An image processing method and system based on entropy-regularized fuzzy non-negative matrix factorization

Abstract

The application discloses an image processing method and system based on entropy regular fuzzy non-negative matrix decomposition, and the image processing method based on entropy regular fuzzy non-negative matrix decomposition comprises the following steps: acquiring an image matrix to be processed; adopting an entropy regular fuzzy non-negative matrix decomposition model to decompose the image matrix into the product of two matrices; and obtaining an image processing result based on the two matrices obtained through the decomposition. The image processing method provided by the application can solve the technical problems of low precision and poor interpretability existing in the process of processing image clustering or hyperspectral unmixing by using a conventional non-negative matrix decomposition model.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of machine learning and image processing, relates to the field of high-dimensional data analysis and processing, and particularly relates to an image processing method and system based on entropy regularized fuzzy non-negative matrix factorization. BACKGROUND

[0002] With the advent of the big data era, image data has become an important information resource, and data mining technology provides a method for quickly and conveniently interpreting information from massive image data.

[0003] In the field of data mining technology, clustering is a method for merging data that are similar to each other in a data set, and is a very important unsupervised knowledge discovery task. In recent decades, various clustering algorithms (for example, k-means algorithm, fuzzy k-means algorithm, mean shift, and the like) have been proposed and have achieved good results; however, these traditional methods are ineffective for unstructured high-dimensional data, such as natural images and remote sensing hyperspectral data, due to the curse of dimensionality problem.

[0004] In fact, the data required to be processed in industry and commerce are all high-dimensional, but the essential characteristics of the data are usually located in a relatively low-dimensional space, and therefore an effective representation tool is generally sought to convert the high-dimensional complex data into low-dimensional data for processing. Non-negative matrix factorization (NMF) is one of the effective methods for solving this problem, which finds two small non-negative matrices such that their product can better approximate the original data; this purely additive local-based data representation method has been proven to be very similar to the cognitive mode of the human brain, and therefore NMF has attracted attention and application. The non-negativity constraint leads to sparsity of the representation, and also makes the NMF method more robust, and NMF has been proven to be a better algorithm than single value decomposition (SVD) or principal component analysis (PCA) in face recognition and text clustering. However, due to the non-convexity of the NMF model, the problem itself is ill-posed, and there is a large search space, which leads to low precision and unsatisfactory results in some problems or data; in addition, in image clustering or remote sensing hyperspectral data mixed pixel decomposition problems, NMF lacks certain interpretability because it does not impose a range constraint on the representation vector. SUMMARY

[0005] The purpose of this invention is to provide an image processing method and system based on entropy regular fuzzy nonnegative matrix factorization (NMF) to solve one or more of the aforementioned technical problems. The image processing method provided by this invention can solve the technical problems of low accuracy and poor interpretability in existing traditional NMF models when processing image clustering or hyperspectral unmixing.

[0006] To achieve the above objectives, the present invention adopts the following technical solution:

[0007] This invention provides an image processing method based on entropy regularized fuzzy nonnegative matrix factorization, comprising the following steps:

[0008] Obtain the image matrix to be processed;

[0009] The image matrix is ​​decomposed into the product of two matrices using an entropy-based regular fuzzy nonnegative matrix decomposition model.

[0010] Based on the two matrices obtained from the decomposition, the image processing results are obtained.

[0011] The entropy-based regularized fuzzy nonnegative matrix factorization model is expressed as follows:

[0012]

[0013]

[0014] In the formula, X is the image matrix to be processed; U represents the decomposed basis matrix, V represents the decomposed representation matrix; K is the number of substances, v ki Let u represent the element in the k-th row and i-th column of the matrix; k x is the k-th column vector of the basis matrix; i represents the column vector of X; Tr() represents the trace of the matrix, where q, μ, and λ are parameters. These respectively indicate that the elements of the decomposed matrix are non-negative; To represent the column sum of the matrix as For fuzzy clustering regularization, -λTr(Vlog(V T )) is the entropy regularization term.

[0015] A further improvement of the present invention is that the step of decomposing the image matrix into the product of two matrices using an entropy-based regularized fuzzy nonnegative matrix factorization model specifically includes:

[0016] Step 1: Solve the entropy-based regular fuzzy nonnegative matrix decomposition model using the Lagrange multiplier method and the Kuhn-Tak condition to obtain the iterative update formula, expressed as follows:

[0017]

[0018]

[0019] In the formula, Λ i =diag(|v i |)∈R K×K , With V. q-1 Both indicate that the calculation is performed element by element on the matrix;

[0020] The augmented representation of matrices X and U is as follows:

[0021] Step 2: Initialize the basis matrix and coefficient matrix and set the parameter values;

[0022] Step 3: According to the iterative update formula obtained in Step 1, the image matrix is ​​decomposed into an entropy regular fuzzy nonnegative matrix in an alternating iterative manner to obtain the fuzzy clustering representation matrix.

[0023] Step 4: Determine whether the preset termination condition has been met; if not, proceed to step 5; if yes, proceed to step 6.

