A hyperspectral band selection method and system based on manifold learning and hilbert-schmidt independence criterion

Abstract

The application discloses a hyperspectral band selection method and system based on manifold learning and a Hilbert-Schmidt independence criterion, and the method comprises the following steps: pre-processing hyperspectral data to obtain a two-dimensional data matrix, and taking the two-dimensional data matrix as manifold data in a high-dimensional space; using a UMAP algorithm to unfold and project the manifold data into a low-dimensional space to obtain an embedding matrix; using the Hilbert-Schmidt independence criterion to measure the nonlinear dependence between data, fitting the data matrix and each column vector of the embedding matrix in sequence to obtain a sparse coefficient matrix; calculating the importance of each band according to the sparse coefficient matrix, taking the maximum element value in the corresponding row vector of each band in the sparse coefficient matrix as the importance of the band, and selecting a band subset with the highest importance according to a preset number of selected bands. The application can select a band subset with the highest representativeness, and effectively improves the accuracy of a subsequent clustering task.

Description

Technical Field

[0001] This invention relates to the field of hyperspectral band selection technology, and in particular to a hyperspectral band selection method and system based on manifold learning and the Hilbert-Schmidt independence criterion. Background Technology

[0002] Hyperspectral images possess high spectral resolution and numerous bands, enabling the acquisition of almost continuous spectral characteristic curves of ground features, containing rich spatial, radiometric, and spectral information. Hyperspectral images are widely used in agricultural remote sensing, environmental remote sensing, resource exploration, and atmospheric science. In agricultural remote sensing, hyperspectral images can be used to monitor crop growth, detect pests and diseases, and estimate the biophysical parameters of vegetation. In environmental remote sensing, hyperspectral images can be used to monitor environmental parameters such as atmospheric composition, water quality, and vegetation cover. In resource exploration, hyperspectral images can be used to identify surface mineral assemblages; based on the analysis of the obtained rock spectral curves, the types and regions of mineral distribution in the area can be determined. Figure 1 As shown; in the field of urban monitoring, hyperspectral remote sensing images can be used to capture radiation sources on the earth's surface, such as nighttime lights and fires, including human residential areas, industrial areas, and fire situations, which can measure the level of human activity and ensure human safety; in the field of land cover classification remote sensing, hyperspectral remote sensing images can be used to accurately identify major land cover categories such as water bodies, buildings, roads, and bare soil, such as... Figure 2 As shown, this can provide accurate land use information for urban planning.

[0003] Hyperspectral images contain hundreds of consecutive narrow spectral bands with high resolution, providing rich spectral information for target recognition and classification in a scene, such as... Figure 3 As shown. However, the narrow spectral bands of hyperspectral images lead to redundancy between adjacent bands. Redundant bands not only increase the model's time and memory requirements but also affect the accuracy of tasks such as classification and clustering. How to eliminate redundant bands in hyperspectral images to improve model efficiency and classification accuracy has become a hot topic in hyperspectral image applications.

[0004] Traditional band selection relies primarily on supervised training; however, supervised training depends on a large number of labels, requiring significant human, material, and financial resources. To overcome the impact of label deficiency on band selection, an increasing number of scholars are shifting their attention to unsupervised band selection, which does not require any prior knowledge or label information.

[0005] Many unsupervised band selection algorithms have been proposed and used for hyperspectral image classification. Constrained Band Selection (CBS) uses constrained energy minimization to linearly constrain the band image while minimizing band correlations provided by other band images. Minimum Variance Principal Component Analysis (MVPCA) based on ranking obtains the eigenvalues ​​and eigenvectors of the transformed image through PCA and constructs a factor matrix, evaluating and ranking band importance based on band information and variance. Successive Projections Algorithm (SPA) transforms the band selection problem into a constrained combinatorial optimization problem. This constrained optimization limits the search range to a small subset of variables, thus reducing search costs. These algorithms are currently mainstream and effective band selection algorithms; however, they all have limitations, preventing them from selecting the optimal subset of bands.

[0006] In summary, although many methods have been proposed to address the band selection problem in hyperspectral images, these methods do not comprehensively consider the influence of the local and global structure of high-dimensional manifold data on band selection, nor can they effectively handle the complex nonlinear relationships commonly found in hyperspectral data, and they cannot adequately address the global redundancy problem. Therefore, an effective algorithm to analyze and process the redundancy of hyperspectral image bands, thereby selecting a set of more information and less redundancy from a limited number of bands, will further enhance the applications of hyperspectral images. Summary of the Invention

[0007] To address the aforementioned problems, this invention proposes a hyperspectral band selection method and system based on manifold learning and the Hilbert-Schmidt independence criterion.

