Multi-Manifold Based Autoencoder Image Classification Method and System

Abstract

The present invention discloses an image classification method and system based on a multi-manifold autoencoder, which aims to achieve effective classification and dimensionality reduction in high-dimensional image data while maintaining the geometric structure of the data. First, a denoising autoencoder is used for pre-training to learn the initial low-dimensional expression of the data in the latent space. Then, each class is assumed to be a manifold space, and the low-dimensional expression and classification of the data are achieved by optimizing the structural consistency and discriminability of the manifold. To this end, the present invention constructs an intra-manifold isometric loss function, an inter-manifold discriminant loss function, a manifold alignment loss function, and a classification loss function. By combining these four loss functions into a total loss function, it is optimized and adjusted based on the pre-trained autoencoder to learn the final low-dimensional expression of the image data, and used for classification prediction of unknown image data. The present invention effectively combines autoencoders and manifold learning to provide a more superior classification solution for image data.

Description

Technical Field

[0001] The present invention belongs to the field of image classification and relates to an image classification method and system based on a multi-manifold autoencoder. Background Art

[0002] Image classification is an important task in the fields of image processing and machine learning. It involves classifying input image data into different categories or labels for further analysis and application. Image classification is widely used in many application fields, including computer vision, pattern recognition, object detection, face recognition, and more. Currently, image classification technology is mainly based on machine learning methods and deep learning methods. Machine learning methods include support vector machines (SVMs), random forests, and deep neural networks. These methods typically rely on large amounts of labeled data for training and use high-dimensional feature representations to represent images. However, image processing and classification face several challenges, such as the curse of dimensionality, overfitting, and computational complexity.

[0003] Deep learning models, such as convolutional neural networks (CNNs), have demonstrated remarkable performance in image classification tasks, capable of learning high-level feature representations from raw pixel-level data. However, deep learning methods also face challenges when processing images. Image processing requires a large number of parameters and computational resources, which can easily lead to overfitting and increased computational complexity. Furthermore, deep learning methods often ignore the intrinsic structure and manifold properties of the data, treating it as a flat vector representation, which can lead to a loss of rich information and underlying structure.

[0004] Therefore, there is a need for an image classification method that can effectively process images and fully utilize the inherent structure of the data. The present invention aims to provide a multi-manifold-based autoencoder image classification method and system. By combining autoencoders and manifold learning, low-dimensional representation and classification of image data are achieved. By maintaining local and global manifold structures, the method of the present invention can improve the accuracy and robustness of image classification and has advantages in image processing. By addressing the problems and limitations of the existing technology, the present invention brings new technical solutions to the field of image classification, with broad application prospects and commercial value. Summary of the Invention

[0005] The purpose of the present invention is to make full use of the characteristics of denoising autoencoders and overcome the defect that deep learning methods often destroy the potential manifold structure of the data. By combining manifold learning methods, the local structure within each manifold and the global structure between manifolds are maintained, and the discriminability of the data is maintained, thereby designing an image classification method and system based on multi-manifold autoencoders.

[0006] Technical solution: To achieve the above-mentioned purpose, the present invention adopts the following technical solution:

[0007] The multi-manifold-based autoencoder image classification method includes the following steps:

[0008] (1) Pre-training the denoising autoencoder by adding noise to the image data enables the encoder to reconstruct the original image data and learn the initial low-dimensional representation of the data in the latent space;

[0009] (2) After the hidden layer of the denoising autoencoder, a multilayer perceptron is connected to predict the category label of the image data based on the potential expression of the data;

[0010] (3) Assuming that each category in the image dataset is located on a compact low-dimensional manifold, in order to maintain the consistency of the geometric structure of the data in the latent low-dimensional space and the original space, and at the same time enhance the discriminability of the data expression in the latent space, the intra-manifold equidistance loss function, the inter-manifold discriminant loss function, the manifold alignment loss function and the classification loss function are constructed and combined into a total loss function; the intra-manifold equidistance loss function maintains the local structure within the manifold by minimizing the pairwise distances between data points in the latent space and in the original space with data points in the same manifold neighborhood; the inter-manifold discriminant loss function forces the pairwise distances between the center points of different manifolds in the latent space to be several times their distances in the original space, so that different manifolds are far away from each other, thereby maintaining the discriminability of the latent expression; the manifold alignment loss function ensures that the learned manifold center points are reliable by minimizing the gap between the manifold center points learned in the latent space and their corresponding true manifold center points;

[0011] (4) By optimizing the above-mentioned total loss function, adjusting the parameters of the pre-trained autoencoder, and obtaining the optimized data potential expression and the optimized network parameters;

[0012] (5) The test image data is passed into the optimized network to predict the category label of the test image data.

