Coal recognition method based on kernel two-way rank order sharing density space preserving projection

Abstract

This invention discloses a coal identification method based on kernel bidirectional rank-order shared density space-preserving projection, which solves the problem of difficulty in capturing the inherent manifold structure of coal data and effectively improves the accuracy of coal identification. The specific implementation process is as follows: (1) Construct a kernel bidirectional rank module through kernel mapping, design a shared nearest neighbor density matrix, and finally integrate the space-preserving projection idea to form a kernel bidirectional rank-order shared density-preserving projection model; (2) Derive the analytical solution of the kernel rank shared density projection direction to obtain the projection matrix of the kernel bidirectional rank-order shared density space; (3) Obtain the kernel rank coal features with good discriminative power directly through the kernel rank shared density projection direction of randomly selected coal test samples, and input them into the classifier to obtain the final coal identification result. Compared with the prior art, the coal identification method of this invention is more accurate and robust.

Description

Technical Field

[0001] This invention relates to a coal identification method based on nuclear bidirectional rank-shared density spatially preserved projection, belonging to the fields of pattern recognition and intelligent coal detection. Background Technology

[0002] Coal, as a crucial basic energy source and industrial raw material in my country, directly impacts the efficiency of coal sorting, processing, utilization, and safe production through accurate identification of its types. This is a core requirement for the intelligent and refined development of the coal industry and a vital technological support for its high-quality development. Spatial learning, as a pattern recognition method, possesses a strong theoretical foundation and practical feasibility. However, in real-world industrial scenarios, coal data exhibits significant characteristics such as high-dimensionality, small sample sizes, nonlinear distribution, and heterogeneous density. This makes it difficult for traditional linear dimensionality reduction methods to capture the inherent manifold structure of the data, and similarity modeling based on a single distance metric is susceptible to density heterogeneity interference, ultimately resulting in low coal identification accuracy and poor robustness. Therefore, this invention, based on spatial learning theory, maps nonlinear coal distribution data to a high-dimensional kernel space through kernel mapping. On this basis, a kernel bidirectional rank module is constructed to effectively identify pseudo-similar samples with unidirectional nearest neighbors but no bidirectional association. A shared nearest neighbor density matrix is ​​designed to adapt to heterogeneous density distributions, and further, the concept of space-preserving projection is integrated to form a kernel bidirectional rank shared density-preserving projection model. Through theoretical derivation of the model, an analytical solution for the kernel rank shared density projection direction is obtained. Based on the kernel rank shared density projection direction, kernel rank coal features with good discriminative power, high robustness, and no redundancy are directly obtained, which effectively improves the accuracy of coal identification. Summary of the Invention

[0003] To address the challenge of capturing the inherent manifold structure of coal data due to its high-dimensionality, small sample size, nonlinear distribution, and heterogeneous density, this invention constructs a kernel-based bidirectional rank-shared density-preserving projection model based on spatial learning theory. Analytical solutions for the kernel-rank shared density projection direction are derived theoretically, allowing for the direct acquisition of kernel-rank coal features with good discriminative power based on this projection direction. The specific implementation steps of this invention are as follows: 1. By collecting images of different types of coal, the image pixels are converted into one-dimensional numerical vectors, and then principal component analysis is used to reduce the dimensionality and obtain a coal data sample set. ,in To represent a sample, Indicates the sample dimension. This indicates the number of samples. The coal data is divided into training and test sets proportionally, and the test set data is randomized for each experiment.

[0004] 2. Construct a kernel bidirectional rank module through kernel mapping.

[0005] The specific construction steps of the kernel bidirectional rank module are as follows: (2a) For the coal data sample set , This yields the inter-sample metric: in satisfy It is symmetric matrix; according to The kernel mapping adaptive parameters are obtained as follows: exist and Based on this, samples were obtained. and Similarity coefficient between them: Simultaneously define a centralized matrix: And thus, a kernel mapping representation is defined: Obtain the kernel mapping representation of the coal data sample set. .

[0006] (2b) Define the distance between samples based on the kernel mapping representation of the coal data samples: Sort the samples in ascending order by the distances between them to obtain the sample index. , Representing the The first sample The nearest neighbor corresponds to the sample index number, defining the sample. The former Nearest neighbor set: It is a sample For the sample The nearest neighbor rank, i.e. exist Ranked in the nearest neighbor list Bit, Representative at The first in the nearest neighbor list One sample, For the sample The Nearest neighbor samples ,definition right rank value: It is a sample right rank value, It is a sample right The rank value, construct and The core bidirectional rank module is as follows: The kernel bidirectional rank module maps nonlinear coal distribution data to a high-dimensional kernel space through kernel mapping, achieving linear separability and effectively preserving the nonlinear discriminative characteristics of coal data. Abandoning the unidirectional nearest neighbor metric approach, it effectively identifies pseudo-similar samples that are unidirectional nearest neighbors but not bidirectionally correlated through bidirectional rank summation and minimum rank normalization.