[0008] To achieve the above objectives, the present invention adopts the following technical solution:

[0009] This invention proposes a hyperspectral band selection method based on manifold learning and the Hilbert-Schmidt independence criterion, comprising:

[0010] The hyperspectral data is preprocessed to obtain a two-dimensional data matrix, which is then regarded as manifold data in a high-dimensional space.

[0011] The UMAP algorithm is used to unfold the manifold data and project it into a low-dimensional space to obtain the embedding matrix;

[0012] The Hilbert-Schmidt independence criterion is used to measure the nonlinear dependence between data. The data matrix is ​​then fitted to each column vector of the embedding matrix in turn to obtain a sparse coefficient matrix.

[0013] The importance of each band is calculated based on the sparse coefficient matrix, and the maximum element value in the row vector corresponding to each band in the sparse coefficient matrix is ​​taken as the importance of that band.

[0014] Select the highest-importance subset of bands based on the preset number of selectable bands.

[0015] Furthermore, the preprocessing of the hyperspectral data includes: scaling the original hyperspectral data points to the range of [0,1], removing background pixels from the normalized data points, and then converting the data matrix into a two-dimensional matrix with dimensions of the number of ground feature pixels and the number of bands.

[0016] Furthermore, the step of using the UMAP algorithm to unfold the manifold data and project it into a low-dimensional space to obtain the embedding matrix includes: finding a specified number of nearest neighbors for each data point; constructing a directed weighted graph based on these nearest neighbors, ensuring that each data point is connected to its nearest neighbor; merging the weights of the two edges between two points to obtain an undirected weighted graph, which is the high-dimensional representation of the input data; initializing the low-dimensional representation and optimizing it to minimize the cross-entropy between the high-dimensional and low-dimensional representations, thus obtaining the embedding matrix; the dimension of the embedding matrix is ​​consistent with the number of categories in the hyperspectral image, and each row of the matrix represents the vector representation of the data in the low-dimensional space.

[0017] Furthermore, a directed weighted graph is constructed based on the nearest neighbors according to the following formula:

[0018]

[0019] in, Represents data point x i Its nearest j-th neighbor The probability that an edge exists between them. Indicates in x i Under the corresponding distance metric d, x i and The distance between them; ρ i and σ i They are x i Nearest neighbor and smoothing normalization factor:

[0020]

[0021]

[0022] Where p represents the number of nearest neighbors for each data point.

[0023] Furthermore, the weights of the two edges between the two points are combined according to the following formula:

[0024]

[0025] Where A represents the adjacency matrix of a directed weighted graph, and A contains elements Ai. ij From x i To x j The probability that a directed edge exists, A Τ Describe the transpose of matrix A. Let B denote the Hadamard product, and let B denote the adjacency matrix of the undirected weighted graph, where B is the number of elements in B. ij It is x i and x j The probability that at least one edge exists between them.

[0026] Furthermore, spectral embedding technology is used to initialize the low-dimensional representation, and a force-directed graph layout algorithm is used to optimize the low-dimensional representation.

[0027] Furthermore, the cross-entropy between the high-dimensional representation and the low-dimensional representation is calculated according to the following formula:

[0028]

[0029] Where E represents the set of all edges in the undirected graph, w h (e) represents the weight of edge e in the high-dimensional space, w l (e) represents the weight of edge e in the low-dimensional space.

[0030] Furthermore, the block HSIC Lasso algorithm is used to fit each column vector of the embedding matrix sequentially; the block HSIC Lasso algorithm measures the nonlinear dependence between data according to the kernel-based Hilbert-Schmidt independence criterion and uses an l1 penalty term to achieve sparsity.

[0031] Furthermore, the step of selecting the most important subset of bands based on the preset number of selected bands includes: sorting the importance of each band in descending order, and selecting the top-ranked bands based on the preset number of selected bands to form a subset of bands.

[0032] Another aspect of this invention proposes a hyperspectral band selection system based on manifold learning and the Hilbert-Schmidt independence criterion, comprising:

[0033] The data preprocessing module is used to preprocess the hyperspectral data to obtain a two-dimensional data matrix, which is regarded as manifold data in a high-dimensional space.

[0034] The manifold learning module is used to unfold and project manifold data into a low-dimensional space using the UMAP algorithm to obtain the embedding matrix;

[0035] The sparse learning module is used to measure the nonlinear dependencies between data using the Hilbert-Schmidt independence criterion by sequentially fitting the data matrix to each column vector of the embedding matrix to obtain a sparse coefficient matrix.

