Data quantitative analysis and factor analysis method

Abstract

The invention relates to a data quantitative analysis and factor analysis method. According to the technical scheme, the method comprises the following steps: firstly, classifying original data, and identifying uniform distribution, skewed distribution and periodic distribution; according to the data distribution, generating a dynamic quantitative standard through a variational auto-encoder VAE model; quantizing the data according to the generated standard, so that each data point is mapped to a quantized value conforming to the feature; taking the quantized data as input; establishing a model for capturing a nonlinear factor relationship in data by introducing a deep neural network; extracting potential factors of the data through an optimization algorithm; combining the output of the self-adaptive data quantification method and the input of the factor analysis method, and sharing learning information by the self-adaptive data quantification method and the factor analysis method through collaborative learning; a multi-task learning MTL algorithm is adopted, so that data quantification and factor analysis are mutually constrained in the training process; the quantitative standard and factor extraction are alternately optimized, so that the quantitative standard and factor extraction complement each other in the whole analysis process.

Description

Technical Field

[0001] The invention relates to data quantitative analysis and factor analysis methods. Background Art

[0002] Although the methods currently used in the market for data quantitative analysis and factor analysis have improved the efficiency of data analysis to a certain extent, there are still many deficiencies and drawbacks. These problems hinder the effectiveness of data-driven decision support systems in practical applications, especially when dealing with complex data sets, dynamic market environments, and high-dimensional nonlinear data analysis. The following will combine the deficiencies of the existing technology, especially the method represented by China Invention Publication No. CN114549076A, to elaborate in detail.

[0003] First, the method of comparing public documents mainly obtains various product information, customer information and competitive product information data of enterprises to conduct big data quantitative analysis of business management. Its advantage is that it can quickly improve the efficiency of competitive product analysis and customer demand analysis. However, this method mainly relies on the extraction and summary analysis of static data, and it is difficult to handle complex data distribution and multi-dimensional, highly nonlinear customer behavior data. In practical applications, enterprise data is often dynamic and complex. For example, the market environment will fluctuate with time, seasons, and policies, and customer preferences and behavior patterns will also change constantly. Traditional quantitative analysis methods based on data aggregation can often only process static data sets and lack the ability to respond flexibly to dynamically changing data. This will lead to the inability to capture the latest market trends in a rapidly changing market scenario, thus missing business opportunities. Secondly, the method of comparing public documents mainly relies on data screening and aggregation algorithms based on preset rules. Although this type of method has certain advantages in scenarios with small data volumes and relatively single features, it is prone to the curse of dimensionality when facing complex data sets with high dimensions and multiple variables. Traditional quantitative analysis methods usually assume that data features are linearly independent, while real business data often contains multiple nonlinear relationships and implicit factors. For example, the purchasing behavior of customers is not only affected by price, but also by multiple factors such as promotion, brand preference, seasonal demand, etc., and the interactions between these factors are often nonlinear. Traditional methods based on linear regression or rule algorithms cannot effectively capture these implicit nonlinear relationships, resulting in a lack of depth and accuracy in the analysis results, which in turn affects the scientific nature of subsequent decisions. Furthermore, the schemes compared with public documents mainly rely on the visualization of data during data processing, rather than in-depth data modeling and factor extraction. Although data visualization can help companies understand market trends more intuitively, it essentially remains at the level of surface data display and cannot deeply explore the potential patterns and hidden factors behind the data. In the modern business environment, decision support methods that rely solely on visual analysis often lack sufficient intelligence and automation, especially in the face of high-frequency data updates and large amounts of unstructured data (such as social media comments, customer feedback), their limitations become increasingly obvious. In addition, existing visualization methods often rely on pre-defined indicators and charts, and the setting of these indicators usually requires empirical judgment, which makes it difficult to flexibly adapt to the rapidly changing market environment. In contrast, the present invention, by introducing the variational autoencoder (VAE) and multi-task learning (MTL) framework, can dynamically adjust the quantization standard and factor extraction process during data quantization and factor analysis, more flexibly respond to changes in complex data sets, and at the same time improve the depth and breadth of data analysis.

