An Image Recognition Method Based on Auto-Encoding Neighborhood Preserving Embedding Algorithm

Abstract

The present invention belongs to the field of image recognition, and particularly relates to an image recognition method based on an auto-encoding neighborhood preserving embedding algorithm; it includes obtaining a dimensionality reduction objective function from a high-dimensional space to a low-dimensional space by using the neighborhood preserving embedding algorithm; obtaining an auto-encoding reconstruction objective function from the low-dimensional space to the high-dimensional space; combining the dimensionality reduction objective function and the reconstruction objective function to construct an objective function of the auto-encoding neighborhood preserving embedding algorithm; solving the optimal mapping matrix by using the gradient descent method according to the objective function; mapping the training set and the test set to the low-dimensional space by using the optimal mapping matrix; predicting the classification labels of each test sample in the test set mapped to the low-dimensional space through the nearest neighbor classification method and the training set mapped to the low-dimensional space; the present invention considers the mapping between the high-dimensional space and the low-dimensional space bidirectionally, enabling the low-dimensional space obtained by this mapping to better represent the original high-dimensional space, retain more structures of the original space, and obtain a better recognition rate.

Description

Technical Field

[0001] The present invention belongs to the field of image recognition, mainly involving the use of pattern recognition and machine learning methods to achieve face recognition and object classification, and specifically relates to an image recognition method based on an autoencoder neighborhood preserving embedding algorithm. Background Art

[0002] With the growth of modern information data and the development of computer technology, image recognition technology has been widely applied in our lives. The most typical scenarios include face recognition, object recognition, etc. On the one hand, image recognition brings many conveniences to life and reduces the tediousness of previous manual recognition; on the other hand, its recognition accuracy is also an issue that must be considered. Because in some important scenarios, such as online real-person authentication, the cost of recognition errors is very high.

[0003] However, image recognition often faces many problems. The most common one is the "curse of dimensionality" problem, that is, the dimension of the original data is too high, and it often contains a lot of redundant information. These redundant information not only affects the accuracy of subsequent recognition work, but also increases the computational complexity and time consumption. Therefore, a series of data dimensionality reduction methods have been proposed to solve the "curse of dimensionality" problem. Data dimensionality reduction methods can be divided into linear and non-linear ones.

[0004] Principal Component Analysis (PCA) and Linear Discriminant Analysis (LDA) are two of the most representative linear data dimensionality reduction techniques. PCA was proposed by Turk and Pentland and is also called eigenfaces in face recognition. There are many different algorithms that can be used to implement principal component analysis, such as eigenvalue, latent variable analysis, factor analysis, etc. LDA was proposed by Fisher in 1936 and is also called Fisherface in face recognition. Its main idea is to maximize the ratio of between-class scatter to within-class scatter, so as to maximize the separability between classes. However, both PCA and LDA are linear methods and are not suitable for processing non-linear data.

[0005] For non - linear problems, many manifold - based data dimensionality reduction methods have been proposed, such as Laplacian Eigenmap (LE), Locally Linear Embedding (LLE), and Isomap. The idea of LE is to use the Laplacian operator of the graph to find the optimal low - dimensional representation that preserves the local neighborhood information of the original manifold. LLE is based on the idea that each data point and a certain number of its nearest neighbors are regarded as a local linear patch of the manifold. The main goal of Isomap is to preserve the best similarity or dissimilarity points on the manifold between any pair of data points, and it is a dimensionality reduction method based on Multidimensional Scaling (MDS).

[0006] However, these manifold - based data dimensionality reduction methods are only defined on the training set and are not convenient to use on the test set. This is called the "out - of - sample" problem. To solve this problem, many linearization methods have been proposed. For example, IsoP projection (Isomap Projection, IsoP) is a linearization algorithm of Isomap, Locality - Preserving Projection (LPP) is a linearization algorithm of LE, and Neighborhood - Preserving Embedding (NPE) is a linearization algorithm of LLE. Specifically, Neighborhood - Preserving Embedding first constructs an adjacency graph through the k - nearest neighbor (KNN) algorithm or ε - nearest neighbor algorithm and calculates the weights on the edges, and then finds the low - dimensional embedding of high - dimensional data through a linear mapping method. This mapping preserves the structure of the original set of data points. Neighborhood - Preserving Embedding not only retains the advantages of Locally Linear Embedding but also overcomes the disadvantage of being only defined on the training set.