[0036] The band importance assessment module is used to calculate the importance of each band based on the sparse coefficient matrix, and the maximum element value in the row vector corresponding to each band in the sparse coefficient matrix is ​​taken as the importance of that band.

[0037] The band selection module is used to select the most important subset of bands based on the preset number of selectable bands.

[0038] Compared with the prior art, the present invention has the following beneficial effects:

[0039] This invention provides a hyperspectral band selection method and system based on manifold learning and the Hilbert-Schmidt independence criterion. The manifold learning process significantly improves the representation of high-dimensional data and effectively handles complex nonlinear relationships present in hyperspectral data. Specifically, this invention captures the inherent topological structure of the input data, unfolds the manifold data, and projects it into a low-dimensional space, accurately preserving the local structure of the data while retaining as much of the global structure as possible. Furthermore, it measures the nonlinear dependence between bands and the low-dimensional representation vector using the kernel-based Hilbert-Schmidt independence criterion (HSIC), fitting the input data matrix to each column vector of the embedding matrix, and employing L1 regularization to achieve sparsity in band selection, enabling a more accurate assessment of the importance of each band.

[0040] Applying this invention to hyperspectral images can significantly reduce the dimensionality of hyperspectral data, select a less redundant and more representative subset of bands, and effectively improve the accuracy of subsequent clustering or classification tasks. Attached Figure Description

[0041] Figure 1 This is an example of the application of hyperspectral remote sensing images in the field of resource exploration.

[0042] Figure 2 This is an example of the application of hyperspectral remote sensing images in the field of land cover classification.

[0043] Figure 3 This is a schematic diagram of the band structure of a hyperspectral image;

[0044] Figure 4A flowchart of a hyperspectral band selection method based on manifold learning and the Hilbert-Schmidt independence criterion is provided for an embodiment of the present invention.

[0045] Figure 5 A flowchart illustrating the band selection principle of a hyperspectral band selection method based on manifold learning and the Hilbert-Schmidt independence criterion, provided for embodiments of the present invention;

[0046] Figure 6 Line graphs showing the clustering results (NMI) of the four band selection algorithms in this embodiment of the invention on the KSC dataset;

[0047] Figure 7 Line graphs showing the clustering results (NMI) of the four band selection algorithms in this embodiment of the invention on the Botswana dataset;

[0048] Figure 8 Line graphs showing the clustering results (NMI) of the four band selection algorithms in this embodiment of the invention on the Indian Pines dataset;

[0049] Figure 9 This is a line graph showing the clustering results (NMI) of the four band selection algorithms in this embodiment of the invention on the Trento dataset;

[0050] Figure 10 Line graph showing the clustering results (ACC) of the four band selection algorithms in this embodiment of the invention on the KSC dataset;

[0051] Figure 11 Line graphs showing the clustering results (ACC) of the four band selection algorithms in this embodiment of the invention on the Botswana dataset;

[0052] Figure 12 Line graphs showing the clustering results (ACC) of the four band selection algorithms in this embodiment of the invention on the Indian Pines dataset;

[0053] Figure 13 Line graphs showing the clustering results (ACC) of the four band selection algorithms in this embodiment of the invention on the Trento dataset;

[0054] Figure 14 The spectral distribution of 20 bands selected on the KSC dataset by the four band selection algorithms in this embodiment of the invention;

[0055] Figure 15 The spectral distribution of 20 bands selected on the Botswana dataset by the four band selection algorithms in this embodiment of the invention is shown.

[0056] Figure 16 Spectral distribution diagrams of selecting 20 bands by four band selection algorithms in the Indian Pines dataset in the embodiments of the present invention;

[0057] Figure 17 Spectral distribution diagrams of selecting 20 bands by four band selection algorithms in the Trento dataset in the embodiments of the present invention;

[0058] Figure 18 Schematic diagram of the architecture of a hyperspectral band selection system based on manifold learning and Hilbert-Schmidt independence criterion provided in the embodiments of the present invention. Detailed implementation manners

[0059] The following further explains and illustrates the present invention in conjunction with the attached drawings and specific embodiments:

[0060] As Figure 4 , Figure 5 shown, a hyperspectral band selection method based on manifold learning and Hilbert-Schmidt independence criterion includes the following steps:

[0061] S101: Preprocess the hyperspectral data to obtain a two-dimensional data matrix, and regard it as manifold data in a high-dimensional space;

[0062] Specifically, scale the original data points to the range of [0, 1] to eliminate the dimensional difference between different bands of the data for subsequent calculations; then remove the background pixels in the normalized data points, and then convert the data matrix into a two-dimensional matrix, and the two dimensions are the number of ground object pixels and the number of bands respectively.