[0004] In addition, the method of comparing public documents mainly focuses on the analysis of existing data within the enterprise, and does not fully consider how to predict future trends and market demands through data modeling. Although this method can improve the efficiency of competitive product analysis and customer demand analysis, it mainly focuses on the summary and review of historical data, and lacks the ability to predict the future. In a highly competitive market environment, companies not only need to understand the current market situation, but also need to be able to predict future market trends in advance in order to gain an advantage in the competition. Traditional methods based on static data analysis cannot respond quickly to market changes, especially when encountering emergencies or market fluctuations, and the effect of their decision support is often unsatisfactory. In contrast, the present invention combines the VAE model with factor analysis to effectively extract the potential factors of the data, and establish a prediction model based on these factors, thereby helping companies achieve more accurate market positioning and strategic decision-making in a dynamic market environment. Summary of the invention

[0005] The purpose of the present invention is to provide a data quantitative analysis and factor analysis method, so as to solve some of the drawbacks and shortcomings pointed out in the background technology.

[0006] The present invention solves the above-mentioned technical problems by adopting the following technical solution, which includes the following steps:

[0007] S1. Adaptive data quantization:

[0008] S1.1. First, classify the original data and identify uniform distribution, skewed distribution, and periodic distribution;

[0009] S1.2. Generate dynamic quantization standards through the variational autoencoder VAE model according to data distribution;

[0010] S1.3, quantize the data according to the generated standard so that each data point is mapped to a quantitative value that meets the characteristics;

[0011] S2. Data dimensionality reduction and feature extraction based on factor analysis:

[0012] S2.1, take the data quantized in S1.3 as input;

[0013] S2.2. Establish a model that captures the nonlinear factor relationship in the data by introducing deep neural networks;

[0014] S2.3, extracting latent factors from data through optimization algorithms;

[0015] S3. Jointly optimized factor analysis and data quantification model:

[0016] S3.1. First, the output of the adaptive data quantization method and the input of the factor analysis method are combined, and the two share learning information through collaborative learning;

[0017] S3.2, adopting the multi-task learning MTL algorithm, so that data quantification and factor analysis constrain each other during the training process;

[0018] S3.3. By alternately optimizing the quantitative criteria and factor extraction, the two complement each other in the entire analysis process;

[0019] S3.4. After joint optimization, the model outputs the quantified data and extracted factors, and uses the factor analysis results to adjust the quantification criteria;

[0020] S4. Quantitative expression of factor analysis results and decision support:

[0021] S4.1. Convert the factors extracted from factor analysis into quantifiable indicators and standardize them to meet the decision-making needs of specific fields;

[0022] S4.2. Construct a quantitative prediction model based on the transformed factors and use regression analysis to predict decision results;

[0023] S4.3. Integrate the quantified factor analysis results into the decision support system to form a complete decision-making basis and provide intelligent decision support based on data quantification and factor analysis.

[0024] Furthermore, the adaptive data quantization method includes:

[0025] The VAE model is used to model the latent space of the data and learn the distribution characteristics of the data. The VAE captures the latent factors of the data through the encoder, maps them to the latent space, and then generates the corresponding quantization standard through the decoder. The quantization standard is generated dynamically during the process, and the quantization standard generation formula is as follows:

[0026]

[0027] in: represents the value obtained after quantizing the data point x; value represents the new value of the data point x after transformation, ranging from 0 to 1; σ(·) is the sigmoid function, that is, Used to map quantized values ​​to a standardized range; It is the integral from the data point x to the quantization standard boundaries a(x) and b(x), where f(t) is the probability density function of the data point x in the latent space; the size of the quantization interval corresponding to the data point x; a(x) and b(x) are the lower and upper bounds of the data point x in the quantization process, respectively.

[0028] Furthermore, the adaptive data quantization method includes:

[0029] The VAE model learns the potential representation of the input data, identifies patterns in the data distribution including peaks, skewness, or periodic changes, and optimizes the quantization criteria so that the quantization process captures the details of the data. The representation of the latent space is given by the following formula:

[0030]

[0031] Where: z(x) is the mapping of data point x in the latent space; through the VAE model, the data point x is transformed into a representation z(x) in the latent space, which captures the potential characteristics of the data; x is the input dataset, which contains all the original data points used to train the model; P θ (z|x) is the conditional probability distribution, which represents the probability distribution of the latent variable z given a data point x; here, θ is the model parameter including the weights of the encoder and decoder, which represents the structure of the latent space learned based on the input data x; dθ is the integration of the model parameters θ, which represents the adjustment of the latent space representation by optimizing the training process.