[0013] Preferably, in step (1), random noise transformation is introduced into the original image training data, the encoder and decoder network structure of the denoising autoencoder is constructed, and the noisy image is used as input to train the denoising autoencoder. The goal is to reconstruct the noise-free image through the training of the encoder and decoder to enhance the robustness of the model.

[0014] Preferably, in step (2), the multi-layer perceptron MLP is composed of multiple fully connected layers, each layer contains multiple neurons, and the mapping relationship between features and categories is established by learning weight parameters.

[0015] As a preference, in step (3), the image data is fed into the network in batches, and the method for updating the center point of each manifold in real time is: Represents the center point of the i-th image data of the current batch in the original space, Indicates the number of image data of category i in the current batch, n i Represents the number of image data of type i so far, then the overall center point of image data of type i in the original space The update formula is

[0016]

[0017] n i The update formula is:

[0018]

[0019] The center point of the i-th type of image data in the latent space The update formula is:

[0020]

[0021] As an advantage, the isometric loss function Loss in the manifold L The definition is as follows:

[0022]

[0023] where Z represents the latent space, x i Represents the i-th image data of the current batch, y i Indicates the label of the i-th image data in the current batch, z i Represents x i The expression in the latent space, represents z i Neighborhood, d X and d Z Respectively represent the calculation function of the distance between two data in the original space and the latent space, π(·)∈{0,1} is the same type indicator function, indicating that y i and y j Are they the same? n represents the number of data in the current batch.

[0024] As a preference, the discrimination loss function Loss between the manifolds D The definition is as follows:

[0025]

[0026] in, is a set of learnable parameters used to estimate the center points of C manifolds in the latent space, d Z (μ i , μ j ) represents the distance between the center point of the i-th manifold and the center point of the j-th manifold in the potential low-dimensional space, represents the center point of the j-th manifold in the original space X, represents the distance between the center point of the i-th manifold and the center point of the j-th manifold in the original space, and the parameter κ determines how far different manifolds are expected to be away from each other.

[0027] Preferably, the alignment loss function is Loss A :

[0028]

[0029] in represents the true center point in the latent space according to the j-th manifold.

[0030] Preferably, the classification loss function is defined as:

[0031]

[0032] where f i Indicates x i The predicted class label of .

[0033] Multi-manifold based autoencoder image classification system, including:

[0034] The encoder pre-training module is used to pre-train the denoising autoencoder by adding noise to the image data, so that the encoder can reconstruct the original image data and learn the initial low-dimensional representation of the data in the latent space;

[0035] The category prediction module is used to connect a multi-layer perceptron after the hidden layer of the denoising autoencoder to predict the category label of the image data based on the potential expression of the data;

[0036] The training loss calculation module assumes that each category in the image dataset lies on a compact low-dimensional manifold. To maintain the consistency of the geometric structure of the data in the latent low-dimensional space and the original space, while enhancing the discriminability of the data expressed in the latent space, it constructs the intra-manifold isometric loss function, the inter-manifold discriminant loss function, the manifold alignment loss function, and the classification loss function, and combines them into an overall loss function.

[0037] The intra-manifold isometric loss function preserves the local structure of the manifold by minimizing the pairwise distances between data points in the latent space and in the original space and in the neighborhood of the same manifold.

[0038] The inter-manifold discriminative loss function keeps different manifolds away from each other by forcing the distance between the center points of different manifolds in the latent space to be several times their distance in the original space, thereby maintaining the discriminativeness of the latent representation.

[0039] The manifold alignment loss function ensures that the learned manifold center points are reliable by minimizing the gap between the manifold center points learned in the latent space and their corresponding true manifold center points;

[0040] The optimization and training module is used to adjust the parameters of the pre-trained autoencoder by optimizing the above-mentioned total loss function to obtain the optimized data potential expression and the optimized network parameters;

[0041] And, the classification test module is used to pass the test image data into the optimized network and predict the category label of the test image data.

[0042] A computer system comprises a memory, a processor and a computer program stored in the memory and executable on the processor, wherein when the computer program is loaded into the processor, the steps of the multi-manifold-based autoencoder image classification method are implemented.