[0024] Step 5: Perform adaptive update of hyperparameter λ, expressed as, In the formula, Let be the entropy regularization parameter for the i-th sample point in the k-th iteration. Let the entropy be the i-th sample point;

[0025] Step 6: Stop the loop and output the basis matrix U and the representation matrix V.

[0026] A further improvement of the present invention is that the image matrix to be processed is a natural image dataset; and the image processing result is a clustering result.

[0027] The steps for obtaining the image processing result based on the two matrices obtained from the decomposition include:

[0028] Let the row number of the largest element in each column of matrix V be the category label; where the largest element in the i-th column is v. ki , indicating that the image corresponding to the i-th column of the matrix X formed by the natural image dataset belongs to the k-th class.

[0029] A further improvement of the present invention is that the image matrix to be processed is a hyperspectral image dataset; and the image processing result is a demixing result.

[0030] The steps for obtaining the image processing result based on the two matrices obtained from the decomposition include:

[0031] Each column of the basis matrix U represents the spectrum of a basic ground feature. The column vectors are reconstructed into a matrix of a predetermined size by rows or columns to obtain the abundance map of the corresponding substance. The brighter the pixel, the greater the abundance value.

[0032] This invention provides an image processing system based on entropy regular fuzzy nonnegative matrix factorization, comprising:

[0033] The acquisition module is used to acquire the image matrix to be processed;

[0034] The decomposition module is used to decompose the image matrix into the product of two matrices using an entropy-based regular fuzzy nonnegative matrix decomposition model.

[0035] The output module is used to obtain the image processing results based on the two matrices obtained from the decomposition.

[0036] The entropy-based regularized fuzzy nonnegative matrix factorization model is expressed as follows:

[0037]

[0038]

[0039] In the formula, X is the image matrix to be processed; U represents the decomposed basis matrix, V represents the decomposed representation matrix; K is the number of substances, v ki Let u represent the element in the k-th row and i-th column of the matrix; k x is the k-th column vector of the basis matrix; i represents the column vector of X; Tr() represents the trace of the matrix, where q, μ, and λ are parameters. These respectively indicate that the elements of the decomposed matrix are non-negative; To represent the column sum of the matrix as For fuzzy clustering regularization, -λTr(Vlog(V T )) is the entropy regularization term.

[0040] A further improvement of the present invention is that, in the decomposition module, the step of decomposing the image matrix into the product of two matrices using an entropy-normalized fuzzy nonnegative matrix decomposition model specifically includes:

[0041] Step 1: Solve the entropy-based regular fuzzy nonnegative matrix decomposition model using the Lagrange multiplier method and the Kuhn-Tak condition to obtain the iterative update formula, expressed as follows:

[0042]

[0043]

[0044] In the formula, Λ i =diag(|v i|)∈R K×K , With V. q-1 Both indicate that the calculation is performed element by element on the matrix;

[0045] The augmented representation of matrices X and U is as follows:

[0046] Step 2: Initialize the basis matrix and coefficient matrix and set the parameter values;

[0047] Step 3: According to the iterative update formula obtained in Step 1, the image matrix is ​​decomposed into an entropy regular fuzzy nonnegative matrix in an alternating iterative manner to obtain the fuzzy clustering representation matrix.

[0048] Step 4: Determine whether the preset termination condition has been met; if not, proceed to step 5; if yes, proceed to step 6.

[0049] Step 5: Perform adaptive update of hyperparameter λ, expressed as, In the formula, Let be the entropy regularization parameter for the i-th sample point in the k-th iteration. Let the entropy be the i-th sample point;

[0050] Step 6: Stop the loop and output the basis matrix U and the representation matrix V.

[0051] A further improvement of the present invention is that the image matrix to be processed is a natural image dataset; and the image processing result is a clustering result.

[0052] The steps for obtaining the image processing result based on the two matrices obtained from the decomposition include:

[0053] Let the row number of the largest element in each column of matrix V be the category label; where the largest element in the i-th column is v. ki , indicating that the image corresponding to the i-th column of the matrix X formed by the natural image dataset belongs to the k-th class.

[0054] A further improvement of the present invention is that the image matrix to be processed is a hyperspectral image dataset; and the image processing result is a demixing result.

[0055] The steps for obtaining the image processing result based on the two matrices obtained from the decomposition include:

[0056] Each column of the basis matrix U represents the spectrum of a basic ground feature. The column vectors are reconstructed into a matrix of a predetermined size by rows or columns to obtain the abundance map of the corresponding substance. The brighter the pixel, the greater the abundance value.

[0057] Compared with the prior art, the present invention has the following beneficial effects:

[0058] The image processing method based on entropy regular fuzzy nonnegative matrix factorization provided by this invention, on the basis of the traditional nonnegative matrix factorization model, considers applying probabilistic simplex constraints to the low-dimensional representation vector of the data, making the model more interpretable; in addition, in order to reduce the uncertainty of the representation vector and improve the well-posedness of the problem, information entropy is introduced into the model, making the data representation more sparsity.