[0032] Furthermore, the adaptive data quantization method includes:

[0033] By adopting a joint optimization approach, we combine the potential representation of VAE with the generation of quantization criteria, so that the quantization value of each data point conforms to the characteristics of the latent space and adapts to changes in the data distribution. We introduce the following calculus optimization method to form an adaptive feedback mechanism between the learning of the latent space and the minimization of the quantization error:

[0034]

[0035] in, is the optimization objective function, which represents the loss function in the quantization process; the loss function measures the difference between the quantized data and the original data and guides the optimization of the latent space representation; N is the total number of data points; x i is the ith data point, is the quantized data point value; by comparing the quantized value With the original data point value x i The difference between them is used to evaluate the accuracy of quantization; It is the square of the quantization error, which indicates the gap between the quantized data and the original data; dx is the integral of all data points, which indicates the sum of the quantization errors over the entire data set.

[0036] Furthermore, the method for establishing the jointly optimized factor analysis and data quantification model is as follows:

[0037] Using the multi-task learning MTL framework, through the mechanism of alternating optimization, the generation of quantitative standards and factor extraction are mutually constrained in the same process; in each training iteration, the parameters of the quantization module are first updated to generate new quantitative standards; then the updated quantitative data are input into the factor analysis module to extract potential factors; according to the results of factor analysis, the quantitative standards are dynamically adjusted in turn; the formula is described as:

[0038]

[0039] in, is the adjusted quantization value, which represents the discretization of the data point x generated by the optimized quantization standard; φ is a nonlinear adjustment function, which is used to map the integral result to the quantization space; h(t) is the distribution weight function of the potential factor, which represents the influence of the potential factor at time y on the data quantization; g(x) is the influencing factor of the data feature, which reflects the influence of the input data x on the quantization standard; c(x) and d(x) are the upper and lower limits of the quantization interval of the data point x. The integral term represents the contribution of the cumulative potential factors to the data within the quantitative interval.

[0040] Furthermore, the method for establishing the jointly optimized factor analysis and data quantification model is as follows:

[0041] By introducing a joint loss function, the data quantization error and the reconstruction error of factor analysis are integrated for collaborative optimization; the goal of data quantization is to map the original data to discrete values, and the joint loss function contains two main parts: data quantization error and factor reconstruction error; the quantization error measures the difference between the quantized data and the original data, while the factor reconstruction error evaluates the degree of match between the potential factors extracted by the factor analysis module and the original data structure; the formula is described as:

[0042]

[0043] in, is a joint loss function that measures the overall optimization goal of data quantization and factor analysis; by minimizing this loss function, the simultaneous optimization of data quantization and factor analysis is achieved; α is the weight coefficient of the quantization error, which is used to adjust the importance of data quantization and factor analysis in optimization; is the data quantization error, indicating the quantized data value The absolute difference between β and the original data x; β is the weight coefficient of factor analysis error, which controls the influence of factor extraction accuracy on overall optimization; z(x) is the potential factor extracted by the factor analysis module; y(x) is the target factor representation, which is used to measure the difference between the factor analysis result and the actual data structure; ||z(x)-y(x)|| 2is the factor reconstruction error, which represents the Euclidean distance between the extracted latent factors and the original factors.

[0044] Furthermore, the method for establishing the jointly optimized factor analysis and data quantification model is as follows:

[0045] An alternating training strategy is adopted. In each training cycle, the parameters of the quantization task are optimized first, and then the quantization parameters are fixed and the parameters of the factor analysis module are optimized. The alternating optimization strategy controls each task to be optimized independently in the shared feature space, while benefiting from the adjustment of the other. The update of the quantization task will directly affect the factor analysis module, and the result of the factor analysis will in turn guide the adjustment of the quantization standard. The formula is described as:

[0046]

[0047] in, is the update increment of the quantization standard, which is used to adjust the parameters of the quantization process in each iteration; γ is the learning rate, which controls the step size of the quantization standard update; f(z) is the potential factor feedback function, which represents the feedback effect of factor z on the quantization standard; is the partial derivative of the quantization standard with respect to the input data x; The integral represents the cumulative feedback effect on the entire data set and is used to adjust the quantification standard.