[0043] The present invention proposes an image classification method and system based on a multi-manifold autoencoder, which combines multi-manifold learning and deep learning to achieve low-dimensional expression and classification of image data in a network framework. First, the autoencoder is used for pre-training to learn the initial low-dimensional representation of the data in the latent space. By constructing multiple sub-loss functions, including the intra-manifold isometric loss function, the inter-manifold discriminant loss function, the manifold alignment loss function and the classification loss function, and combining them into a total loss function, the pre-trained autoencoder is optimized and adjusted to learn the final low-dimensional expression of the image data and use it for classification prediction. This method makes full use of the nonlinear feature discovery ability of deep learning and the local structure preservation ability of manifold learning, so that classification and dimensionality reduction can be effectively achieved when processing large-scale image data, and the geometric structure of the image data can be maintained.

[0044] The present invention aims to solve the problem that with the rapid development of the Internet era, diverse data are constantly accumulating, generating a large number of data sets with higher dimensions, more comprehensive information, and more complex styles, which has led to greater challenges for traditional machine learning dimensionality reduction technology. We propose a multi-manifold autoencoder to combine multi-manifold learning in machine learning and autoencoders in today's popular deep learning into a network framework. By using multi-manifold learning to retain the local structure in each sub-manifold and ensure the distinguishability between different manifolds, the deep learning network structure is used to control the local and global structures between manifolds. In this way, while solving complex images, the original structural information between image data can also be retained. In experiments on handwritten digital images and facial data images, we verified that the classification performance of our proposed model is better than many models based on autoencoder algorithms. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 The figure is a schematic diagram of the model structure and loss function of an embodiment of the present invention. The figure details the execution process of the present invention, which consists of four sub-loss functions and the basic structure of the denoising autoencoder. DETAILED DESCRIPTION

[0046] The technical solution of the present invention is described in detail below with reference to the accompanying drawings and specific embodiments.

[0047] An embodiment of the present invention discloses an image classification method based on an autoencoder of multiple manifolds. The main technical idea is: first, a denoising autoencoder is used to learn the initial low-dimensional representation of the image data in the pre-training stage. Then, the autoencoder is combined with manifold learning, and the structural consistency and discriminability of the manifold are optimized by using the intra-manifold isometric loss function, the inter-manifold discriminant loss function, the manifold alignment loss function and the classification loss function. Then, by optimizing and adjusting the total loss function, the final low-dimensional expression of the image data is learned. Finally, the learned model is used to perform classification prediction on unknown image data. This method effectively combines autoencoders and manifold learning, providing a superior image classification solution that can achieve dimensionality reduction and classification of high-dimensional image data while maintaining the geometric structure of the data.

[0048] The detailed execution steps of the embodiment of the present invention are as follows:

[0049] 1. Data Preprocessing

[0050] Preprocessing of high-dimensional image data, including data cleaning, feature extraction and normalization, is done to reduce noise and redundant information and prepare for subsequent operations. Assume that the image dataset X has N training samples, and each sample Sampled from C different manifolds, labeled y i We performed appropriate data preprocessing steps to ensure data quality and consistency. The embodiment of the present invention divides the data into training data and test data equally, and divides the data into batches and feeds them into the network in sequence.

[0051] 2. Denoising Autoencoder Pre-training

[0052] Denoising autoencoder pre-training is to learn the low-dimensional representation of data from high-dimensional image data by training an autoencoder model. First, noise is added to the original image data and then input into the autoencoder for training. The goal of the autoencoder is to learn the potential expression of the data by reconstructing the input data. During the pre-training process, the autoencoder optimizes its own parameters by minimizing the reconstruction error between the input and the reconstruction. In this way, the autoencoder can learn the key features in the data and remove noise, thereby obtaining a more accurate data representation. In this embodiment, random noise transformations such as Gaussian noise or salt and pepper noise are introduced to the original image training data. The encoder and decoder network structure of the denoising autoencoder is constructed. Using noisy images as input, the denoising autoencoder is trained. The goal is to reconstruct noise-free images through the training of the encoder and decoder to enhance the robustness of the model.

[0053] 3. Multi-manifold autoencoder model construction

[0054] The pre-trained autoencoder is combined with manifold learning to construct a multi-manifold autoencoder model. It is assumed that the data of each category forms a manifold space, and the low-dimensional expression and classification of the data are achieved by optimizing the structural consistency and discriminability of the manifold. The purpose of connecting a multi-layer perceptron (MLP) after the hidden layer of the denoising autoencoder in this embodiment is to associate the potential expression of the image data with the category label to achieve the image classification task. The hidden layer learns the meaningful feature expression of the image data through the autoencoder, and then passes these features to the MLP for classification. The MLP consists of multiple fully connected layers, each layer contains multiple neurons, and the mapping relationship between features and categories is established by learning weight parameters.