[0059] In this invention, fuzzy clustering regularization and entropy regularization are introduced into the basic nonnegative matrix factorization (NMF) model, and a multiplicative iterative formula for optimizing the objective function is derived based on the Lagrange multiplier method and the Kuhn-Tak condition. The constructed model and algorithm are applied to the problem of natural image clustering and unmixing remote sensing hyperspectral data. The effectiveness and advancement of the proposed model and method are demonstrated through a large number of numerical experiments and comparative results. Attached Figure Description

[0060] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art are briefly introduced below; obviously, the drawings described below are some embodiments of the present invention, and those skilled in the art can obtain other drawings based on these drawings without creative effort.

[0061] Figure 1 This is a flowchart illustrating an image processing method based on entropy regular fuzzy nonnegative matrix decomposition provided in an embodiment of the present invention.

[0062] Figure 2 This is a flowchart illustrating an image processing method based on entropy regular fuzzy nonnegative matrix decomposition, provided in another embodiment of the present invention.

[0063] Figure 3 This is a schematic diagram comparing the basis matrix and representation matrix extracted by the ERF-NMF method provided in this embodiment of the invention with existing NMF methods on the Yale and COIL20 datasets; wherein, Figure 3 In the example, (a), (d), and (g) are sample examples from the COIL20, Yale, and MNIST datasets, respectively. Figure 3 In the middle, (b), (e), and (h) are respectively the basis matrices generated by NMF based on the above sample examples; Figure 3 In the table, (c), (f), and (i) are respectively the basis matrices generated by ERF-NMF based on the above sample examples; Figure 3 In the diagrams, (j) and (k) are respectively visualizations of the coefficient matrices learned by NMF and ERF-NMF on the Yale dataset;

[0064] Figure 4 This is a schematic diagram illustrating the results of unmixing three hyperspectral data using the ERF-NMF method provided in this embodiment of the invention; wherein, Figure 4 In the middle (a), the original hyperspectral image from the Samson dataset is shown. Figure 4 (b), (c), and (d) are abundance maps of different substances after the Samson dataset was unmixed, respectively. Figure 4 (e) is the original hyperspectral image from the Jasper dataset. Figure 4 In the middle, (f), (g), (h), and (i) are respectively the abundance maps of different substances after the Jasper dataset is unmixed; Figure 4 In the middle (j), the original hyperspectral image of the Urban dataset is shown. Figure 4 In the image, (k), (l), (m), and (n) are abundance maps of different substances after unmixing the Urban dataset.

[0065] Figure 5 This is a schematic diagram illustrating the use of the method provided in this embodiment of the invention to record company attendance.

[0066] Figure 6 This is a schematic diagram of an image processing system based on entropy regular fuzzy nonnegative matrix decomposition provided in an embodiment of the present invention. Detailed Implementation

[0067] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0068] It should be noted that the terms "first," "second," etc., in the specification, claims, and accompanying drawings of this invention are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of the invention described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover a non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0069] The present invention will now be described in further detail with reference to the accompanying drawings:

[0070] Please see Figure 1 The present invention provides an image processing method based on entropy regular fuzzy nonnegative matrix factorization, comprising the following steps:

[0071] Obtain the image matrix to be processed; wherein, the image matrix is ​​a natural image dataset or a hyperspectral image dataset;

[0072] The image matrix is ​​decomposed into the product of two matrices using an entropy-based regular fuzzy nonnegative matrix decomposition model.

[0073] Based on the two matrices, the image processing result is obtained; specifically, when the image matrix is ​​a natural image dataset, the obtained image processing result is a clustering result; when the image matrix is ​​a hyperspectral image dataset, the obtained image processing result is a demixing result.

[0074] The entropy-based regularized fuzzy nonnegative matrix factorization model is expressed as follows:

[0075]

[0076]

[0077] In the formula, X is an M×N image matrix to be processed, where each column represents a pixel of a natural image or hyperspectral data; U represents the decomposed basis matrix; V represents the decomposed representation matrix; K is the cluster number or the number of substances in the hyperspectral data; and v ki Let u represent the element in the k-th row and i-th column of the matrix; k x represents the k-th column vector of the basis matrix; i represents the column vector of data X; Tr() represents the trace of the matrix, where q, μ, and λ are parameters. These respectively indicate that the elements of the decomposed matrix are non-negative. This represents a matrix whose column sum is 1, i.e., a probabilistic simplex constraint; For fuzzy clustering regularization, -λTr(Vlog(V T )) is the entropy regularization term.

[0078] The image processing method provided by the above embodiments of the present invention can solve the technical problems of low accuracy and poor interpretability in the processing of image clustering or hyperspectral unmixing by existing traditional non-negative matrix factorization models; the technical solution provided by the embodiments of the present invention has good accuracy and interpretability.

[0079] Please see Figure 2 This invention provides an image processing method based on entropy regular fuzzy nonnegative matrix factorization, the specific steps of which include:

[0080] Step S1: Based on entropy regularization and fuzzy clustering regularization, construct the following objective function, with the expression:

[0081]

[0082]

[0083] In the formula, X is an M×N matrix, where each column represents a pixel of a natural image or hyperspectral data; U represents the decomposed basis matrix; V represents the decomposed representation matrix; K is the cluster number or the number of substances in the hyperspectral data; and v ki Let u represent the element in the k-th row and i-th column of the matrix; k x represents the k-th column vector of the basis matrix; i represents the column vector of data X; Tr() represents the trace of the matrix, where q, μ, and λ are parameters. These respectively indicate that the elements of the decomposed matrix are non-negative. To represent a matrix whose column sum is 1, i.e., a probabilistic simplex constraint; in particular, For fuzzy clustering regularization, -λTr(Vlog(V T )) is the entropy regularization term.

