:

[0076]

[0077] The optimal solution of the membership of all sample points can be obtained for

[0078]

[0079] Step 3: Fix s and Y and solve for m

[0080] At this time, the objective function subproblem is rewritten as

[0081]

[0082] Taking the partial derivative of the objective function subproblem with respect to m equal to 0, we can get

[0083]

[0084] At this point, s, Y and m are updated, and the next iteration is repeated until the cluster center m is no longer updated, that is, its change is less than a certain threshold. It is used to filter 20 noise-contaminated image samples. Finally, c purer clusters can be obtained, from which the cluster centroid m in each cluster is used to represent the band in the cluster, thereby obtaining the representative band subset At this time, the band selection subset is obtained and input into the classifier for training, which can effectively improve the performance of hyperspectral image object classification. Take the Indian Pines hyperspectral image dataset (220 bands, each band image pixel size is 145×145) as an example. When the number of bands polluted by noise such as water vapor is 20, the Baseline is the average result of 10 classifications of unknown label data by the KNN classifier trained with the original known label data. Our Method is the average result of 10 classifications of unknown label data after feature selection by the K nearest neighbor classifier trained with known label data after feature extraction using the band selection method proposed in this invention.

[0085] Figure 3 The number of training samples for each of the 16 categories of data was empirically set to [10, 280, 166, 46, 96, 146, 6, 94, 4, 194, 490, 118, 40, 252, 76, and 18]. A KNN classifier was trained based on samples with known labels. The classification results show that the baseline method is calculated using the raw data, while our method performs feature selection on the raw data and then calculates the features of all selected pixels. When the number of bands, c, is selected from 1 to 200, the feature selection method combined with the classification method achieves higher accuracy.

[0086] The above description is only a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any technician familiar with this technical field can easily think of various equivalent modifications or replacements within the technical scope disclosed in the present invention, and these modifications or replacements should all be included in the scope of protection of the present invention.

Claims

1. A robust band selection method for hyperspectral images based on maximum entropy fuzzy clustering, characterized by Here are the steps: Step 1: Obtain image data information to construct a data matrix For hyperspectral image data with a spectral band feature dimension of d, the number of pixel samples in a single band is n. The image data of each band is stretched into a row vector of 1×n, where u and v are the length and width of the single band hyperspectral image, respectively, so n=u×v; the hyperspectral image data with a total number of bands of d is converted into the target data matrix Each row of the matrix represents the hyperspectral image of the i-th band; the image of each band represents a data sample; if the number of selected band features is c, the cluster centers of c clusters can be randomly initialized, that is, the initial is the centroid of the jth cluster; Step 2: Establish a robust band selection framework for hyperspectral images based on maximum entropy fuzzy clustering When processing hyperspectral image data containing noise, the cluster centers are initialized to the noise data; inspired by the entropy metric, a dynamic information entropy graph Y is constructed to reduce the sensitivity of the algorithm to the initialized cluster centers in low signal-to-noise ratio data, and the "sample-cluster centroid" metric function is modified to be based on l 2,1 The global robustness measurement method of norm sparse learning is used to further improve the robustness of the algorithm to noisy data; the optimization goal is s.t.Y≥0,Y1=1,s T 1=k,0≤s≤1 in is the fuzzy membership, and the centroid matrix of the cluster is The matrix Y represents each element y ij Indicates the membership of the i-th sample to the j-th cluster; Used to filter nk noise data, s i is the value of the i-th element of s; Step 3: Alternate iterative optimization of the objective function The alternating iterative optimization method is used to solve the three variables m, Y, and s in the objective function. First, m and Y are initialized, and s is calculated according to the formula. Then, s and m are fixed, and different optimizations are performed on real samples and noise data to obtain Y. Then, s and Y are fixed, and m is solved according to the formula. This cycle repeats until convergence. Step 4: Optimize the It is used to filter the image bands polluted by noise, and finally obtain c purer clusters, from which the cluster centroid m in each cluster represents the band in the cluster, thereby obtaining the representative band subset 2. The method for robust band selection of hyperspectral images based on maximum entropy fuzzy clustering according to claim 1, characterized in that: Step 3 is as follows: Step 3.1: Introducing auxiliary variables The first term of the conversion optimization goal is a smoothing term: s.t.Y≥0,Y1=1,s T 1=k,0≤s≤1 According to the random initialization of c cluster centers, the initial Initialize all elements in Y to y ij =1 / c; Considering that the initial probability of the sample distribution in each class is equal, define To classify the sample x with a certain membership degree i The value obtained by weighting and summing the distances to all cluster centers; Arrange in order from smallest to largest The corresponding s can be calculated i : Step 3.2: Optimize the real sample and noise data to get Y In step 3.1, we get the s corresponding to the first k samples closest to all cluster centers. i =1, the s corresponding to the remaining samples i =0; e i Sort them in ascending order and place the corresponding samples x i Sorting can get the sorted data matrix Its corresponding sorted membership matrix Step 3.2.1: For real samples, when the sample corresponding to s i = 1, the problem can be equivalently transformed into The optimal membership degree corresponding to the selected real sample is obtained by optimizing the Lagerrange multiplier method Step 3.2.2: For the noise data in the optimization process, when the sample corresponding to s i = 0, the optimal membership value corresponding to the noise data in the optimization process is The optimal solution of the membership of all sample points can be obtained for Step 3.3: Take the partial derivative of the objective function with respect to m and get it equal to 0. At this point, m, Y, and s are updated, and the next iteration is performed again until m no longer changes.

3. A computer system, characterized in that include: One or more processors, and a computer-readable storage medium for storing one or more programs, wherein when the one or more programs are executed by the one or more processors, the one or more processors are enabled to implement the method of claim 1.

4. A computer-readable storage medium, characterized in that Computer-executable instructions are stored, and when the instructions are executed, they are used to implement the method of claim 1.

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