[0007] However, the Neighborhood - Preserving Embedding algorithm and all its improved methods only consider the one - way mapping from the high - dimensional space to the low - dimensional space. Since the mapping is one - way, the low - dimensional embedded data may not be able to "represent" the original data very accurately and effectively. Summary of the Invention

[0008] To solve the above problems, the present invention provides an image recognition method based on the auto - encoding Neighborhood - Preserving Embedding algorithm, including the following steps:

[0009] S1. Obtain a picture data set and divide it into a training set, a validation set, and a test set;

[0010] S2. Initialize the parameters of the auto - encoding Neighborhood - Preserving Embedding algorithm, including the number of nearest neighbors k, the target dimension d to be reduced to, the gradient descent step size α, the target function stop threshold ε, and the maximum number of iterations tmax and the hyperparameters of the objective function;

[0011] S3. Using the validation set obtained in S1, obtain the optimal hyperparameters λ and γ of the objective function of the autoencoder neighborhood preserving embedding algorithm through grid search;

[0012] S4. Obtain the objective function of the neighborhood preserving embedding algorithm and the autoencoder reconstruction objective function, and construct the objective function of the autoencoder neighborhood preserving embedding algorithm by combining the optimal hyperparameters λ and γ of the objective function

[0013] S5. According to the objective function of the autoencoder neighborhood preserving embedding algorithm obtained in S4 Use the gradient descent method to solve the optimal mapping matrix;

[0014] S6. Using the optimal mapping matrix, map both the training set and the test set into the low-dimensional space;

[0015] S7. Predict and classify each test sample in the test set through the nearest neighbor classification method to obtain the predicted labels.

[0016] Furthermore, during the iterative training process, dynamically change the gradient descent step size α according to the loss value of the objective function of the autoencoder neighborhood preserving embedding algorithm.

[0017] Furthermore, step S4 obtains the objective function of the neighborhood preserving embedding algorithm that maps from the high-dimensional space to the low-dimensional space, and its specific process includes:

[0018] S41. Obtain the k nearest neighbor points of each training sample in the training set to construct the neighborhood graph G;

[0019] S42. Construct the weight matrix W according to the neighborhood graph G to calculate the high-dimensional objective function, and its expression is:

[0020]

[0021] The restriction on W is:

[0022] where, x i represents the i-th training sample, and W ij represents the item in the i-th row and j-th column of the weight matrix W;

[0023] S43. Use the weight matrix W obtained in S42 and the following objective function to calculate the low-dimensional data, and obtain the low-dimensional training samples in the low-dimensional space, and its expression is:

[0024]

[0025] where, YY T=I is a constraint term used to remove any scale factor of the projection, y i Represents x i Corresponding samples in low-dimensional space.

[0026] Furthermore, the neighborhood preserving embedding algorithm is to find a mapping matrix from high-dimensional space to low-dimensional space and map the high-dimensional data to low-dimensional space through this mapping matrix. This process is expressed as:

[0027] y i =A T x i

[0028] With the goal of obtaining the best mapping matrix, the objective function of the neighborhood preserving embedding algorithm is expressed as follows according to the training set matrix X and the weight matrix W:

[0029]

[0030] Where A represents the mapping matrix, M = (IW) T (IW), X represents the matrix composed of training samples in the original training set, I represents the corresponding identity matrix, and the superscript T of the parameter represents the transpose of the matrix.

[0031] Furthermore, with the goal of optimizing the mapping matrix, the autoencoder reconstruction objective function is constructed, which is expressed as:

[0032]

[0033] Among them, m represents the number of training samples in the training set, and A is the mapping matrix.