[0084] Step S2: Solve the objective function based on the Lagrange multiplier method and the Kuhn-Tak condition to obtain the iterative update formula; the iterative formula derived from the above objective function is shown below:

[0085]

[0086]

[0087] Among them, Λ i =diag(|v i |)∈R K×K , With V. q-1 Both represent element-wise computation of the matrix; to satisfy the constraint that the column sum of the matrix is ​​1 (i.e., the probabilistic simplex), the matrices X and U are augmented as follows:

[0088]

[0089] After augmenting the matrix in this way, a loss related to δ will occur when the sum of the columns in matrix V is not 1.

[0090] Step S3: Initialize the basis matrix and coefficient matrix and set the parameter values.

[0091] Step S4: According to the iterative update formula obtained in step S2 above, perform entropy regular fuzzy nonnegative matrix decomposition on the natural image or hyperspectral data in an alternating iterative manner to obtain the fuzzy clustering representation matrix V;

[0092] Step S5: Determine whether the termination condition has been met. If not, proceed to step S6; if yes, proceed to step S7.

[0093] Step S6: Perform adaptive update of hyperparameter λ, as follows:

[0094]

[0095] in, Let be the entropy regularization parameter for the i-th sample point in the k-th iteration. Let the entropy be the i-th sample point;

[0096] Step S7: Stop the loop, output the basis matrix U and the clustering representation matrix V, and make clustering determination based on them.

[0097] In this embodiment of the invention, the step of obtaining clustering results from matrix factorization results includes:

[0098] The original matrix X is decomposed into a basis matrix U and a clustering representation matrix V;

[0099] For natural image clustering: focus on the clustering representation matrix V, and take the row number of the largest element in each column of V as the classification label: the largest element in the i-th column is v. ki , indicating that the photo corresponding to the i-th column of the matrix X formed by the natural image dataset belongs to the k-th class.

[0100] For the unmixing problem of remote sensing hyperspectral data: focus on the basis matrix U, where each column of U represents the spectrum of a basic ground object. Reconstruct the column vectors into a matrix of a specified size by row or column to form the abundance map of the corresponding material, where the brighter the pixel, the greater its abundance value.

[0101] The Entropy Regularized Fuzzy Nonnegative Matrix Factorization (ERF-NMF) method provided in this invention can effectively improve the accuracy of clustering or unmixing (including accuracy AC and normalized mutual information NMI) for natural image clustering or remote sensing hyperspectral data unmixing, making the decomposition results more sparsity and interpretable.

[0102] To better demonstrate the effectiveness of the ERF-NMF method provided in this embodiment of the invention, the following comparisons are made with this invention using various clustering and hyperspectral unmixing methods for different natural image datasets and remote sensing hyperspectral data datasets. The comparison methods include:

[0103] Basic nonnegative matrix factorization (NMF) method;

[0104] Constrained Nonnegative Matrix Factorization (CNMF);

[0105] K-means;

[0106] Nonnegative Local Coordinate Factorization (NLCF);

[0107] Graph regularized nonnegative matrix factorization (GNMF);

[0108] Joint Sparsity and Low-Rank Constrained Non-Negative Matrix Factorization (SLRNMF);

[0109] Total Variation Regularized Reweighted Sparse Nonnegative Matrix Factorization (TV-RSNMF).

[0110] The natural image dataset and hyperspectral data dataset used in the embodiments of the present invention respectively include:

[0111] The COIL20 dataset contains 32×32 pixel grayscale images of 20 objects viewed from different angles, with 72 images of each object taken from different angles.

[0112] The Yale dataset contains 32×32 pixel grayscale images of 15 people, with 11 images of each person taken from different expressions or angles.

[0113] The MNIST dataset contains 28×28 pixel grayscale images of the 10 digits from 0 to 9, with approximately 400 handwritten images for each digit.

[0114] Samson dataset: The data consists of 952×952 pixels, with each pixel recorded on 156 channels, covering wavelengths from 401nm to 889nm, with a spectral resolution of 3.13nm;

[0115] Jasper dataset: The data contains 512×614 pixels, with each pixel recorded in 224 channels ranging from 380nm to 2500nm, and a spectral resolution of 9.46nm.

[0116] Urban dataset: The data consists of 307×307 pixels, with each pixel corresponding to a 2×2 square meter area. It records 162 channels ranging from 400nm to 2500nm, with a spectral resolution of 10nm.

[0117] Please see Figure 3 In this embodiment of the invention, the ERF-NMF method disclosed in this embodiment of the invention is compared with the above seven existing methods on the above dataset. The results are shown in Tables 1 to 3. Figure 3 As shown.

[0118] Table 1. Comparison of results between the ERF-NMF method of this invention and existing methods on the COIL20 dataset.

