An intelligent clustering method for urine sediment impurity microscopic images based on deep autoencoding

Abstract

The present invention is applicable to the field of medical image processing technology and provides an intelligent clustering method for urine sediment impurity microscopic images based on deep autoencoding, comprising the following steps: firstly, data enhancement, normalization and standardization preprocessing are performed on the microscopic images of urine sediment tangible component impurity samples to improve the generalization of the model; then, the data is input into the model and the number of clusters is changed. k The optimal number of clusters is determined by comparing the CH index, DBI index, and intra-cluster and inter-cluster distance ratio. The preprocessed image is then fed into a deep autoencoder (DAE) for feature extraction. The extracted latent features are clustered using the K-Means algorithm, and cluster centers are iteratively updated until convergence. This method lays a key foundation for the accurate identification of massive amounts of valid samples and is of great significance in promoting the development of intelligent medical instruments and improving their detection performance.

Description

Technical Field

[0001] The present invention belongs to the technical field of medical image processing, and in particular relates to an intelligent clustering method for urine sediment impurity microscopic images based on deep autoencoding. Background Art

[0002] As people's living standards continue to improve, healthcare issues have become a focus of social attention, driving a rapid increase in medical data. Medical testing is a key component of medical diagnosis and treatment, helping people gain a deeper understanding of the onset and progression of diseases and providing a crucial basis for the design and optimization of prognosis and treatment plans.

[0003] In the field of medical testing, the analysis and detection of urine formed elements is of great significance. It provides key information for the diagnosis of urinary system and kidney diseases, the assessment of disease severity, and the monitoring of treatment effects by analyzing components such as cells, casts, and crystals in urine. However, there are a large number of impurity samples of various types in clinical samples of urine formed elements, and the morphology of some impurity samples is very similar to that of valid category samples. The presence of these impurities not only increases the complexity of sample analysis, but also brings great difficulties to the subsequent accurate identification of massive valid category samples. Therefore, how to achieve accurate and efficient recognition of massive medical microscopic images and effectively apply them in medical testing instruments has become a key issue affecting the testing performance of medical instruments, and has always been a technical problem that medical instrument R&D companies need to overcome.

[0004] Early methods for detecting medical cells and formed elements relied primarily on microscopy, chemical testing, immunoassays, and automated analysis. With the continuous advancement of technology, medical samples can now be processed and tested using instruments. These instruments read and analyze the components in the sample, converting them into analyzable data. In image processing, traditional methods such as edge detection, texture features, morphological filtering, and template matching were initially used. These methods are often designed for specific tasks and involve superficial learning of image features.

[0005] However, the number of medical images collected by current medical instruments during the examination process is huge. The actual microscopic images of urine sediment samples obtained clinically contain dozens of different types of visible components, and the morphological differences of these visible components are relatively large. In addition, there are many impurities in urine visible samples, and the amount of impurities accounts for nearly 60% of the total sample volume. The microscopic images of some urine sediment visible component impurity samples are as follows: Figure 1As shown in the figure, these impurities have complex characteristics such as complex morphology, varying sizes, unbalanced numbers, and partial overlap with valid samples, posing significant challenges to recognition. Furthermore, the characteristics of some cell categories are extremely similar, and the number of samples available for a few categories is limited, making it difficult to accurately extract sample features during clustering. Furthermore, it is necessary to consider the underfitting problem caused by the small sample size and the decrease in overall recognition accuracy caused by the partial overlap of impurity samples with valid samples. Furthermore, the significant differences in sample size between different categories make it difficult for traditional image recognition methods to achieve ideal recognition results.