[0048] The data quantitative analysis and factor analysis method of the present invention has the following significant beneficial effects:

[0049] By introducing the variational autoencoder (VAE) model, adaptive quantization method and factor analysis technology, the present invention can accurately quantize complex data and reduce information loss by extracting potential factors. Compared with the traditional static quantization method, the present invention dynamically adjusts the quantization standard to make data quantization more in line with the actual distribution, thereby improving the accuracy and efficiency of data analysis.

[0050] The multi-task learning (MTL) framework and alternating training strategy are used to organically combine data quantification and factor analysis tasks. The adjustment of the quantification standard and the factor extraction process interact with each other, and by jointly optimizing the loss function, the quantified data and the extracted factors more accurately reflect the intrinsic characteristics of the data. Compared with the independent data processing and factor analysis in traditional methods, this method significantly improves the overall performance and reliability of data processing.

[0051] Through VAE and joint optimization mechanism, the present invention can maintain high analysis accuracy when the data distribution is complex or dynamically changing. Especially when processing high-dimensional, nonlinear or periodic data, the method can effectively extract hidden features and generate adaptive quantitative standards to ensure the robustness of the analysis results. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] Figure 1 It is a flow chart of the data quantitative analysis and factor analysis method of the present invention.

[0053] Figure 2 This is a flow chart of the adaptive data quantization method of the present invention.

[0054] Figure 3 The present invention is a flowchart of a method for establishing a jointly optimized factor analysis and data quantification model. DETAILED DESCRIPTION

[0055] The specific implementation modes of the present invention will be described in detail below in conjunction with the accompanying drawings.

[0056] Combined with Figure 1 , the implementation steps of data quantitative analysis and factor analysis methods include the following core steps:

[0057] S1. Adaptive data quantization: First, the original data set is preprocessed and classified to identify the distribution characteristics of the data. This includes identifying whether the data presents characteristics such as uniform distribution, skewed distribution or periodic distribution. In the data classification stage, statistical methods and distribution analysis tools are used to detect the shape, central tendency and fluctuation pattern of the data to determine the distribution type of the data. After identifying the data distribution type, the variational autoencoder (VAE) model is used to generate adaptive dynamic quantization standards. The VAE model learns the potential distribution of the data through its encoder and decoder structure and performs probabilistic modeling on the data. Specifically, the encoder part of the VAE first maps the input data into the latent space to generate the latent representation of the data; then, the decoder reconstructs the data from the latent space to capture the implicit structural characteristics of the input data. In this way, the VAE can identify the complex distribution characteristics of the data and generate a quantization standard that matches it. The original data is quantized according to the dynamic quantization standard generated by the VAE model. The core of the quantization process is to map the data to a suitable discrete interval based on the latent characteristics and distribution pattern of the data, thereby improving the representation accuracy of the data. Each data point is mapped to a quantization value interval that conforms to its distribution characteristics according to the generated quantization standard to ensure that information loss is minimized during the quantization process. For example, for data with skewed distribution, the quantization standard will automatically adjust the interval density, using finer quantization levels in high-frequency areas and looser quantization intervals in low-frequency areas to fully retain the effective information of the data. Ultimately, the results of adaptive quantization make the data more representative and accurate in the subsequent factor analysis steps, thereby providing higher quality data input for further analysis.

[0058] The second step of the data quantification analysis and factor analysis method is data dimensionality reduction and feature extraction based on factor analysis. First, the data that has been adaptively quantized in the previous step is used as input to ensure that the input data maintains the consistency and integrity of the data features after quantization. On this basis, a deep neural network (DNN) is introduced to establish an analysis model that can capture the nonlinear factor relationship in the data. Traditional factor analysis methods usually assume that there is a linear relationship between the factors of the data, which has great limitations when processing high-dimensional and complex data sets. Therefore, the use of deep neural networks in this step can effectively overcome these limitations. Specifically, the multi-layer structure and nonlinear activation function of the deep neural network model can better capture the potential nonlinear relationship in the data, thereby deeply mining the hidden patterns in the data. In order to further improve the accuracy and stability of the model, feature learning is performed on the input quantized data. The first few layers of the network are used to extract the underlying features of the data, while the subsequent layers focus on identifying the potential factor structure of the data. In the process of factor extraction, optimization algorithms (such as gradient descent, Adam optimization algorithm, etc.) are used to adjust the parameters of the deep neural network to minimize the data reconstruction error and improve the accuracy of factor extraction. Through this optimization method, the model can gradually converge to the optimal latent factor representation, thereby extracting low-dimensional factors with explanatory power from high-dimensional data. These latent factors can not only effectively reduce the dimension of the data, but also retain the key features in the data, improving the efficiency and accuracy of data analysis and subsequent tasks.