[0063] For example, given a hyperspectral image, the two-dimensional matrix can be expressed as X = [x1, x2,..., x N , N represents the number of ground object pixels of the hyperspectral image, and M represents the number of bands of the hyperspectral image. When selecting as few bands as possible, the ultimate goal of band selection is to include as much data information as possible. Therefore, if D bands (D < M) are to be selected, the sample set after band selection is X' = [x'1, x'2,... x' N , The number of bands is reduced from the original M to D, and the selected D bands are the subset of bands that contain the most information under the specified number of bands.

[0064] S102: Use the UMAP algorithm to unfold and project the manifold data into a low-dimensional space to obtain an embedding matrix;

[0065] Specifically, a specified number of nearest neighbors are found for each data point, and a directed weighted graph is constructed based on these nearest neighbors, ensuring that each point is connected to its nearest neighbor; the weights of the two edges between two points are merged to obtain an undirected weighted graph, which is the high-dimensional representation of the input data; the low-dimensional representation is initialized and optimized to minimize the cross-entropy between the high-dimensional and low-dimensional representations.

[0066] For the input data matrix X, first find each p nearest neighbors Then define each x i The corresponding nearest neighbor point ρ i and smoothing normalization factor σ i :

[0067]

[0068]

[0069] in Indicates in x i Under the corresponding distance metric d, x i The distance between it and its j-th nearest neighbor. ρ i Ensure x i The probability that at least one edge is connected to another point is 1.

[0070] Next, we construct a weighted graph G = (V, E, W). V is the set of all vertices in the sample set X, E is the set of all directed edges in the graph, and W represents the weight of each edge, defined as follows:

[0071]

[0072] in Representing point x i The probability that an edge exists between a point and its j-th nearest neighbor. The graph is asymmetric in this case because there may be two directed edges between two points, and the weights of these edges are not necessarily equal. To address this, the weights of the two edges between the two points are combined, as shown in the following formula:

[0073]

[0074] Where A represents the adjacency matrix of a directed weighted graph, and A contains elements Ai. ij From x i To x j The probability that a directed edge exists, A Τ Describe the transpose of matrix A. Let B denote the Hadamard product, and let B denote the adjacency matrix of the undirected weighted graph, where B is the number of elements in B. ij It is x i and x jThe probability that at least one edge exists between them. This completes the construction of the high-dimensional graph representation. Graph G is an undirected weighted graph with adjacency matrix B.

[0075] Next, the high-dimensional data is projected onto a low-dimensional space to find the corresponding low-dimensional representation, which is then optimized. In the low-dimensional space, the relationship between two points is defined by the following formula:

[0076] Φ(y i ,y j )=(1+a(y i -y j ) 2b ) -1

[0077] The default values ​​for a and b are 1.93 and 0.79, respectively, which are used to adjust the clustering of low-dimensional data after mapping.

[0078] During low-dimensional representation initialization, using spectral embedding techniques can accelerate algorithm convergence. Subsequently, a force-directed graph layout algorithm is used to continuously adjust the positions of data points in the low-dimensional space, enabling the high-dimensional graph representation G to converge more quickly from point {y}. i The low-dimensional graph formed by |1≤i≤N} represents the minimum cross-entropy between S, and the cross-entropy is defined as follows:

[0079]

[0080] Where E represents the set of all edges in the undirected graph, w h (e) represents the weight of edge e in the high-dimensional space, w l (e) represents the weight of edge e in the low-dimensional space. The first term represents the weight w in the high-dimensional space. h (e) When it is large, it acts as an "attraction" force because when w l (e) The larger the value, the smaller this term will be; that is, the closer the distance between points in the lower dimensions, the smaller this term will be. The second term has higher weights w in the higher dimensions. h (e) When it is small, it acts as a "repulsive force" because by minimizing w... l (e) can be minimized, meaning that the greater the distance between low-dimensional points, the smaller this term becomes. Overall, the balance of these two "forces" will cause the low-dimensional representation to tend towards a state that can relatively accurately reflect the overall topological structure of the high-dimensional data.

[0081] The resulting low-dimensional graph representation of S corresponds to the embedding matrix. This is the representation of popular data in high-dimensional space in low-dimensional space. Each row of Y represents the coordinate representation of the data in K-dimensional space, where K is usually the same as the number of categories in the hyperspectral data.