[0034] Furthermore, according to the neighborhood preserving embedding algorithm objective function, the autoencoder reconstruction objective function and the optimal objective function hyperparameters λ and γ, the objective function of the autoencoder neighborhood preserving embedding algorithm is constructed. It is expressed as:

[0035]

[0036] in, represents the error between high-dimensional data and low-dimensional data in the original neighborhood preserving embedding algorithm, Indicates the original neighborhood preservation embedding algorithm The constraints of represents the reconstruction error between the original high-dimensional data and the reconstructed high-dimensional data, A represents the mapping matrix, X represents the matrix composed of the training samples in the original training set, M = (IW) T (IW), I represents the identity matrix, and d represents the target dimension to be reduced.

[0037] Further, step S5 maintains the objective function of the embedding algorithm according to the self-encoding neighborhood The gradient descent method is used to solve the optimal mapping matrix. The specific process includes:

[0038] S51. In the tth iteration, through the objective function Calculate the partial derivative value corresponding to the current mapping matrix, expressed as:

[0039]

[0040]

[0041]

[0042]

[0043] S52. Update the mapping matrix according to the partial derivative values ​​obtained in S51, expressed as:

[0044]

[0045] Among them, α represents the gradient descent step size, A t Represents the mapping matrix updated at the tth iteration.

[0046] S53.According to A t Calculate the objective function When the objective function The value is less than the stop threshold ε of the objective function or reaches the maximum number of iterations t max When t as the optimal mapping matrix.

[0047] Beneficial effects of the present invention:

[0048] The present invention aims to improve the problem that the low-dimensional space obtained in the existing data dimensionality reduction technology cannot well represent the original high-dimensional space. Specifically, the idea of ​​the autoencoder is introduced into the neighborhood-preserving embedding algorithm, so that the algorithm not only considers the error from the original high-dimensional space to the low-dimensional space, but also considers the error from the original high-dimensional space to the reconstructed high-dimensional space. Such a two-way consideration of the mapping can retain more useful information in the high-dimensional data, making the obtained low-dimensional space data more representative. Thus, a higher recognition accuracy rate is obtained in the image recognition task. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 This is a flow chart of the image recognition method based on the self-encoding neighborhood preserving embedding algorithm of the present invention;

[0050] Figure 2It is a structural diagram of the self-encoding neighborhood preserving embedding algorithm of the present invention;

[0051] Figure 3 Schematic diagram of some samples in various data sets in the embodiments of the present invention;

[0052] Figure 4 A line graph showing the relationship between the recognition rate and the subspace dimension of an embodiment of the present invention on the MNIST data set (50 training samples);

[0053] Figure 5 A line graph showing the relationship between the recognition rate and the subspace dimension of an embodiment of the present invention on the COIL-20 dataset (10 training samples);

[0054] Figure 6 A line graph showing the relationship between the recognition rate of the Extended Yale B face dataset (20 training samples) and the subspace dimension according to an embodiment of the present invention;

[0055] Figure 7 It is a line graph showing the relationship between the recognition rate and the subspace dimension of the embodiment of the present invention on the ORL face dataset (6 training samples);

[0056] Figure 8 The relationship between the recognition rate and the subspace dimension of the embodiment of the present invention in the FERET face data set (5 training samples);

[0057] Figure 9 This is the convergence curve of the self-encoding neighborhood preserving embedding algorithm according to the embodiment of the present invention. DETAILED DESCRIPTION

[0058] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0059] Although image recognition has entered a relatively mature stage and has been widely used in real life, there are still many problems. One of the main problems is that the dimension of the image is too high, and the image contains too much redundant information, such as background information. These redundant information will not only increase the amount of computational complexity of post-processing, but will also greatly affect the accuracy of recognition. Based on this, many data dimensionality reduction methods have been proposed, among which the neighborhood preserving embedding algorithm is an efficient and effective algorithm. Its main idea is to provide a mapping that allows high-dimensional data to remain adjacent in the corresponding low-dimensional space. However, the neighborhood preserving embedding algorithm and its improved method only consider one direction from high-dimensional space to low-dimensional space. This method may not be able to accurately and comprehensively obtain low-dimensional data representing the original sample. Therefore, the present invention introduces the idea of ​​autoencoding to overcome the above-mentioned shortcomings. According to the paradigm of the autoencoder, the algorithm is divided into two stages, such as Figure 2 As shown in Figure 1. The first step is to encode the high-dimensional space data into the corresponding low-dimensional space using the original neighborhood preserving embedding algorithm. The second stage is to reconstruct the original high-dimensional data from the low-dimensional data using the autoencoder idea and minimize the error between the original high-dimensional data and the reconstructed high-dimensional data. The second stage can retain more useful information in the original high-dimensional data, so that the target embedding can more accurately and comprehensively represent the original high-dimensional data.