[0006] In recent years, artificial intelligence and deep learning technologies have demonstrated tremendous potential and value in multiple fields. Coupled with the urgent need for intelligent development of medical testing instruments, intelligent networks have gradually been applied to the field of medical cell analysis and identification, bringing new development opportunities to this field. However, the diversity and complexity of urine tangible samples make model design and training more difficult, and existing clustering methods have problems with low accuracy and slow clustering speed. To this end, the present invention proposes an intelligent clustering method for urine sediment impurity microscopic images based on deep autoencoding. Summary of the Invention

[0007] The purpose of the present invention is to provide an intelligent clustering method for urine sediment impurity microscopic images based on deep autoencoding, aiming to solve the problems raised in the above background technology.

[0008] The purpose of the present invention is achieved through the following technical solutions:

[0009] A method for intelligent clustering of urine sediment impurity microscopic images based on deep autoencoding, comprising the following steps:

[0010] Step 1: Data enhancement, normalization and standardization preprocessing of the microscopic image of urine sediment visible component impurities sample;

[0011] Step 2: Calculate the performance index to determine the optimal number of clusters;

[0012] By adjusting the number of clusters k , compare the DBI index, CH index and intra-cluster and inter-cluster distance ratio to determine the optimal number of clusters;

[0013] Step 3: The deep autoencoder intelligently acquires image features and performs K-means clustering;

[0014] After determining the optimal number of clusters, all impurity samples are trained using a deep clustering method based on deep autoencoders and K-means.

[0015] Furthermore, the specific steps of step 1 are as follows:

[0016] Step 11: Training data processing, the specific operations are as follows:

[0017] Data augmentation: For training data, random cropping, horizontal flipping, color jittering, and random grayscale augmentation strategies are used;

[0018] Normalization: Convert the image to a PyTorch tensor Tensor and normalize the pixel values ​​from [0, 255] to [0, 1];

[0019] Step 12: Test data processing;

[0020] Perform random cropping and normalization;

[0021] Step 13: Standardization;

[0022] The normalized data is normalized by formula 1 so that the pixel values ​​of each channel obey the standard normal distribution:

[0023] Formula 1: ;

[0024] in is the normalized pixel value, is the original pixel value, is the mean used for normalization, is the standard deviation used for normalization.

[0025] Furthermore, in the data enhancement step, a portion of the image is randomly selected and resized to a specified size through random cropping; the image is horizontally flipped with a probability of 50%; the image is color-dithered with a probability of 80% to change the brightness, contrast, saturation and hue; and the color image is converted to a grayscale image with a probability of 20%.

[0026] Furthermore, in step 2, the calculation formulas for the DBI index, CH index, and intra-cluster to inter-cluster distance ratio are as follows:

[0027] Formula 2: ;

[0028] in is the number of clusters, It is a cluster The average distance inside It is a cluster The average distance inside It is a cluster and clusters the distance between them;

[0029] Formula 3: ;

[0030] in It is a cluster The number of data points, It is a cluster A set of data points, x It is a cluster Internal data points, It is a cluster The center of mass, is the centroid of the entire dataset, is the total number of data points;

[0031] Formula 4: ;

[0032] in is the ratio of the intra-cluster distance to the inter-cluster distance, It is a cluster and clusters The Euclidean distance between It is a cluster Euclidean distance from internal data points to the centroid; The number of clusters is k When , the number of combinations between any two categories;

[0033] The calculated difference k The DBI index, CH index and intra-cluster and inter-cluster distance ratio corresponding to the value are comprehensively compared to finally determine the optimal number of clusters ;

[0034] The process of comprehensive comparison is: k The DBI index, CH index and intra-cluster and inter-cluster distance ratio corresponding to the value are normalized. Based on the characteristic that the smaller the DBI index value, the higher the clustering density, the inverse operation is performed on it; the number of clusters is plotted. k Draw a scatter plot of the relationship between the performance indicators and the performance indicators, calculate the points in the performance indicator curve where the absolute value of the slope exceeds the preset threshold, merge and remove the slope mutation points of all indicators, and perform frequency statistics on the number of clusters. If the cluster number exists in the set of slope mutation points of any performance indicator, the count value of the cluster number is increased by 1; finally, the cluster number with the highest count value is determined as the optimal cluster number;