[0007] 3. Construct a kernel bidirectional rank-shared density-preserving projection model to obtain the kernel rank-shared density projection direction.

[0008] The specific construction steps of the kernel two-way rank-shared density-preserving projection model are as follows: Based on the kernel bidirectional rank module, define the sample Local neighborhood density: The larger the sample size, the better. The sparser the local area, The smaller the value, the better the sample size. The more stable the local structure, the better. To eliminate the influence of dimensions, a global average density of the dataset is defined: Based on this, a shared nearest neighbor density matrix is ​​constructed, which is defined as follows: The shared nearest neighbor density matrix comprehensively considers the Euclidean distance between samples, the overlap of local neighborhood structures, and the difference in local density, and can adaptively characterize the true proximity relationship of samples in high-dimensional space.

[0009] For a shared nearest neighbor density matrix, its diagonal matrix is ​​defined as: Thus, the Laplace matrix is ​​obtained. Further define the divergence that characterizes the local neighborhood: Define the divergence that characterizes the global samples: And define the normalization matrix: use express The rank of the normalized matrix Perform eigenvalue decomposition: Obtain the eigenvectors: And the eigenvalue diagonal matrix: Take before indivual In Obtain the projection matrix: Construct a kernel-based bidirectional rank-order shared density-preserving projection model: in The trace of a matrix is ​​the sum of the elements on its diagonal. express An identity matrix of order 1 is used to constrain the projection, ensuring that the projected features are independent of each other.

[0010] The kernel bidirectional rank shared density-preserving projection model is an optimization model that integrates kernel bidirectional rank modules and shared density constraints into spatially preserved projection. It achieves the extraction and dimensionality reduction of coal features through a constrained minimization objective.

[0011] 4. Through theoretical derivation of the model, an analytical solution for the kernel-rank shared density projection direction is obtained. By randomly sampling test set data, kernel-rank coal features with good discriminative power, high robustness, and no redundancy are directly obtained from the coal sample data based on the kernel-rank shared density projection direction. Finally, a classifier is used for classification to obtain the coal identification results.

[0012] The method of the present invention has the following advantages: (1) The present invention constructs a kernel bidirectional rank module, which maps coal data to a high-dimensional linearly separable space through kernel mapping, retains the nonlinear discriminative features of coal data, and avoids the problem of losing key structural information by traditional linear measurement methods; then, the neighborhood structure association between samples is characterized by bidirectional rank summation and minimum rank normalization, which effectively identifies pseudo-similar samples that are unidirectional nearest neighbors but not bidirectionally related. (2) The present invention designs a shared nearest neighbor density matrix, incorporates local density and global density constraints under the kernel bidirectional rank module, effectively distinguishes coal / gangue samples that are close in distance but have large density differences, avoids feature aliasing caused by density heterogeneity, improves feature discriminability, and integrates the idea of ​​space-preserving projection to construct a kernel bidirectional rank shared density-preserving projection model, accurately captures the real proximity relationship of high-dimensional coal data, and significantly improves the robustness and accuracy of coal identification; (3) This invention obtains the analytical solution of the kernel-rank shared density projection direction through theoretical derivation. By constraining the projection features with the identity matrix, redundancy and scaling deviation of the projection features are avoided, and interference between different categories is reduced. Based on the kernel-rank shared density projection direction, kernel-rank coal features with good discriminative power, high robustness, and no redundancy are directly obtained, thus achieving more accurate coal identification. Attached Figure Description

[0013] The present invention will be further described below with reference to the accompanying drawings and examples.

[0014] Figure 1 This is a flowchart of the present invention, wherein... This represents the number of coal categories.

[0015] Figure 2 It is the classification accuracy under increasing sample size. Detailed Implementation

[0016] The specific implementation steps of this invention are as follows: 1. By collecting images of different types of coal, the image pixels are converted into one-dimensional numerical vectors, and then principal component analysis is used to reduce the dimensionality and obtain a coal data sample set. ,in To represent a sample, Indicates the sample dimension. This indicates the number of samples. The coal data is divided into training and test sets proportionally, and the test set data is randomized for each experiment.

[0017] 2. Based on the kernel bidirectional rank-order shared density-preserving projection model, the model is as follows: The analytical solution of the model is transformed into a generalized eigenvalue problem, which is solved by constructing the Lagrange equation. The resulting column vector... yes of The largest generalized eigenvector is also the direction of the kernel rank shared density projection.