[0060] Based on the above analysis, the present invention proposes an image recognition method based on a self-encoding neighborhood preserving embedding algorithm, such as Figure 1 As shown, the following steps are included:

[0061] S1. Obtain an image dataset and divide it into a training set, a validation set, and a test set.

[0062] Specifically, it is necessary to vectorize the data in the training set, validation set, and test set, and then combine the vectorized data in each set into a corresponding matrix.

[0063] S2. Initialize the parameters of the self-encoding neighborhood preserving embedding algorithm, including the number of neighboring points k, the reduced target dimension d, the gradient descent step size α, the objective function stop threshold ε, and the maximum number of iterations t max and objective function hyperparameters.

[0064] S3. Using the validation set obtained in S1, the optimal objective function hyperparameters λ and γ of the autoencoder neighborhood preserving embedding algorithm are obtained through grid search.

[0065] S4. Obtain the objective function of the neighborhood-preserving embedding algorithm and the autoencoder reconstruction objective function, and construct the objective function of the autoencoder neighborhood-preserving embedding algorithm by combining the optimal objective function hyperparameters λ and γ

[0066] Specifically, step S4 uses a neighborhood preserving embedding algorithm to obtain the objective function of mapping a high-dimensional space to a low-dimensional space, and the specific process includes:

[0067] S41. Obtain k nearest points of each training sample in the training set to construct a proximity graph G;

[0068] S42. Construct an objective function based on the neighboring graph G to calculate the weight matrix W, which is expressed as:

[0069]

[0070] The constraints are:

[0071] Among them, x i represents the i-th training sample, W ij Represents the entry in row i and column j of the weight matrix W;

[0072] S43. The weight matrix W obtained in S42 and the following objective function are used to calculate the low-dimensional data, which is expressed as:

[0073]

[0074] Among them, YY T =I is a constraint term used to remove any scale factor of the projection, y i Represents x i Corresponding samples in low-dimensional space.

[0075] Specifically, the neighborhood preserving embedding algorithm is to find a mapping matrix from high-dimensional space to low-dimensional space and map the high-dimensional data to low-dimensional space through this mapping matrix. This process is expressed as:

[0076] y i =A T x i (4)

[0077] With the goal of optimizing the mapping matrix, the objective function of formula (3) is converted into the neighborhood preserving embedding algorithm objective function of formula (5) according to the training set matrix X and the weight matrix W, which is expressed as:

[0078]

[0079] Where A represents the mapping matrix, M = (IW) T (IW), X represents the matrix composed of training samples in the original training set, I represents the corresponding identity matrix, and the superscript T of the parameter represents the transpose of the matrix.

[0080] Specifically, the objective of optimizing the mapping matrix is ​​to obtain the autoencoder reconstruction objective function, which is expressed as:

[0081]

[0082] Where m represents the number of training samples in the training set.

[0083] Specifically, according to the neighborhood preserving embedding algorithm objective function, the autoencoder reconstruction objective function, and the optimal objective function hyperparameters λ and γ, the objective function of the autoencoder neighborhood preserving embedding algorithm with the goal of optimizing the mapping matrix is ​​finally obtained: It is expressed as:

[0084]

[0085] in, represents the error between high-dimensional data and low-dimensional data in the original neighborhood preserving embedding algorithm, Indicates the original neighborhood preservation embedding algorithm The constraints of represents the reconstruction error between the original high-dimensional data and the reconstructed high-dimensional data, and d represents the target dimension reduced to.