[0035] Furthermore, the specific steps of step 3 are as follows:

[0036] Step 31: Add noise to the preprocessed image and input it into DAE for feature extraction;

[0037] In the encoder part of the DAE, the input data is first processed by a fully connected layer, followed by a nonlinear transformation using the ReLU activation function. Then, another fully connected layer is used to map the input data to a low-dimensional latent space. In the decoder part of the DAE, the latent space data from the encoder is first received by a fully connected layer, then nonlinearly transformed using the ReLU activation function. Finally, another fully connected layer is used, and the output is activated using the Sigmoid function to achieve image reconstruction. The model is trained using the mean squared error loss function and the Adam optimizer. The network parameters are optimized over five training cycles.

[0038] Step 32: Obtaining potential feature vectors;

[0039] After training is completed, the encoder part of the DAE is extracted to obtain the representation of the input data in the latent space, that is, the latent feature vector;

[0040] Step 33: Cluster the extracted potential features using the K-Means algorithm;

[0041] The K-Means method calculates the Euclidean distance between the sample and the cluster center and iteratively updates the cluster center until convergence; the number of clusters is set to the optimal number of clusters and initialized with a random seed;

[0042] Step 34: Visualize and analyze the clustering results;

[0043] Use the PCA method to reduce high-dimensional features to two dimensions and draw a scatter plot to intuitively display the distribution of each cluster; different colors represent different cluster categories to evaluate the separability of feature distribution;

[0044] Step 35: Evaluate clustering effect;

[0045] Calculate the CH index and DBI index to measure the inter-cluster distance and intra-cluster compactness; customize the calculation of inter-cluster distance and intra-cluster distance, and calculate the intra-cluster to inter-cluster distance ratio to evaluate the overall quality of clustering.

[0046] Compared with the prior art, the present invention has the following beneficial effects:

[0047] Based on the deep network and clustering model, this paper proposes a new method that uses deep autoencoders (DAE) for feature extraction and uses the K-means method for clustering. First, the data is preprocessed, including data enhancement, normalization and standardization, to improve the generalization of the model; then the data is input into the model and the number of clusters is changed. kThe optimal number of clusters is determined by comparing the CH index, DBI index, and intra-cluster and inter-cluster distance ratio. The preprocessed image is then fed into the DAE for feature extraction. The extracted latent features are clustered using the K-Means algorithm, and cluster centers are iteratively updated until convergence. This method lays a key foundation for the accurate identification of large numbers of valid samples and is of great significance in promoting the development of intelligent medical instruments and improving their detection performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1 Microscopic images of some urine sediment impurity samples.

[0049] Figure 2 Flowchart of image preprocessing.

[0050] Figure 3 Flowchart for determining the optimal number of clusters.

[0051] Figure 4 Flowchart for extracting features and clustering impurity samples.

[0052] Figure 5 Flow chart of the method of the present invention.

[0053] Figure 6 These are microscopic images of some pre-processed urine sediment samples containing tangible impurities; (a) is the original cluster image, (b) is the cluster image enhanced using the random horizontal flipping technique, and (c) is the cluster image enhanced using the random cropping technique.

[0054] Figure 7 is the number of clusters k Relationship curve with performance indicators.

[0055] Figure 8 The following are comparison diagrams of the PCA dimensionality reduction scatter plots of five clustering methods; (a) is the K-means PCA dimensionality reduction scatter plot, (b) is the SC PCA dimensionality reduction scatter plot, (c) is the AE PCA dimensionality reduction scatter plot, (d) is the DDC PCA dimensionality reduction scatter plot, and (e) is the DAE PCA dimensionality reduction scatter plot. DETAILED DESCRIPTION

[0056] In order to have a clearer understanding of the technical features, objectives and beneficial effects of the present invention, the technical solution of the present invention is now described in detail below, but it should not be understood as limiting the scope of implementation of the present invention.