[0055] 4. Loss Function Optimization

[0056] In this paper, a total of four loss functions are introduced to optimize model performance, including the intra-manifold isometry loss function, the inter-manifold discrimination loss function, the manifold alignment loss function, and the classification loss function. These loss functions can preserve the structural features within the manifold and enhance the distinguishability between manifolds, thereby improving classification accuracy.

[0057] a) Calculate the isometric loss function within the manifold: Maintain the local structure within the manifold by minimizing the pairwise distance between data points in the latent space and the original space and the data points in the same manifold neighborhood. L The function definition is as follows:

[0058]

[0059] where Z represents the latent space, x i Represents the i-th training image data of the current batch, y i Represents xi The true category label, z i Represents x i The expression in the latent space, represents z i The neighborhood of can be determined using the kNN algorithm. X and d Z Respectively represent the calculation function of the distance between two data in the original space and the latent space. Because it is the data in the neighborhood, the Euclidean distance is generally used for calculation. π(.)∈{0,1} is the same indicator function, indicating that y i and y j Are they the same? n represents the total number of data in the current batch.

[0060] b) Calculate the inter-manifold discriminative loss function: By forcing the distance between the center points of different manifolds in the latent space to be κ times their distance in the original space, different manifolds are kept away from each other, thereby maintaining the discriminativeness of the latent expression. The loss function is defined as:

[0061]

[0062] in, is a set of learnable parameters used to estimate the center points of C manifolds in the latent space, d Z (μ i , μ j ) represents the distance between the center point of the i-th manifold and the center point of the j-th manifold in the potential low-dimensional space, represents the center point of the j-th manifold in the original space X, The distance between the center of the i-th manifold and the center of the j-th manifold in the original space. The parameter κ determines how far apart we want different manifolds to be from each other. The larger the κ, the greater the distance between different manifolds. κ is usually 3.

[0063] Calculation of the center point of the category manifold: Since the image data is fed into the network in batches rather than all at once, the center point of each manifold needs to be updated in real time. Indicates the center point of the i-th type of data in the current batch in the original space, Indicates the number of data of category i in the current batch, n i Represents the number of type i data so far, then the overall center point of type i data (i.e., the i-th manifold) in the original space is The update formula is

[0064]

[0065] n i The update formula is:

[0066]

[0067] Similarly, the center point of the i-th category data in the latent space is The update formula is:

[0068]

[0069] c) Calculate the manifold alignment loss function: By minimizing the manifold center point (μ j ) and its corresponding real manifold center point The gap between them ensures that the learned manifold center point is reliable. The loss function is defined as:

[0070]

[0071] in represents the true center point of the j-th manifold in the latent space.

[0072] d) Calculate the classification loss function: Measure the classification performance of the learned latent expression by calculating the classification loss of the current batch of image data:

[0073]

[0074] where f i Indicates x i The predicted category label of . Combining the above loss sub-functions, the complete loss function is

[0075] L=Loss C +αLoss L +βLoss D +γLoss A

[0076] Where α, β and γ are weight coefficients respectively.

[0077] In summary, the intra-manifold equidistance loss function is used to maintain the equidistance between data points within each manifold, the inter-manifold discrimination loss function increases the distinguishability between different manifolds, the manifold alignment loss function maintains the relative positional relationships between data points within different manifolds, and the classification loss function is used to measure the model's performance in classification tasks. By comprehensively optimizing these loss functions, the algorithm of this invention can simultaneously consider the local structure and global structure of the data, the distinguishability between manifolds, and the classification accuracy, thereby achieving accurate classification of high-dimensional data.

[0078] A pre-trained autoencoder is optimized and adjusted to learn the final low-dimensional representation of the image data. Specifically, during the optimization and training phase, we randomly initialize the network parameters and define the optimization objective function. Backpropagation is used to calculate gradients and update the network parameters. Simultaneously, the autoencoder parameters, manifold centers, and low-dimensional representations of the data points are adjusted to minimize the loss function. Through an iterative optimization process, we obtain an optimized latent representation of the data and network parameters, enabling the network to better learn and represent the input data, thereby achieving accurate classification results. This optimization and training process is designed to improve network performance and enhance classification accuracy and robustness.