[0086] S5. Objective function of the self-encoding neighborhood preserving embedding algorithm obtained from S4 The gradient descent method is used to solve the optimal mapping matrix. The specific process includes:

[0087] S51. In the tth iteration, according to the objective function Calculate the partial derivative value corresponding to the mapping matrix updated at the t-1th iteration; expressed as:

[0088]

[0089] in:

[0090]

[0091]

[0092]

[0093] S52. Update the mapping matrix according to the partial derivative value, expressed as:

[0094]

[0095] Among them, α represents the gradient descent step size, A t Represents the mapping matrix updated at the tth iteration.

[0096] S53.According to A t Calculate the objective function When the objective function The value is less than the stop threshold ε of the objective function or reaches the maximum number of iterations t max When t as the optimal mapping matrix.

[0097] S6. Use the optimal mapping matrix A to map both the training set and the test set into a low-dimensional space.

[0098] S7. Use the nearest neighbor classification method to predict and classify each test sample in the test set to obtain a prediction label.

[0099] In the embodiment, the Figure 3 The different data sets shown implement the content of the present method, thereby verifying the effectiveness of the present method.

[0100] Table 1 MNIST dataset test accuracy

[0101]

[0102] Table 2 COIL-20 dataset test accuracy

[0103]

[0104] Table 3. Test accuracy of Extended Yale B face dataset

[0105]

[0106] Table 4 ORL face dataset test accuracy

[0107]

[0108] Table 5. Test accuracy of FERET face dataset

[0109]

[0110] The above test results are all obtained through the steps of the present invention. The first row in the above table indicates the number of training samples, such as 30trains means that the number of training samples is 30; the data items in the table respectively represent the accuracy, standard deviation and the dimension of obtaining the best data, such as 76.54±0.88(25), which means that the accuracy of the item is 76.54%, the standard deviation is 0.88, and the dimension of obtaining the data is 25. Among them, for the algorithms containing the neighboring parameter k: Locality Preserving Projection (LPP), Neighborhood Preserving Projections (NPP), Neighborhood Preserving Embedding (NPE), Orthogonal Neighborhood Preserving Projections (ONPP), Complete Neighborhood Preserving Embedding (CNPE), Weighted Neighborhood Preserving Ensemble Embedding (WNPEE) and Neighborhood preserving embedding with autoencoder (NPEAE) provided by the present invention, all numbers with an interval of 5 from 5 to 25 are tested, and then the one with the highest recognition rate is selected as the result, and the following is obtained: Figures 4 - 8 The relationship between dimension and accuracy. The target dimension takes a value of 5 every interval from 10 to 100, and the best result is taken as the result of the corresponding number of test samples. It can be seen from these line graphs that: 1. As an improved method of neighborhood preserving embedding, the self-encoding neighborhood preserving embedding algorithm shows obvious performance improvement on all data sets. This improvement is attributed to the additional reconstruction term introduced in the self-encoding neighborhood preserving embedding algorithm, which helps to capture more information from the original high-dimensional space. 2. The present invention compares the performance of the self-encoding neighborhood preserving embedding algorithm with several other manifold learning methods, including LPP, NPP, NPE, ONPP, CNPE, ENPE and WNPEE. The results show that the self-encoding neighborhood preserving embedding algorithm outperforms all other methods in terms of recognition rate, which proves the effectiveness of the method proposed in the present invention. 3. The self-encoding neighborhood preserving embedding algorithm outperforms other data sets in all dimensions. In particular, on some data sets, the self-encoding neighborhood preserving embedding algorithm can achieve better performance even in low dimensions. Figure 9The convergence curve of the self-encoding neighborhood preserving embedding algorithm is shown. It can be seen that it converges within 100-150 steps, which also shows the effectiveness of this method.

[0111] The hyperparameters λ and γ of the autoencoder neighborhood preserving embedding algorithm are optimally obtained by grid search on the validation set. The optimal values ​​for each data set are as follows:

[0112]