[0057] The present invention provides a method for intelligent clustering of urine sediment impurity microscopic images based on deep autoencoding, the flow chart of which is as follows: Figure 5 As shown, the method includes the following steps:

[0058] Step 1: Perform data augmentation, normalization, and standardization preprocessing on the microscopic images of urine sediment impurities. The goal is to reduce the influence of external factors such as lighting and contrast, allowing the model to focus on semantic features rather than brightness or color distribution. This also accelerates training and improves the convergence rate of gradient descent. The specific steps are as follows (see Figure 2 ):

[0059] Step 11: Training data processing, the specific operations are as follows:

[0060] Data augmentation: For training data, random cropping, horizontal flipping, color jittering, and random grayscale enhancement strategies are used. Through random cropping, a part of the image is randomly selected and resized to a specified size ( ) to increase data diversity and allow the model to learn objects of different scales; flip the image horizontally with a probability of 50% to enhance the model's adaptability to different perspectives; jitter the image color with a probability of 80% to change the brightness, contrast, saturation and hue to prevent the model from overfitting the color features; convert the color image to grayscale image with a probability of 20% to enable the model to extract information from the grayscale features.

[0061] Normalization: Convert the image to a PyTorch tensor to facilitate deep learning calculations in PyTorch. At the same time, the pixel value [0, 255] is normalized to [0, 1], making it more suitable for neural network training and gradient calculation.

[0062] Step 12: Test data processing;

[0063] Perform random cropping and normalization (same as the random cropping and normalization operations in training data processing) to ensure the stability and consistency of the test data.

[0064] Step 13: Standardization;

[0065] The normalized data is normalized by formula 1 so that the pixel values ​​of each channel obey the standard normal distribution:

[0066] Formula 1: ;

[0067] in is the normalized pixel value, is the original pixel value, is the mean used for normalization, is the standard deviation used for normalization.

[0068] Step 2: Calculate the performance index to determine the optimal number of clusters; the specific steps are as follows (see Figure 3 ):

[0069] Number of traversal clusters (Different numbers of clusters are processed in turn) and the three performance indicators, Davies-Bouldin index (DBI index), Calinski-Harabasz index (CH index) and intra-cluster and inter-cluster distance ratio, are calculated respectively. The calculation formulas are as follows:

[0070] Formula 2: ;

[0071] in is the number of clusters, It is a cluster The average distance inside It is a cluster The average distance inside It is a cluster and clusters The distance between them.

[0072] Formula 3: ;

[0073] in is the number of clusters, It is a cluster The number of data points, It is a cluster A set of data points, x It is a cluster Internal data points, It is a cluster The center of mass, is the centroid of the entire dataset, is the total number of data points.

[0074] Formula 4: ;

[0075] in is the ratio of the intra-cluster distance to the inter-cluster distance, is the number of clusters, It is a cluster and clusters The Euclidean distance between It is a cluster Euclidean distance from internal data points to the centroid; The number of clusters is k When , the number of combinations between any two categories.

[0076] The smaller the DBI index, the larger the CH index and the ratio of intra-cluster to inter-cluster distance, which means the clustering is dense and the clustering effect is better. k The DBI index, CH index and intra-cluster and inter-cluster distance ratio corresponding to the value are comprehensively compared to finally determine the optimal number of clusters .

[0077] The process of comprehensive comparison is: k The DBI index, CH index and intra-cluster and inter-cluster distance ratio corresponding to the value are normalized:

[0078] Formula 5: ;

[0079] in Represents a vector The minimum value in Represents a vector The maximum value in Indicates the value after normalization;

[0080] Based on the characteristic that the smaller the DBI index value, the higher the clustering density, the inverse operation is performed on it; the number of clusters is plotted k Draw a scatter plot of the relationship between each performance indicator, calculate the points in each performance indicator curve where the slope changes significantly (i.e., the absolute value of the slope exceeds the mean of the absolute value of the slope change), merge and remove duplicates from the slope mutation points of all indicators, and perform frequency statistics on each cluster number - if a certain cluster number exists in the set of slope mutation points of a certain performance indicator, the count value of the cluster number is increased by 1; finally, the cluster number with the highest count value is determined as the optimal cluster number.