[0079] 5. Classification Prediction

[0080] When applying a multi-manifold autoencoder for classification prediction, unknown image data is first input into the model. Using a trained multi-manifold autoencoder, the image data is mapped into a low-dimensional latent space, obtaining its low-dimensional representation. The trained classifier is then used to perform classification predictions on the low-dimensional representation, determining the image's category. To evaluate classification performance and improve the model, metrics such as accuracy, recall, and F1 score can be calculated. Based on these evaluation results, model parameters can be adjusted, and training data can be added to improve classification accuracy. Through repeated experiments and validation, the model's robustness and generalization capabilities can be ensured.

[0081] Figure 1 A schematic diagram showing the model structure and final loss function of the multi-manifold-based autoencoder image classification method and system.

[0082] Table 1 shows the classification performance of an embodiment of the present invention (a multi-manifold autoencoder image classification method, abbreviated as MMAEIC) on four image datasets. We used USPS, Pendigits, Fashion-MNIST, and CIFAR-10 to verify the classification performance of the present invention. The USPS digit database is a standard dataset for handwritten digit recognition, containing 28x28 black-and-white images of the ten digits 0-9. Fashion-MNIST is a clothing image dataset provided by the German company Zalando, consisting of a training set of 60,000 samples and a test set of 10,000 samples. The Pendigits dataset contains processed image features, with each set of data having an original dimension of 16. CIFAR-10 is a small dataset for general object recognition, containing RGB color images of 10 categories: airplanes, cars, birds, cats, deer, dogs, frogs, horses, ships, and trucks. The image size is 32x32, and the dataset contains 50,000 training images and 10,000 test images.

[0083] Table 1: Performance (Accuracy) of MMAEIC and other methods on four datasets

[0084]

[0085] Based on the same inventive concept, an embodiment of the present invention discloses a multi-manifold-based autoencoder image classification system, comprising: an encoder pre-training module for pre-training a denoising autoencoder by adding noise to image data, so that the encoder can reconstruct the original image data and learn the initial low-dimensional representation of the data in a latent space; a category prediction module for connecting a multi-layer perceptron after the hidden layer of the denoising autoencoder to predict the category label of the image data based on the latent representation of the data; a training loss calculation module for assuming that each category in the image dataset is located on a compact low-dimensional manifold. In order to maintain the consistency of the geometric structure of the data in the latent low-dimensional space and the original space while enhancing the discriminability of the data expression in the latent space, an intra-manifold isometric loss function, an inter-manifold discriminant loss function, a manifold alignment loss function, and a classification loss function are constructed and combined into a total loss function; an optimization and training module for adjusting the pre-trained autoencoder parameters by optimizing the above-mentioned total loss function to obtain an optimized data latent representation and optimized network parameters; and a classification test module for passing test image data into the optimized network to predict the category label of the test image data.

[0086] Based on the same inventive concept, an embodiment of the present invention discloses a computer system, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the computer program is loaded into the processor, the steps of the multi-manifold-based autoencoder image classification method are implemented.

Claims

1. Multi-manifold based autoencoder image classification method, characterized by: The steps include: (1) Pre-training the denoising autoencoder by adding noise to the image data enables the encoder to reconstruct the original image data and learn the initial low-dimensional representation of the data in the latent space; (2) After the hidden layer of the denoising autoencoder, a multilayer perceptron is connected to predict the category label of the image data based on the potential expression of the data; (3) Assuming that each category in the image dataset is located on a compact low-dimensional manifold, in order to maintain the consistency of the geometric structure of the data in the latent low-dimensional space and the original space, and at the same time enhance the discriminability of the data expression in the latent space, the intra-manifold equidistance loss function, the inter-manifold discriminant loss function, the manifold alignment loss function and the classification loss function are constructed and combined into a total loss function; the intra-manifold equidistance loss function maintains the local structure within the manifold by minimizing the pairwise distances between data points in the latent space and in the original space with data points in the same manifold neighborhood; the inter-manifold discriminant loss function forces the pairwise distances between the center points of different manifolds in the latent space to be several times their distances in the original space, so that different manifolds are far away from each other, thereby maintaining the discriminability of the latent expression; the manifold alignment loss function ensures that the learned manifold center points are reliable by minimizing the gap between the manifold center points learned in the latent space and their corresponding true manifold center points; (4) By optimizing the above-mentioned total loss function, adjusting the parameters of the pre-trained autoencoder, and obtaining the optimized data potential expression and the optimized network parameters; (5) The test image data is passed into the optimized network to predict the category label of the test image data.