[0113] Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions and variations may be made to the embodiments without departing from the principles and spirit of the present invention, and that the scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. An image recognition method based on the auto - encoding neighborhood preserving embedding algorithm, characterized in that, it includes the following steps: S1. Obtain a picture dataset and divide it into a training set, a validation set, and a test set; S2. Initialize the parameters of the auto - encoding neighborhood preserving embedding algorithm, including the number of neighbor points k, the target dimension d to be reduced to, the gradient descent step size α, the target function stop threshold ε, the maximum number of iterations t max and the hyperparameters of the target function; S3. Use the validation set obtained in S1 to obtain the optimal hyperparameters λ and γ of the objective function of the auto - encoding neighborhood preserving embedding algorithm through grid search; S4. Obtain the objective function of the neighborhood preserving embedding algorithm and the autoencoder reconstruction objective function, and construct the objective function of the autoencoder neighborhood preserving embedding algorithm by combining the optimal objective function hyperparameters λ and γ The neighborhood preserving embedding algorithm is to find a mapping matrix from a high - dimensional space to a low - dimensional space and map the high - dimensional data to the low - dimensional space through this mapping matrix. This process is expressed as: y i = A T x i Taking obtaining the optimal mapping matrix as the goal, represent the objective function of the neighborhood preserving embedding algorithm according to the training set matrix X and the weight matrix W as: where A represents the mapping matrix, M = (I - W) T (I - W), X represents the matrix formed by the training samples in the original training set, I represents the identity matrix, and the superscript T of the parameter represents the transpose of the matrix; Obtain the auto - encoding reconstruction objective function, expressed as: where m represents the number of training samples in the training set, and A is the mapping matrix; Construct the objective function of the autoencoder neighborhood preserving embedding algorithm according to the objective function of the neighborhood preserving embedding algorithm, the autoencoder reconstruction objective function, and the optimal objective function hyperparameters λ and γ It is expressed as: Among them, represents the error between the original high-dimensional data and the low-dimensional data in the original neighborhood preserving embedding algorithm, represents the constraint term for in the original neighborhood preserving embedding algorithm; represents the reconstruction error between the original high-dimensional data and the reconstructed high-dimensional data. A represents the mapping matrix, X represents the matrix composed of training samples in the original training set, M = (I - W) T (I - W), I represents the identity matrix, and d represents the target dimension to which it is reduced; S5. The objective function of the auto-encoding neighborhood preserving embedding algorithm obtained according to S4 Use the gradient descent method to solve the optimal mapping matrix; S6. Use the optimal mapping matrix to map both the training set and the test set into the low - dimensional space; S7. Predict and classify each test sample in the test set through the nearest - neighbor classification method to obtain prediction labels.

2. The image recognition method based on the auto - encoding neighborhood preserving embedding algorithm according to claim 1, characterized in that, During the iterative training process, the gradient descent step size α is dynamically changed according to the loss value of the objective function of the auto-encoding neighborhood preserving embedding algorithm ​ 3. The image recognition method based on the auto - encoding neighborhood preserving embedding algorithm according to claim 1, characterized in that, The process of step S4 to obtain the objective function of the neighborhood preserving embedding algorithm that maps from a high - dimensional space to a low - dimensional space specifically includes: S41. Obtain the k nearest neighbor points of each training sample in the training set to construct a neighborhood graph G; S42. Construct a high - dimensional objective function according to the neighborhood graph G to calculate the weight matrix W, and its expression is: The limitation on W is as follows: where x i represents the i-th training sample, and W ij represents the term in the i-th row and j-th column of the weight matrix W; S43. Use the weight matrix W obtained in S42 and the following objective function to calculate the low - dimensional data, and its expression is: Among them, YY T = I is a constraint for any scale factor used to remove the projection, y i represents x i The corresponding sample in the low-dimensional space.

4. The image recognition method based on the auto - encoding neighborhood preserving embedding algorithm according to claim 1, characterized in that, Step S5 is based on the objective function of the auto-encoding neighborhood preserving embedding algorithm The gradient descent method is used to solve the optimal mapping matrix, and its specific process includes: S51. In the t-th iteration, through the objective function calculate the partial derivative value corresponding to the mapping matrix updated in the (t - 1)-th iteration, expressed as: S52. Update the mapping matrix according to the partial derivative value obtained in S51, expressed as: where α represents the gradient descent step size, and A t represents the mapping matrix updated at the t-th iteration; S53. According to A t Calculate the objective function value. When the value of the objective function is less than the objective function stop threshold ε or reaches the maximum number of iterations t max , stop the iteration and take A t as the optimal mapping matrix.

Images