[0081] Step 3: Deep Autoencoder (DAE) intelligently acquires image features and performs K-means clustering;

[0082] After determining the optimal number of clusters, all impurity samples are trained using a deep clustering method based on DAE and K-means. The specific steps are as follows (see Figure 4 ):

[0083] Step 31: Add noise to the preprocessed image and input it into DAE for feature extraction;

[0084] In the DAE encoder, a fully connected layer first processes the input data, then applies a nonlinear transformation to the data using the ReLU activation function. This is followed by another fully connected layer to map the input data into a low-dimensional latent space. In the DAE decoder, a fully connected layer receives the latent space data from the encoder, applies a nonlinear transformation using the ReLU activation function, and then passes through another fully connected layer. Finally, the output is activated using the Sigmoid activation function to reconstruct the image. This process enables the model to learn data features while also providing denoising capabilities. The model is trained using the mean squared error (MSE) loss function and the Adam optimizer, optimizing network parameters over five training cycles.

[0085] Step 32: Obtaining potential feature vectors;

[0086] After training, the encoder portion of the DAE is extracted to obtain a representation of the input data in latent space, known as a latent feature vector. This vector, used as input for subsequent clustering analysis, can reduce redundant information in high-dimensional data and improve clustering stability.

[0087] Step 33: Cluster the extracted potential features using the K-Means algorithm;

[0088] The K-Means method calculates the Euclidean distance between the sample and the cluster center and iteratively updates the cluster center until convergence. The number of clusters is set to the optimal number of clusters and initialized with a random seed to ensure the reproducibility of the experiment.

[0089] Step 34: Visualize and analyze the clustering results;

[0090] Use PCA to reduce high-dimensional features to two dimensions and create a scatter plot to visually display the distribution of each cluster. Different colors represent different cluster categories to assess the separability of feature distribution.

[0091] Step 35: Evaluate clustering effect;

[0092] The CH index and DBI index are calculated to measure the distance between clusters and the compactness within clusters. In addition, the inter-cluster distance and intra-cluster distance are calculated by custom calculation, and the intra-cluster to inter-cluster distance ratio is calculated to evaluate the overall quality of clustering.

[0093] The specific implementation of the present invention is described in detail below with reference to specific embodiments. Example

[0094] The experimental environment configuration used in this embodiment is: Python version 3.11.4, CUDA version 12.3, Pytorch version 2.3.0, graphics card model RTX3050, and video memory 4GB.

[0095] We selected 40,089 microscopic images of viscous impurities in clinical urine sediment collected from different patients in different hospitals. Each image contained only a single impurity sample or partially overlapping samples. First, we preprocessed the collected sample images, including data enhancement, normalization, and standardization. Figure 6 The following figure shows the microscopic images of some urine sediment impurity samples after pretreatment; (a) is the original cluster image, (b) is the cluster image enhanced by random horizontal flipping technology, and (c) is the cluster image enhanced by random cropping technology. It can be seen that the image in (b) is horizontally flipped, and the upper left corner of the image in (c) is cropped, which increases the diversity of the data samples. The number of clusters is then adjusted. The optimal number of clusters is determined by comparing the DBI index, CH index and intra-cluster and inter-cluster distance ratio The specific data are shown in Table 1:

[0096] Table 1 Number of clusters k Relationship with various performance indicators

[0097]