[0119]

[0120] Table 2. Comparison of results between the ERF-NMF of this invention and existing methods on the Yale dataset.

[0121]

[0122] Table 3. Comparison of results between the ERF-NMF of this invention and existing methods on the MNIST dataset.

[0123]

[0124] Please refer to Tables 1 to 3 above. Tables 1 to 3 respectively show the clustering results of the ERF-NMF method disclosed in this embodiment of the invention and seven other existing clustering methods on the COIL20, Yale, and MNIST datasets. The results show that the method provided in this embodiment of the invention has better accuracy (AC) and mutual information (NMI) than other methods under different cluster count settings, especially in terms of average precision (Avg.). In the experiments of this embodiment of the invention, for each given number of clusters, sample categories corresponding to that number of clusters were randomly selected, and then 10 independent experiments were conducted for comparative analysis; the final experimental result was the average of the 10 experiments. Combining the experimental results of the three image datasets, it is easy to see that the ERF-NMF method of this invention shows significant advantages in accuracy (AC) and mutual information (NMI). For example, on the handwritten digit set MNIST, it can be found that compared with the other seven methods, when the value of the number of clusters is different, the ERF-NMF clustering method of this invention has the highest accuracy and mutual information. Furthermore, the ERF-NMF method of this invention also showed good advantages on the classic face recognition dataset Yale. In summary, by comparing it with currently popular matrix factorization-based clustering methods on multiple datasets, it can be found that the entropy-regularized fuzzy nonnegative matrix factorization image clustering method proposed in this embodiment of the invention has higher clustering accuracy.

[0125] Please see Figure 3 , Figure 3 This paper presents a visual comparison of the feature extraction process in image clustering analysis using the ERF-NMF method of the present invention and the traditional nonnegative matrix factorization (NMF). Figure 3 In the middle, (a), (d), and (g) are sample examples from the COIL20, Yale, and MNIST datasets, respectively. Figure 3 In this context, (b), (e), and (h) are the basis matrices generated by NMF; Figure 3 In this context, (c), (f), and (i) are the basis matrices generated by ERF-NMF; Figure 3 In the diagram, (j) and (k) are visualizations of the coefficient matrices learned by NMF and ERF-NMF on the Yale dataset, respectively. In this embodiment of the invention, the original image is compared with the basis vectors extracted by ERF-NMF. It is found that the features extracted by ERF-NMF are very similar to the original image in the sample, which explains why the features extracted by the ERF-NMF algorithm can be very close to the original image. From (j) and (k), it can be seen that the coefficient matrix obtained by ERF-NMF decomposition has more black parts, which represents better sparsity.

[0126] The comparison results show that the features extracted by the method of this invention are partial features of the image, which are more localized and sparsity-oriented, thus providing better interpretability. To quantify the sparsity analysis, Table 4 presents a comparison of the sparsity of the two methods on the Yale dataset under different cluster numbers K. The comparison results show that the representation learned by the ERF-NMF method of this invention is more dilute.

[0127] Table 4. Comparison of sparsity between the ERF-NMF and NMF methods of this invention on the Yale dataset under different cluster sizes K.

[0128]

[0129] Furthermore, the model constructed in this invention is highly suitable for solving the problem of hyperspectral data mixed pixel decomposition, i.e., the hyperspectral unmixing problem. Hyperspectral unmixing is the process of decomposing mixed pixels in hyperspectral data acquired by a hyperspectral sensor into different basic ground feature spectra, also known as endmembers, and the proportion of these basic ground features in each mixed pixel. From a methodological perspective, hyperspectral unmixing can be viewed as a fuzzy clustering problem of pixels, falling under the research scope of pattern recognition and machine learning; it can also be viewed as a blind signal separation problem, belonging to the research content of signal processing. Although hyperspectral unmixing has been applied to many practical problems, many unsolved issues remain, making it a hot topic in remote sensing spectral image research both domestically and internationally.

[0130] Mathematically, the hyperspectral unmixing problem is equivalent to a nonnegative matrix factorization problem with probabilistic simplex constraints. Therefore, it is very suitable for solving using the ERF-NMF model constructed in this invention. To further verify the performance of the method of this invention, this embodiment will test the method of this invention with three actual hyperspectral datasets, and the results are as follows. Figure 4 As shown. Figure 4 In the diagram, the first column contains the original hyperspectral data, and the remaining graphs show the abundance of different substances obtained from the solution. Figure 4 Brighter pixels indicate a higher abundance value (maximum 1), while darker pixels indicate a lower abundance value (minimum 0). As can be seen from their abundance maps, the ERF-NMF method proposed in this invention can clearly unmix and determine the content and distribution of different substances, making the results more interpretable and practically significant.