[0059] The third step of the data quantization analysis and factor analysis method is to jointly optimize the factor analysis and data quantization model. First, the adaptive data quantization results generated in the first two steps are organically combined with the input data of the factor analysis model to ensure the consistency and integrity of the data in the subsequent analysis process. By combining the adaptively quantized data with the factor analysis input, the collaborative learning of the two can be achieved, so that the data quantization module and the factor analysis module share learning information under the same framework, thereby improving the overall analysis effect. In order to further improve the analytical ability of the model, this step adopts the multi-task learning (MTL) algorithm so that data quantization and factor analysis constrain each other during the training process. Specifically, the multi-task learning framework allows data quantization and factor analysis modules to share some model parameters, so that the two tasks can influence each other during the training process. For example, when the quantization module adjusts the discretization standard of the data, the factor analysis module will promptly adjust the factor extraction strategy to ensure that more representative potential factors are extracted from the new data distribution. In order to achieve this collaborative optimization, an alternating optimization strategy is adopted, that is, in each training iteration, the quantization standard is first updated, and then the parameters of the factor analysis module are readjusted based on the new quantization data. Conversely, when the factor analysis module discovers important latent factors in the data, it will in turn adjust the standards of the quantization module to make the data quantization process more in line with the actual feature distribution. This alternating optimization strategy ensures that the data quantization and factor analysis modules complement each other throughout the training process, thereby achieving an overall optimization effect. After multiple rounds of joint optimization, the model finally outputs the quantized data and the latent factors extracted from the data. While obtaining the factor analysis results, the results of these factor analyses are further used to adjust the quantization standards to improve the accuracy and stability of the overall data processing.

[0060] The fourth step of data quantitative analysis and factor analysis methods is the quantitative expression and decision support of factor analysis results. First, the potential factors extracted from the previous step of factor analysis are converted into quantifiable indicators. This conversion process aims to concretize the abstract results of factor analysis so that they can be better used in practical application scenarios. In order to ensure that the converted factor indicators can adapt to the decision-making needs of specific fields, these indicators need to be standardized, including adjusting their scale and distribution so that the impact of different factors can be compared on a unified quantitative scale. This standardization process can not only eliminate the dimensional differences between different factors, but also improve the consistency and accuracy of factor indicators in prediction and decision-making. Next, based on the converted and standardized factor indicators, a quantitative prediction model is constructed. Regression analysis methods are usually used to establish these prediction models to make full use of the information in the factor indicators to predict decision results. For example, linear regression, ridge regression or other more complex machine learning regression algorithms can be used to predict the change trend or future results of the target variable based on the factor indicators. These prediction models can help identify the contribution of different factors to the decision results, thereby providing a scientific basis for decision-making in the fields of enterprise, finance, and medical care. Finally, the quantified factor analysis results are integrated into the decision support system to make it a core component of intelligent decision support. At this stage, the factor indicators that have undergone standardization and regression analysis will be integrated into the decision-making system database to form a complete basis for decision-making. By combining the results of factor analysis with actual business needs, the system can automatically generate data-driven decision recommendations, thereby helping decision makers to formulate strategic plans more efficiently.

[0061] Embodiment 1:

[0062] Combined with Figure 2 , assume that a large supermarket chain wants to analyze its customer behavior data to improve marketing effectiveness and optimize commodity inventory management. The supermarket has accumulated a large amount of customer transaction data, including each customer's purchase record, purchase frequency, time interval, purchased commodity category and other information. Due to the large amount of data and complex distribution (including uniform distribution, skewed distribution and periodic fluctuations), traditional data processing methods are difficult to effectively mine potential patterns. Therefore, the supermarket decided to adopt the data quantification analysis and factor analysis method of the present invention, adaptively quantize customer data through the variational autoencoder (VAE) model, and extract the potential features hidden behind the data in combination with factor analysis technology to optimize marketing strategies and inventory management.