[0098] Normalize the relationship between each performance index. Considering that the DBI index should be smaller, it is negated. Draw the number of clusters. and the relationship scatter plot of each performance indicator (such as Figure 7 As shown in the figure, calculate the points where the slope changes significantly (i.e., the absolute value of the slope exceeds the mean of the absolute value of the slope change) in each performance indicator. After merging and removing duplicates from the slope mutation points of all indicators, perform frequency statistics on each cluster number. If a cluster number exists in the slope mutation point set of a certain performance indicator, the cluster number count value is increased by 1. Finally, find the cluster number with the highest count value, use it as the optimal cluster number, and output it. After calculation, the optimal cluster number in this embodiment is 6. Determine the optimal cluster number Afterwards, all impurity samples are trained using a deep clustering method based on DAE and K-means. The specific operations are performed according to steps 31 to 35 of this method, where the number of clusters is set to 6 in step 33.

[0099] To compare the clustering effects, the present invention also uses the traditional K-means method, spectral clustering (SC), autoencoder (AE) and deep discriminative clustering (DDC) to cluster the microscopic images of the clinical urine sediment impurity samples. To ensure the same comparison conditions, the traditional K-means method, SC, AE and DDC divide all secretion impurity samples into six categories, and the number of parameter training times is 10. The scatter plots of the clustering results of the five clustering algorithms are drawn by PCA dimensionality reduction, as shown in the figure below. Figure 8 As shown, the horizontal axis represents the first principal component after PCA dimensionality reduction, the vertical axis represents the second principal component after PCA dimensionality reduction, and the color depth represents the clustering category. The performance indicators of each clustering algorithm are calculated, and the results are shown in Table 2:

[0100] Table 2 Performance indicators of five clustering algorithms

[0101]

[0102] From the performance index data, the DAE algorithm has the smallest DBI, the largest CH index and Ratio. Figure 8The PCA dimensionality reduction scatter plots of the various clustering algorithms show that while the K-means and SC scatter plots show a certain clustering trend, they are generally vague, with low inter-class distinction, making it difficult to clearly define different categories. AE's scatter plots are chaotic, with no clear cluster structure. DDC's scatter plots are too dispersed, making it difficult to clearly discern the cluster structure, resulting in unsatisfactory clustering results. DAE's scatter plots exhibit a distinct linear distribution, and compared to the other plots, the data points have a certain distribution pattern, which allows for distinguishing different data regions to a certain extent, with a more pronounced clustering trend for similar data. Overall, the DAE method achieves the best clustering results, effectively demonstrating the effectiveness of the DAE algorithm for clustering urine sediment impurities.

[0103] The above are only preferred embodiments of the present invention. It should be pointed out that for those skilled in the art, several variations and improvements can be made without departing from the concept of the present invention. These should also be regarded as the scope of protection of the present invention. These will not affect the effect of the implementation of the present invention and the practicality of the patent.

Claims

1. A method for intelligent clustering of urine sediment impurity microscopic images based on deep autoencoding, characterized in that: The following steps are involved: Step 1: Data enhancement, normalization and standardization preprocessing of the microscopic image of urine sediment visible component impurities sample; Step 2: Calculate the performance index to determine the optimal number of clusters; By adjusting the number of clusters k , compare the DBI index, CH index and intra-cluster and inter-cluster distance ratio to determine the optimal number of clusters; Step 3: The deep autoencoder intelligently acquires image features and performs K-means clustering; After determining the optimal number of clusters, all impurity samples are trained using a deep clustering method based on deep autoencoders and K-means; The specific steps of step 3 are as follows: Step 31: Add noise to the preprocessed image and input it into DAE for feature extraction; In the encoder part of the DAE, the input data is first processed by a fully connected layer, followed by a nonlinear transformation using the ReLU activation function. Then, another fully connected layer is used to map the input data to a low-dimensional latent space. In the decoder part of the DAE, the latent space data from the encoder is first received by a fully connected layer, then nonlinearly transformed using the ReLU activation function. Finally, another fully connected layer is used, and the output is activated using the Sigmoid function to achieve image reconstruction. The model is trained using the mean squared error loss function and the Adam optimizer. The network parameters are optimized over five training cycles. Step 32: Obtaining potential feature vectors; After training is completed, the encoder part of the DAE is extracted to obtain the representation of the input data in the latent space, that is, the latent feature vector; Step 33: Cluster the extracted potential features using the K-Means algorithm; The K-Means method calculates the Euclidean distance between the sample and the cluster center and iteratively updates the cluster center until convergence; the number of clusters is set to the optimal number of clusters and initialized with a random seed; Step 34: Visualize and analyze the clustering results; Use the PCA method to reduce high-dimensional features to two dimensions and draw a scatter plot to intuitively display the distribution of each cluster; different colors represent different cluster categories to evaluate the separability of feature distribution; Step 35: Evaluate clustering effect; Calculate the CH index and DBI index to measure the inter-cluster distance and intra-cluster compactness; customize the calculation of inter-cluster distance and intra-cluster distance, and calculate the intra-cluster to inter-cluster distance ratio to evaluate the overall quality of clustering.