[0131] The Entropy Regularized Fuzzy Nonnegative Matrix Factorization (ERF-NMF) method provided in this invention can be applied to image clustering analysis and the unmixing of remote sensing hyperspectral data. Specifically, using MATLAB as the implementation tool and the Yale face dataset, this paper provides a detailed implementation and explanation of the image clustering and hyperspectral unmixing method based on the Entropy Regularized Fuzzy Nonnegative Matrix Factorization (ERF-NMF) model. In the specific implementation, taking photos of 15 individuals with different expressions collected from the Yale University face dataset as an example, this dataset contains 11 photos of each individual, totaling 165 photos; each photo consists of 32×32 pixels; and each pixel has a value in the range [0, 255]. The dataset arranges the 1024 pixels of each photo into a row, with 15 individuals and 11 photos of each individual, resulting in 165 rows. The face dataset formed by this arrangement is a 165×1024 matrix X, where the values ​​of the elements range from [0, 255], and it is a nonnegative matrix. Furthermore, by transposing matrix X, each column of the matrix physically represents a photograph. The clustering process using the ERF-NMF method proposed in this invention is as follows:

[0132] Step S1: Construct the objective function for the decomposition of the nonnegative matrix X based on entropy regularization and fuzzy clustering regularization.

[0133] Step S2: Based on the Lagrange multiplier method and the Kuhn-Tucker condition, solve the objective function to obtain the iterative update formula. Specifically, introduce Λ i =diag(|v i |)∈R K×K ;

[0134] Since for any matrix A, we have ||A|| 2 =Tr(AA T Therefore, the objective function can be rewritten as follows:

[0135]

[0136] Furthermore, let ψ jk and φ ki The constraints are u jk ≥0 and v ki The Lagrange multipliers corresponding to ≥0. Define matrix Ψ = [ψ jk ] and Φ = [φ ki Then the Lagrange function of the objective function O is:

[0137]

[0138] Among them, symbols And V. q-1Both represent operations on each element of the matrix. Furthermore, we define c = diag(X) T X)∈R N In the formula, C = (c, ..., c) T ∈R K×N Define d = diag(U T U)∈R K Then, in the formula, D = (d, ..., d) ∈ R K×N The symbol 1 represents a K×N matrix whose elements are all 1s. Note the following Kuhn-Tucker conditions:

[0139]

[0140]

[0141]

[0142] right Taking the partial derivatives with respect to U and V, and multiplying both sides by U and V, we get:

[0143]

[0144]

[0145] In particular, to satisfy the constraint that the column sum of the coefficient matrix is ​​1, we extend the matrices X and U as follows:

[0146]

[0147] This leads to the following multiplication update formula:

[0148]

[0149]

[0150] Step S3: Initialize the basis matrix and coefficient matrix and set the parameter selection range. Specifically, this invention uses random numbers or random selection from the samples to initialize the basis matrix U; the parameter selection range is generally set by first roughly trying approximate values ​​and selecting the range around the parameter values ​​that perform well; here we set q = 1.0:0.1:1.4, μ = 4:0.1:5.5, λ = 0.3:0.1:2.1; and simultaneously set the number of categories K = 2:1:15;

[0151] Step S4: Following the iterative update formula described above, perform entropy-normalized fuzzy nonnegative matrix decomposition on the Yale image X using an alternating iterative method to obtain the representation matrix V. Then, set the representation matrix as the cluster label. Specifically, input the iterative update formula into the MATLAB program, setting the iteration stop condition to 400 iterations. When the iteration stops, the decomposed basis matrix U and coefficient matrix V will be obtained. At this point, take the row containing each column of V as the classification label; for example, the largest element in the i-th column is v. ki If X is a column i, then the photo corresponding to the i-th column belongs to the k-th class.

[0152] Step S5: Determine whether the termination condition (e.g., maximum number of iterations) is met. If not, proceed to step S6; if met, proceed to step S7.

[0153] Step S6: Select a new set of parameters and automatically update the hyperparameter λ as follows.

[0154]

[0155] Specifically, the parameter value is incremented by one step, the value of λ is updated according to the above formula, and then the next loop begins; where, the parameter for the i-th sample point in the k-th iteration is defined as... It is the entropy value;

[0156] Step S7: Stop the loop, output the basis matrix U and the clustering representation matrix V, and make clustering determination based on them.

[0157] Please see Figure 5 This invention first assumes the following scenario: A company has 10 employees, and a camera at the company entrance needs to identify the employees to record attendance. In this hypothetical situation, the most critical issue is employee identification, that is, using the collected employee image dataset to identify which employee's face is captured by the camera. The specific implementation steps of this invention are as follows:

[0158] Step S0: Collect 10 photos of each employee under different expressions and lighting conditions, each photo being 100×100 pixels; tile the 10,000 pixels of a single photo into a column, and organize the 100 photos of the 10 employees into a 10,000×100 matrix X.

[0159] Steps S1 to S7 correspond to the specific implementation steps of the image clustering and hyperspectral unmixing method based on entropy regular fuzzy nonnegative matrix factorization proposed in this embodiment of the invention, including:

[0160] Step S1: Construct the objective function based on entropy regularization and fuzzy clustering regularization.

[0161] Step S2: Solve the objective function based on the Lagrange multiplier method and the Kuhn-Tak condition to obtain the iterative update formula.

[0162] Step S3: Initialize the basis matrix and coefficient matrix and set the parameter values.