[0082] S103: Use the Hilbert-Schmidt independence criterion to measure the nonlinear dependence between data, and fit the data matrix to each column vector of the embedding matrix in turn to obtain a sparse coefficient matrix;

[0083] Specifically, the method used to sequentially fit the data matrix to each column vector of the embedding matrix is ​​the block HSIC Lasso algorithm. The block HSIC Lasso algorithm measures the nonlinear dependencies between data based on the kernel-based Hilbert-Schmidt independence criterion and uses an l1 penalty term to achieve sparsity.

[0084] Represent the input matrix as The input data is then divided into N / h partitions. h is the number of samples in each block. Then, for the embedding matrix Y obtained in step S102, the partitioned data is embedded into each column y of Y. i The sparse coefficient vector is fitted using the block HSIC Lasso algorithm:

[0085]

[0086] in This represents the vector of the k-th band in the l-th partition. HSIC b (u k ,y i )and Both are based on kernel independence measures. tr represents a trace. and It is the central Gram matrix. and This is the Gram matrix calculated using a kernel function; here, a Gaussian kernel function is used. F It is the Frobenius norm, where H is a function of... The defined central matrix, if i = j, then δ ij =1, otherwise 0.

[0087] If the kth band corresponds to y i Strong correlation, then HSIC b (u k ,y i The value of α will be very large. To minimize the above expression, α k The value should also be large; if the k-th band is related to y i If unrelated, then HSIC b (u k ,y i The value of α will be close to 0. kThis will be eliminated by the L1 regularization term. Therefore, it is possible to select y. i Strongly correlated bands. If band u k and u l If it is strongly correlated, then HSIC b (u k ,u l The value of α will be very large. To minimize the above expression, α k and α l Any one of them tends to approach 0, so redundant bands can be removed.

[0088] Since the data was partitioned before fitting the sparse coefficient vector, to avoid the influence of partitioning, given P random permutations of N data points, HSIC is then used. b The bagging version of the estimator is defined as follows:

[0089]

[0090] Therefore, the above minimization problem can be rewritten as:

[0091]

[0092] The final solution α i =[α 1i ,...,α Mi ] Τ ,||α i ||1 is α i The l1 norm, λ is the control α i The sparsity regularization parameter α. i Essentially includes approximation of y i The combination coefficients of the time band. Due to the sparsity of the solution, a sparse matrix will eventually be obtained, allowing us to find the relationship with y. i The most relevant and least redundant band corresponds to α. i The non-zero coefficients in.

[0093] Step S103 ultimately yields K sparse coefficient vectors. That is, a sparse coefficient matrix

[0094] S104: Calculate the importance of each band based on the sparse coefficient matrix. Specifically, the maximum element value in the row vector corresponding to each band in the sparse coefficient matrix is ​​the importance of that band.

[0095] Specifically, in the sparse coefficient matrix, each α i Corresponding to a category, α i Each item in the table represents a wavelength band, α i,jThe larger the value, the greater the importance of the j-th band to the i-th category. Therefore, the formula for band importance is defined as follows:

[0096]

[0097] Where, α i,j It is α i The j-th element.

[0098] S105: Select the most important subset of bands based on the preset number of selectable bands.

[0099] Specifically, the importance of each band is sorted in descending order, and the top D bands are selected to form a band subset.

[0100] To verify the effectiveness of the present invention, the following experimental data are provided.

[0101] The method provided in this embodiment of the invention is referred to as the MUNFS algorithm. This method was implemented using PyCharm Community Edition 2022.3.2 for Windows and run on a personal computer equipped with a 2.50GHz Intel Core i9 processor and 16GB of RAM. Based on this experimental environment, the MUNFS algorithm provided in this embodiment of the invention was compared with existing technologies such as MCFS-I, LaplacianScore (Lap_score), NDFS (Nonnegative Discriminative Feature Selection), and others.

[0102] The experiment used four hyperspectral datasets, the basic information of which is shown in Table 1, and the detailed information is as follows:

[0103] The Kennedy Space Center (KSC) dataset was created in 1996 at the Kennedy Space Center in Florida, USA, using the Airborne Visible Infrared Imaging Spectroradiometer (AVIRI). It is a 512×614-pixel hyperspectral dataset. AVIRI has a wavelength range of 400-2500 nm and a spatial resolution of 18 meters. The dataset actually used 176 bands for training, representing 13 land cover types.

[0104] The Botswana dataset was acquired by NASA's EO-1 satellite between 2001 and 2004, with image sizes of 1476×256. The EO-1 sensor operates in the wavelength range of 400-2500 nm, with a spatial resolution of approximately 20 meters. Originally consisting of 242 bands, after removing noisy bands, a total of 145 bands remained, representing 14 land cover types.