[0018] 3. A training sample feature set in a low-dimensional space is obtained from the coal data through kernel-rank shared density projection. Coal test samples are randomly selected, and the extracted test samples are then directly subjected to kernel-rank shared density projection to obtain kernel-rank coal features with good discriminative power. Finally, a classifier is used for classification to obtain the coal identification results.

[0019] The effectiveness of this invention was further verified through the following experiments: The dataset was taken from a large mine in Huainan area, and selected data on three typical coal types: anthracite, lignite and peat. All data samples were uniformly input with a dimension of 100*100. Figure 2 This is a graph showing the trend of coal identification accuracy as the number of training samples increases. From... Figure 2 As can be seen, with the gradual increase in the number of training samples, the recognition accuracy of the method described in this invention shows a continuous upward trend, and the recognition results exhibit excellent stability. Experimental results demonstrate that the coal identification method disclosed in this invention is accurate, effective, stable, and reliable, capable of accurately identifying different types of coal, and possesses strong practicality and technical application value.

Claims

1. A coal identification method based on kernel-based bidirectional rank-order shared density spatially preserving projection, characterized in that, The method includes the following steps: (1) By collecting images of different types of coal, the image pixels are converted into one-dimensional numerical vectors, and then principal component analysis is used to reduce the dimensionality to obtain a coal data sample set. ,in To represent a sample, Indicates the sample dimension. This indicates the number of samples. The coal data is divided into training and test sets proportionally, and the test set data is randomized for each experiment. (2) Construct a kernel bidirectional rank module through kernel mapping; (3) Construct a kernel bidirectional rank-order shared density-preserving projection model; (4) The model is theoretically derived to obtain the analytical solution of the kernel rank shared density projection direction. Based on the kernel rank shared density projection direction, the kernel rank coal features with good discriminative power are directly obtained, and the classifier is used for classification to obtain the coal identification results.

2. The coal identification method based on kernel bidirectional rank-order shared density spatial preservation projection according to claim 1, characterized in that... Step (2) involves constructing a bidirectional rank module using kernel mapping, and the steps are as follows: (2a) For the coal data sample set , , build and The core bidirectional rank module is as follows: in It is a sample right rank value, It is a sample right The rank value; for the sample The Nearest neighbor samples ,definition right rank value: in , Representing the The first sample The sample index number corresponding to the nearest neighbor. Representative at The first in the nearest neighbor list One sample, It is a sample For the sample The nearest neighbor rank, i.e. exist Ranked in the nearest neighbor list Bit, defining sample The former Nearest neighbor set: in The distance between samples is determined by sorting them in ascending order of their distances. in It is a sample The kernel mapping representation, It is a sample The kernel mapping representation; (2b) Constructing a kernel mapping representation of the coal data sample set Define kernel mapping representation: in It is a centralized matrix. , Indicates sample and Similarity coefficient between them: in The kernel mapping adaptive parameter is defined as follows: in Represents the nearest neighbor number. The metric representing the distance between samples is defined as follows: satisfy It is A symmetric matrix.

3. The coal identification method based on kernel bidirectional rank-order shared density spatial preservation projection according to claim 1, characterized in that... The steps for constructing the kernel bidirectional rank-shared density-preserving projection model described in step (3) are as follows: By combining the kernel bidirectional rank module, a kernel bidirectional rank shared density-preserving projection model is constructed: in The trace of a matrix is ​​the sum of the elements on its diagonal. express An identity matrix of order 1 is used to constrain the projection, ensuring that the projected features are independent of each other. The projection matrix is ​​defined as follows: in Representing feature dimension, Indicates the number of features. Represents the normalized matrix The eigenvectors obtained by eigenvalue decomposition: in It is the eigenvector matrix. It is an eigenvalue diagonal matrix, and the normalization matrix is ​​defined. : in The rank of the projection matrix is ​​the rank of the projection matrix. In Take the front indivual In That is, the projection matrix ; The divergence used to characterize the global samples is defined as: in Represents a diagonal matrix; The divergence used to characterize a local neighborhood is defined as: in Represents the Laplace matrix, A diagonal matrix is ​​defined as: in The shared nearest neighbor density matrix constructed based on the kernel bidirectional rank module is defined as follows: in The global average density of the dataset, used to eliminate the influence of dimensions, is defined as: in Indicates sample Local neighborhood density, The larger the sample size, the better. The sparser the local area, The smaller the value, the better the sample size. The more stable the local structure, the more it is defined as: The shared nearest neighbor density matrix comprehensively considers the Euclidean distance between samples, the overlap of local neighborhood structures, and the difference in local density, and can adaptively characterize the true proximity relationship of samples in high-dimensional space.

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