[0163] Step S4: According to the iterative update formula obtained in step S2 above, perform entropy regular fuzzy nonnegative matrix decomposition on the natural image or hyperspectral data in an alternating iterative manner to obtain the fuzzy clustering representation matrix V;

[0164] Step S5: Determine whether the termination condition has been met. If not, proceed to step S6; if yes, proceed to step S7.

[0165] Step S6: Perform adaptive update of hyperparameter λ;

[0166] Step S7: Stop the loop, output the basis matrix U and the clustering representation matrix V, and make clustering determination based on them;

[0167] Step S8: For a 100×100 pixel photo taken by the camera at the entrance on the day of an employee's attendance, following the method of organizing single photos in Step S0, flatten it into a 10000×1 vector x, and solve the equation Uv=x, where U is the basis matrix output in Step S7, v is the unknown quantity to be solved, and x is the vector organized from the single photo. The row number c of the maximum value component in v is taken as the category to which photo x belongs, i.e., photo x is a photo of employee c. Thus, the method provided by this embodiment of the invention can be used to complete face recognition and attendance recording.

[0168] The above describes the specific application of the method provided in the embodiments of the present invention for natural image processing; for the application of hyperspectral data unmixing, please refer to the description of hyperspectral unmixing above. In summary, this invention belongs to the field of general data analysis and processing technology. Specifically, it relates to an entropy regularized fuzzy nonnegative matrix factorization (ERF-NMF) high-dimensional matrix representation model and method, and applies it to the clustering of natural images and the unmixing problem of remote sensing hyperspectral data. The invention includes: applying probabilistic simplex constraints to the low-dimensional representation vector of the data to make the model more interpretable; introducing information entropy into the model to reduce the uncertainty of the representation vector, making the data representation more sparsity; introducing fuzzy clustering regularization and entropy regularization into the basic nonnegative matrix factorization model to construct the objective function of entropy regularized fuzzy nonnegative matrix factorization; deriving a multiplicative iterative algorithm for optimizing the objective function based on the Lagrange multiplier method and the Kuhn-Tak condition to solve for the low-dimensional representation vector of the data; applying the constructed model and algorithm to the clustering of natural images and the unmixing problem of remote sensing hyperspectral data, and demonstrating the effectiveness and advancement of the proposed model and method through numerous numerical experiments and comparative results. This invention enables the representation to have probabilistic interpretation by normalizing the representation vector, and introduces the concept of entropy from information theory to limit the uncertainty of data representation. It effectively combines the advantages of nonnegative matrix factorization and fuzzy clustering, and has excellent results in natural image data clustering and hyperspectral data unmixing.

[0169] The following are embodiments of the apparatus of the present invention, which can be used to execute embodiments of the method of the present invention. For details not omitted in the apparatus embodiments, please refer to the embodiments of the method of the present invention.

[0170] Please see Figure 6 In one embodiment of the present invention, an image processing system based on entropy regular fuzzy nonnegative matrix factorization is provided, comprising:

[0171] The acquisition module is used to acquire the image matrix to be processed;

[0172] The decomposition module is used to decompose the image matrix into the product of two matrices using an entropy-based regular fuzzy nonnegative matrix decomposition model.

[0173] The output module is used to obtain the image processing results based on the two matrices obtained from the decomposition.

[0174] The entropy-based regularized fuzzy nonnegative matrix factorization model is expressed as follows:

[0175]

[0176]

[0177] In the formula, X is the image matrix to be processed; U represents the decomposed basis matrix, V represents the decomposed representation matrix; K is the number of substances, v ki Let u represent the element in the k-th row and i-th column of the matrix; k x is the k-th column vector of the basis matrix; i represents the column vector of X; Tr() represents the trace of the matrix, where q, μ, and λ are parameters. These respectively indicate that the elements of the decomposed matrix are non-negative; To represent the column sum of the matrix as For fuzzy clustering regularization, -λTr(Vlog(V T )) is the entropy regularization term.

[0178] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0179] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0180] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0181] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0182] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the specific implementation of the present invention. Any modifications or equivalent substitutions that do not depart from the spirit and scope of the present invention should be covered within the scope of protection of the claims of the present invention.

Claims

1. An image processing method based on entropy-regular fuzzy nonnegative matrix decomposition, characterized in that, Includes the following steps: Obtain the image matrix to be processed; The image matrix is ​​decomposed into the product of two matrices using an entropy-based regular fuzzy nonnegative matrix decomposition model. Based on the two matrices obtained from the decomposition, the image processing results are obtained. The entropy-based regularized fuzzy nonnegative matrix factorization model is expressed as follows: ； ； In the formula, The image matrix to be processed; Represents the basis matrix after decomposition. Represents the representation matrix after decomposition; The number of substances. Let represent the element in the k-th row and i-th column of the matrix; is the k-th column vector of the basis matrix; express Column vectors; Represents the trace of a matrix. , , For parameters, These respectively indicate that the elements of the decomposed matrix are non-negative; To represent a matrix where the column sum is 1, For fuzzy clustering regularization, This is the entropy regularization term.