[0105] The Indian Pines dataset was created in 1992 using the AVIRIS sensor in Indiana, USA, and a 145×145 section was cropped and labeled. After removing 20 water absorption bands, the dataset actually contains 200 bands representing 16 land cover types.

[0106] The Trento dataset was captured in a rural area south of Trento, Italy, using the AISA Eagle sensor. This sensor has a wavelength range of 0.40–0.98 μm and a spatial resolution of 1 m. The dataset contains 600 × 166 images, 63 bands, and includes 6 land cover types.

[0107] Table 1 Basic Information of Hyperspectral Dataset

[0108] KSC 512×614 5211 176 13 Botswana 1476×256 3248 145 14 Indian Pines 145×145 10249 200 16 Trento 166×600 30214 63 6

[0109] Next, we will evaluate the quality of the band subsets selected by the four methods using clustering performance assessment. Here, we will use two clustering performance evaluation metrics, NMI (Normalized Mutual Information) and ACC (Accuracy), to evaluate the performance of the methods. The definitions of NMI and ACC are as follows.

[0110] After selecting a subset of bands, it is used for data clustering. Assuming T is the true label of the sample and C is the clustering result after band selection, NMI is defined as follows:

[0111]

[0112] Where H(T) and H(C) represent the entropy of T and C respectively, and MI(T,C) represents the mutual information between T and C, which is defined as follows:

[0113]

[0114] Where p(t) i ) and p(c i ) represent the points selected from the dataset that belong to t. i or c i The probability of p(t). i ,c i ) indicates that any point selected from the dataset that simultaneously belongs to t i and c i The joint probability. The value of NMI is between 0 and 1. When the value of NMI is larger, it indicates that the consistency between the clustering results and the true labels is higher, and the performance of the band selection method is better.

[0115] Accuracy measures the ratio between the number of correctly assigned samples in the clustering results and the total number of samples, and is defined as follows:

[0116]

[0117] Where, N correct This represents correctly assigned samples, and N represents the total number of samples. The value of ACC is between 0 and 1. An ACC of 1 indicates that the clustering result of the samples is completely consistent with the true labels, while an ACC of 0 indicates that the clustering result of the samples is completely inconsistent with the true labels.

[0118] In the experiment, four band selection algorithms were used to select bands. K-means clustering was then performed on the data based on the selected bands, and the quality of the selected band subsets was evaluated using two clustering performance metrics. Because the K-means algorithm has a certain degree of randomness, it was randomly initialized five times in the experiment, and the mean of each evaluation metric was used as the final result.

[0119] Table 2 shows the detailed clustering performance of the four methods when selecting 30 bands. Each row in Table 2 represents the clustering results of the four algorithms, and the last column, ALL, represents the clustering results using all bands of the dataset. The clustering results are evaluated using both NMI and ACC metrics. Bold text indicates the best result on that dataset. As can be observed from the table, when using the NMI metric, MUNFS outperforms MCFS-I, LaplacianScore (Lap_score), and NDFS by 5.215%, 5.722%, and 1.275%, respectively, on the four datasets. When using the ACC metric, MUNFS outperforms MCFS-I, LaplacianScore, and NDFS by 6.565%, 6.675%, and 0.572%, respectively, on the four datasets. This information indicates that MUNFS performs best on hyperspectral datasets.

[0120] Table 2. Clustering results (%) of the band selection method on the hyperspectral dataset.

[0121]

[0122] In this embodiment, a dotted line graph was plotted to observe the impact of selecting different bands on the algorithm's performance. Different colors and patterns in the graph represent different band selection methods, the X-axis represents the number of selected bands, and the Y-axis represents the clustering results.

[0123] Figures 6-9 The clustering results (NMI) of the four band selection algorithms are shown on the KSC, Botswana, Indian Pines and Trento datasets, respectively, as a function of the number of selected bands. Figures 10-13The figures show the clustering accuracy (ACC) of four band selection algorithms on the KSC, Botswana, Indian Pines, and Trento datasets, varying with the number of bands selected. As can be seen from these figures, the MUNFS method exhibits the best performance on all hyperspectral datasets. While MUNFS performs poorly on the Trento dataset when only a few bands are selected, it performs exceptionally well on the KSC, Botswana, and Indian Pines datasets. The more bands selected, the better MUNFS performs on hyperspectral datasets, which is particularly evident on the Trento dataset. This is because using more bands often makes the spectral features of ground objects easier to distinguish. Furthermore, on most datasets, MUNFS outperforms the algorithm using all bands. For example, on the KSC dataset, MUNFS achieves an NMI of 57.1% when selecting 5 bands, compared to only 55.3% when using all 176 bands. Therefore, MUNFS performs better with only a few bands than with all bands. This demonstrates that the spectral bands in hyperspectral images have high redundancy and proves the effectiveness of the MUNFS algorithm.