2. The method for intelligent clustering of urine sediment impurity microscopic images based on deep autoencoding according to claim 1, characterized in that: The specific steps of step 1 are as follows: Step 11: Training data processing, the specific operations are as follows: Data augmentation: For training data, random cropping, horizontal flipping, color jittering, and random grayscale augmentation strategies are used; Normalization: Convert the image to a PyTorch tensor Tensor and normalize the pixel values ​​from [0, 255] to [0, 1]; Step 12: Test data processing; Perform random cropping and normalization; Step 13: Standardization; The normalized data is normalized by formula 1 so that the pixel values ​​of each channel obey the standard normal distribution: Formula 1: ; in is the normalized pixel value, is the original pixel value, is the mean used for normalization, is the standard deviation used for normalization.

3. The method for intelligent clustering of urine sediment impurity microscopic images based on deep autoencoding according to claim 2, characterized in that: In the data augmentation step, a portion of the image is randomly selected and resized to a specified size through random cropping; the image is horizontally flipped with a probability of 50%; the image is color-dithered to change brightness, contrast, saturation, and hue with a probability of 80%; and the color image is converted to a grayscale image with a probability of 20%.

4. The method for intelligent clustering of urine sediment impurity microscopic images based on deep autoencoding according to claim 1, characterized in that: In step 2, the calculation formulas for the DBI index, CH index, and intra-cluster and inter-cluster distance ratio are as follows: Formula 2: ; in is the number of clusters, It is a cluster The average distance inside It is a cluster The average distance inside It is a cluster and clusters the distance between them; Formula 3: ; in It is a cluster The number of data points, It is a cluster A set of data points, x It is a cluster Internal data points, It is a cluster The center of mass, is the centroid of the entire dataset, is the total number of data points; Formula 4: ; in is the ratio of the intra-cluster distance to the inter-cluster distance, It is a cluster and clusters The Euclidean distance between It is a cluster Euclidean distance from internal data points to the centroid; The number of clusters is k When , the number of combinations between any two categories; The calculated difference k The DBI index, CH index and intra-cluster and inter-cluster distance ratio corresponding to the value are comprehensively compared to finally determine the optimal number of clusters ; The process of comprehensive comparison is: k The DBI index, CH index and intra-cluster and inter-cluster distance ratio corresponding to the value are normalized. Based on the characteristic that the smaller the DBI index value, the higher the clustering density, the inverse operation is performed on it; the number of clusters is plotted. k A scatter plot of the relationship between the performance indicators is drawn, and the points in the performance indicator curve where the absolute value of the slope exceeds the preset threshold are calculated. After the slope mutation points of all indicators are merged and deduplicated, the frequency of each cluster number is counted. If the cluster number exists in the slope mutation point set of any performance indicator, the count value of the cluster number is increased by 1; finally, the cluster number with the highest count value is determined as the optimal cluster number.

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