2. The multi-manifold-based autoencoder image classification method according to claim 1, characterized in that In step (1), random noise transformation is introduced into the original image training data to construct the encoder and decoder network structure of the denoising autoencoder. The noisy image is used as input to train the denoising autoencoder. The goal is to reconstruct the noise-free image through the training of the encoder and decoder to enhance the robustness of the model.

3. The multi-manifold based autoencoder image classification method according to claim 1, characterized in that In step (2), the multi-layer perceptron (MLP) consists of multiple fully connected layers, each of which contains multiple neurons, and the mapping relationship between features and categories is established by learning weight parameters.

4. The multi-manifold based autoencoder image classification method according to claim 1, characterized in that In step (3), the image data is fed into the network in batches, and the method for updating the center point of each manifold in real time is: Represents the center point of the i-th image data of the current batch in the original space, Indicates the number of image data of category i in the current batch, n i Represents the number of image data of type i so far, then the overall center point of image data of type i in the original space The update formula is n i The update formula is: The center point of the i-th type of image data in the latent space The update formula is:

5. The multi-manifold based autoencoder image classification method according to claim 1, characterized in that The manifold isometric loss function Loss L The definition is as follows: where Z represents the latent space, x i Represents the i-th image data of the current batch, y i Indicates the label of the i-th image data in the current batch, z i Represents x i The expression in the latent space, represents z i Neighborhood, d X and d Z Respectively represent the calculation function of the distance between two data in the original space and the latent space, π(·){0,1} is the same type indicator function, indicating that y i and y j Are they the same? n represents the number of data in the current batch.

6. The multi-manifold based autoencoder image classification method according to claim 1, characterized in that The discriminant loss function Loss between the manifolds D The definition is as follows: in, is a set of learnable parameters used to estimate the center points of C manifolds in the latent space, d Z (μ i , μ j ) represents the distance between the center point of the i-th manifold and the center point of the j-th manifold in the potential low-dimensional space, represents the center point of the j-th manifold in the original space X, represents the distance between the center point of the i-th manifold and the center point of the j-th manifold in the original space, and the parameter κ determines how far different manifolds are expected to be away from each other.

7. The multi-manifold based autoencoder image classification method according to claim 1, characterized in that The alignment loss function is Loss A : in represents the true center point in the latent space according to the j-th manifold.

8. The multi-manifold based autoencoder image classification method according to claim 1, characterized in that The classification loss function is defined as: where f i Indicates x i The predicted class label, y i Represents x i The label of , n represents the number of data in the current batch.

9. Multi-manifold based autoencoder image classification system, characterized by, include: The encoder pre-training module is used to pre-train the denoising autoencoder by adding noise to the image data, so that the encoder can reconstruct the original image data and learn the initial low-dimensional representation of the data in the latent space; The category prediction module is used to connect a multi-layer perceptron after the hidden layer of the denoising autoencoder to predict the category label of the image data based on the potential expression of the data; The training loss calculation module assumes that each category in the image dataset lies on a compact low-dimensional manifold. To maintain the consistency of the geometric structure of the data in the latent low-dimensional space and the original space, while enhancing the discriminability of the data expressed in the latent space, it constructs the intra-manifold isometric loss function, the inter-manifold discriminant loss function, the manifold alignment loss function, and the classification loss function, and combines them into an overall loss function. The intra-manifold isometric loss function preserves the local structure of the manifold by minimizing the pairwise distances between data points in the latent space and in the original space and in the neighborhood of the same manifold. The inter-manifold discriminative loss function keeps different manifolds away from each other by forcing the distance between the center points of different manifolds in the latent space to be several times their distance in the original space, thereby maintaining the discriminativeness of the latent representation. The manifold alignment loss function ensures that the learned manifold center points are reliable by minimizing the gap between the manifold center points learned in the latent space and their corresponding true manifold center points; The optimization and training module is used to adjust the parameters of the pre-trained autoencoder by optimizing the above-mentioned total loss function to obtain the optimized data potential expression and the optimized network parameters; And, the classification test module is used to pass the test image data into the optimized network and predict the category label of the test image data.

10. A computer system comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the computer program is loaded into a processor, the steps of the multi-manifold based autoencoder image classification method according to any one of claims 1 to 8 are implemented.

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