2. The image processing method based on entropy regular fuzzy nonnegative matrix decomposition according to claim 1, characterized in that, The step of decomposing the image matrix into the product of two matrices using an entropy-based regularized fuzzy nonnegative matrix factorization model specifically includes: Step 1: Solve the entropy-based regular fuzzy nonnegative matrix decomposition model using the Lagrange multiplier method and the Kuhn-Tak condition to obtain the iterative update formula, expressed as follows: ； ； In the formula, , and Both indicate that the calculation is performed element by element on the matrix; matrix , Augmented representation is, ; Step 2: Initialize the basis matrix and coefficient matrix and set the parameter values; Step 3: According to the iterative update formula obtained in Step 1, the image matrix is ​​decomposed into an entropy regular fuzzy nonnegative matrix in an alternating iterative manner to obtain the fuzzy clustering representation matrix. Step 4: Determine whether the preset termination condition has been met; if not, proceed to step 5; if yes, proceed to step 6. Step 5: Perform hyperparameter settings λ The adaptive update is represented as, In the formula, Let be the entropy regularization parameter for the i-th sample point in the k-th iteration. Let the entropy be the i-th sample point; Step 6: Stop the loop and output the base matrix. and representation matrix .

3. The image processing method based on entropy regular fuzzy nonnegative matrix decomposition according to claim 2, characterized in that, The image matrix to be processed is a natural image dataset; The image processing result is a clustering result; The steps for obtaining the image processing result based on the two matrices obtained from the decomposition include: taking the representation matrix. The row number of the largest element in each column is the category label; where the largest element in the i-th column is... , representing the matrix formed by the natural image dataset. The image corresponding to the i-th column belongs to the k-th class.

4. The image processing method based on entropy regular fuzzy nonnegative matrix decomposition according to claim 2, characterized in that, The image matrix to be processed is a hyperspectral image dataset; The image processing result is the demixing result; The steps for obtaining the image processing result based on the two matrices obtained from the decomposition include: basis matrix Each column represents the spectrum of a basic ground feature. The column vectors are reconstructed into a matrix of a predetermined size by rows or columns to obtain the abundance map of the corresponding substance; where the brighter the pixel, the greater the abundance value.

5. An image processing system based on entropy-regular fuzzy nonnegative matrix factorization, characterized in that, include: The acquisition module is used to acquire the image matrix to be processed; The decomposition module is used to decompose the image matrix into the product of two matrices using an entropy-based regular fuzzy nonnegative matrix decomposition model. The output module is used to obtain the image processing results based on the two matrices obtained from the decomposition. The entropy-based regularized fuzzy nonnegative matrix factorization model is expressed as follows: ； ； In the formula, The image matrix to be processed; Represents the basis matrix after decomposition. Represents the representation matrix after decomposition; The number of substances. Let represent the element in the k-th row and i-th column of the matrix; is the k-th column vector of the basis matrix; express Column vectors; Represents the trace of a matrix. , , For parameters, These respectively indicate that the elements of the decomposed matrix are non-negative; To represent a matrix where the column sum is 1, For fuzzy clustering regularization, This is the entropy regularization term.

6. The image processing system based on entropy regular fuzzy nonnegative matrix factorization according to claim 5, characterized in that, The decomposition module includes the following steps: Decomposing the image matrix into a product of two matrices using an entropy-based regularized fuzzy nonnegative matrix decomposition model. Step 1: Solve the entropy-based regular fuzzy nonnegative matrix decomposition model using the Lagrange multiplier method and the Kuhn-Tak condition to obtain the iterative update formula, expressed as follows: ； ； In the formula, , ; matrix , Augmented representation is, ; Step 2: Initialize the basis matrix and coefficient matrix and set the parameter values; Step 3: According to the iterative update formula obtained in Step 1, the image matrix is ​​decomposed into an entropy regular fuzzy nonnegative matrix in an alternating iterative manner to obtain the fuzzy clustering representation matrix. Step 4: Determine whether the preset termination condition has been met; if not, proceed to step 5; if yes, proceed to step 6. Step 5: Perform hyperparameter settings λ The adaptive update is represented as, In the formula, Let be the entropy regularization parameter for the i-th sample point in the k-th iteration. Let the entropy be the i-th sample point; Step 6: Stop the loop and output the base matrix. and representation matrix .

7. The image processing system based on entropy regular fuzzy nonnegative matrix factorization according to claim 6, characterized in that, The image matrix to be processed is a natural image dataset; The image processing result is a clustering result; The steps for obtaining the image processing result based on the two matrices obtained from the decomposition include: taking the representation matrix. The row number of the largest element in each column is the category label; where the largest element in the i-th column is... , representing the matrix formed by the natural image dataset. The image corresponding to the i-th column belongs to the k-th class.

8. The image processing system based on entropy regular fuzzy nonnegative matrix factorization according to claim 6, characterized in that, The image matrix to be processed is a hyperspectral image dataset; The image processing result is the demixing result; The steps for obtaining the image processing result based on the two matrices obtained from the decomposition include: basis matrix Each column represents the spectrum of a basic ground feature. The column vectors are reconstructed into a matrix of a predetermined size by rows or columns to obtain the abundance map of the corresponding substance; where the brighter the pixel, the greater the abundance value.

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