[0124] To more intuitively see the distribution of bands selected by various methods, a band distribution interval experiment is used to demonstrate the distribution of bands selected by the four methods on each hyperspectral dataset. Figures 14-17The distribution of the 20 bands selected by four band selection algorithms on the KSC, Botswana, Indian Pines, and Trento datasets is shown respectively. In the right-hand color bar of the figure, different colors correspond to different spectral ranges. The vertical axis represents the four methods, and the horizontal axis represents the 20 bands selected by each method. Comparing the band selection results of these algorithms, it can be seen that MUNFS's selected band set covers almost all band intervals, while the other three comparative algorithms select bands concentrated in a small number of intervals. Taking the Indian Pines dataset as an example, MCFS-I, LaplacianScore, and NDFS concentrate their band selection in the 50-125, 100-175, and 1-75 intervals, respectively. Unlike these methods, MUNFS selects bands in all spectral intervals, indicating that this algorithm can select a richer and more comprehensive subset of bands from a limited number of bands. This is primarily because the method fully utilizes both local and global information in its data analysis, effectively capturing the nonlinear dependencies between bands in hyperspectral images. This results in a more comprehensive analysis and a better solution to the redundancy problem in band selection. In contrast, the MCFS-I and NDFS algorithms significantly outperform the MUNFS method on the same dataset. This may be because these methods only use local or global information in their data processing and fail to detect nonlinear relationships between bands, leading to suboptimal band selection schemes. The LaplacianScore algorithm, however, does not address redundancy issues. Therefore, applying this algorithm to hyperspectral images with high band redundancy makes it easier to select a subset of highly redundant bands.

[0125] In summary, the MUNFS method proposed in this invention can greatly improve the representation of high-dimensional data by capturing the underlying topological structure of the data, thereby generating higher-quality embeddings for manifold data. It measures the nonlinear dependence between bands and low-dimensional representation vectors through the kernel-based Hilbert-Schmidt independence criterion, and uses L1 regularization to achieve sparsity in band selection, which can select the most representative and low-redundancy subset of bands, thereby improving the accuracy of subsequent clustering or classification tasks.

[0126] Based on the above embodiments, such as Figure 18 As shown, this invention also proposes a hyperspectral band selection system based on manifold learning and the Hilbert-Schmidt independence criterion, comprising:

[0127] The data preprocessing module is used to preprocess the hyperspectral data to obtain a two-dimensional data matrix, which is regarded as manifold data in a high-dimensional space.

[0128] The manifold learning module is used to unfold and project manifold data into a low-dimensional space using the UMAP algorithm to obtain the embedding matrix;

[0129] The sparse learning module is used to measure the nonlinear dependencies between data using the Hilbert-Schmidt independence criterion by sequentially fitting the data matrix to each column vector of the embedding matrix to obtain a sparse coefficient matrix.

[0130] The band importance assessment module is used to calculate the importance of each band based on the sparse coefficient matrix, and the maximum element value in the row vector corresponding to each band in the sparse coefficient matrix is ​​taken as the importance of that band.

[0131] The band selection module is used to select the most important subset of bands based on the preset number of selectable bands.

[0132] In summary, this invention captures the inherent topological structure of the input data, unfolds the manifold data, and projects it into a low-dimensional space. This allows for accurate preservation of the local structure of the data while retaining as much of the global structure as possible. Furthermore, by measuring the nonlinear dependency between bands and the low-dimensional representation vector using the kernel-based Hilbert-Schmidt Independence Criterion (HSIC), the input data matrix is ​​fitted to each column vector of the embedding matrix. Simultaneously, l1 regularization is used to achieve sparsity in band selection, enabling a more accurate assessment of the importance of each band. This invention can significantly reduce the dimensionality of hyperspectral data, select a less redundant and more representative subset of bands, and effectively improve the accuracy of subsequent clustering or classification tasks.

[0133] The above description is only a preferred embodiment of the present invention. It should be noted that those skilled in the art can make several improvements and modifications without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A hyperspectral band selection method based on manifold learning and the Hilbert-Schmidt independence criterion, characterized in that, include: The hyperspectral data is preprocessed to obtain a two-dimensional data matrix, which is then regarded as manifold data in a high-dimensional space. The UMAP algorithm is used to unfold the manifold data and project it into a low-dimensional space to obtain the embedding matrix; The Hilbert-Schmidt independence criterion is used to measure the nonlinear dependence between data. The data matrix is ​​then fitted to each column vector of the embedding matrix in turn to obtain a sparse coefficient matrix. The importance of each band is calculated based on the sparse coefficient matrix, and the maximum element value in the row vector corresponding to each band in the sparse coefficient matrix is ​​taken as the importance of that band. Select the highest-importance subset of bands based on the preset number of selectable bands.

2. The hyperspectral band selection method based on manifold learning and the Hilbert-Schmidt independence criterion according to claim 1, characterized in that, The preprocessing of the hyperspectral data includes: scaling the original hyperspectral data points to the range of [0,1], removing background pixels from the normalized data points, and then converting the data matrix into a two-dimensional matrix with dimensions of the number of ground feature pixels and the number of bands.

3. The hyperspectral band selection method based on manifold learning and the Hilbert-Schmidt independence criterion according to claim 1, characterized in that, The process of using the UMAP algorithm to unfold and project manifold data into a low-dimensional space to obtain the embedding matrix includes: finding a specified number of nearest neighbors for each data point; constructing a directed weighted graph based on these nearest neighbors, ensuring that each data point is connected to its nearest neighbor; merging the weights of the two edges between two points to obtain an undirected weighted graph, which is the high-dimensional representation of the input data; initializing the low-dimensional representation and optimizing it to minimize the cross-entropy between the high-dimensional and low-dimensional representations, thus obtaining the embedding matrix.

4. The hyperspectral band selection method based on manifold learning and the Hilbert-Schmidt independence criterion according to claim 3, characterized in that, Construct a directed weighted graph based on nearest neighbors using the following formula: in, Represents data point x i Its nearest j-th neighbor The probability that an edge exists between them. Indicates in x i Under the corresponding distance metric d, x i and The distance between them; ρ i and σ i They are x i Nearest neighbor and smoothing normalization factor: Where p represents the number of nearest neighbors for each data point.

5. The hyperspectral band selection method based on manifold learning and the Hilbert-Schmidt independence criterion according to claim 3, characterized in that, The weights of the two edges between two points are combined according to the following formula: Where A represents the adjacency matrix of a directed weighted graph, and A contains elements Ai. ij From x i To x j The probability that a directed edge exists, A Τ Describe the transpose of matrix A. Let B denote the Hadamard product, and let B denote the adjacency matrix of the undirected weighted graph, where B is the number of elements in B. ij It is x i and x j The probability that at least one edge exists between them.

6. The hyperspectral band selection method based on manifold learning and the Hilbert-Schmidt independence criterion according to claim 3, characterized in that, Spectral embedding technique is used to initialize the low-dimensional representation, and force-directed graph layout algorithm is used to optimize the low-dimensional representation.

7. The hyperspectral band selection method based on manifold learning and the Hilbert-Schmidt independence criterion according to claim 3, characterized in that, The cross-entropy between the high-dimensional and low-dimensional representations is calculated using the following formula: Where E represents the set of all edges in the undirected graph, w h (e) represents the weight of edge e in the high-dimensional space, w l (e) represents the weight of edge e in the low-dimensional space.

8. The hyperspectral band selection method based on manifold learning and the Hilbert-Schmidt independence criterion according to claim 1, characterized in that, The block HSIC Lasso algorithm is used to fit the data matrix to each column vector of the embedding matrix in turn.

9. The hyperspectral band selection method based on manifold learning and the Hilbert-Schmidt independence criterion according to claim 1, characterized in that, The step of selecting the most important band subset based on the preset number of selected bands includes: sorting the importance of each band in descending order, and selecting the top-ranked bands based on the preset number of selected bands to form a band subset.

10. A hyperspectral band selection system based on manifold learning and the Hilbert-Schmidt independence criterion, characterized in that, include: The data preprocessing module is used to preprocess the hyperspectral data to obtain a two-dimensional data matrix, which is regarded as manifold data in a high-dimensional space. The manifold learning module is used to unfold and project manifold data into a low-dimensional space using the UMAP algorithm to obtain the embedding matrix; The sparse learning module is used to measure the nonlinear dependencies between data using the Hilbert-Schmidt independence criterion by sequentially fitting the data matrix to each column vector of the embedding matrix to obtain a sparse coefficient matrix. The band importance assessment module is used to calculate the importance of each band based on the sparse coefficient matrix, and the maximum element value in the row vector corresponding to each band in the sparse coefficient matrix is ​​taken as the importance of that band. The band selection module is used to select the most important subset of bands based on the preset number of selectable bands.

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