[0063] S1: Application of Adaptive Data Quantization Methods

[0064] First, the supermarket uses the VAE model to model the latent space of its customer data. Since customer purchasing behavior has obvious time and product category preferences, it is necessary to capture the latent factors of the data through the encoder part of the VAE to identify customer behavior patterns. VAE maps high-dimensional raw data (such as purchase frequency, product category, purchase amount) to a low-dimensional representation in the latent space through the encoder, and reconstructs the data through the decoder to learn the distribution characteristics of the data. The quantization standard generated by the VAE model is used to adaptively quantize customer behavior data to ensure that important features of the data are retained during the quantization process. Specifically, the quantization standard generated by VAE uses the following formula:

[0065]

[0066] Formula explanation:

[0067] The value obtained after quantizing the customer behavior data point x represents the new value of the data after the quantization transformation, ranging from 0 to 1.

[0068] σ(·): is the sigmoid function, that is Used to map quantized values ​​to a normalized range to ensure that the output values ​​are between 0 and 1.

[0069] It is the integral from the data point x to the quantization standard boundaries a(x) and b(x), where f(t) is the probability density function of the data point x in the latent space, reflecting the distribution density of the data in this interval.

[0070] a(x) and b(x): are the upper and lower limits of the quantization interval, respectively, and are dynamically adjusted according to the behavioral characteristics of different customers.

[0071] The supermarket is set to analyze the following three dimensions of data: customer purchase frequency (number of purchases per month), purchase amount (average amount of each purchase), and purchase category (product variety). The supermarket models these data through VAE and obtains the following parameters: the distribution characteristics of purchase frequency are positively skewed, the purchase amount is uniformly distributed, and the distribution of purchase categories shows periodic fluctuations.

[0072] The quantitative interval of purchase frequency is set to 2.15 times / month, the quantitative interval of purchase amount is set to 50,500 yuan, and the quantitative interval of purchase category is set to 1.10 categories.

[0073] For purchase frequency, set The integral result is 0.8. After the sigmoid function transformation, we get The value is 0.69.

[0074] Substitute into the formula to calculate:

[0075]

[0076] Therefore, the quantitative value of the customer's purchase frequency is 0.69, which indicates that the customer's purchase frequency is close to the upper range of the overall customer base, and thus it can be inferred that the customer's purchase activity is relatively high.

[0077] S2: Data Dimensionality Reduction and Feature Extraction for Factor Analysis

[0078] Using the adaptively quantified data as input, the supermarket then uses a deep neural network to build a model that captures the nonlinear factor relationships in customer data. The multi-layer structure of the neural network extracts the deep characteristics of customer behavior, such as potential factors such as purchase propensity, promotion sensitivity, and loyalty. These factors are extracted through an optimization algorithm to ensure that the extracted factors can effectively explain the changes in customer behavior data. After factor analysis, three key factors are extracted: promotion responsiveness (F1), product variety preference (F2), and seasonal demand fluctuations (F3).

[0079] S3: Factor analysis and data quantification for joint optimization

[0080] To further improve the analysis results, the supermarket jointly optimized the quantitative data and factor analysis results in the previous steps. Through the multi-task learning (MTL) algorithm, the quantitative criteria and factor extraction interact with each other during the training process. For example, when the factor analysis finds that some customers are highly responsive to promotions, the quantitative module will dynamically adjust the quantitative criteria of purchase frequency based on this information to highlight the importance of this feature. Conversely, when the quantitative module readjusts the quantitative criteria, the factor analysis module will re-optimize the extraction of potential factors based on the new data. After multiple rounds of alternating optimization, the supermarket obtained more accurate customer segmentation results.

[0081] S4: Quantitative expression of factor analysis results and decision support

[0082] After completing the joint optimization, the supermarket converts the extracted factors into quantifiable indicators and standardizes them. For example, the value of the promotion responsiveness factor F1 is standardized to the interval of 0,1 to facilitate comparison between different customers. Based on the standardized factors, the supermarket constructs a regression model to predict the customer's future purchasing behavior. In the regression analysis, the weight coefficient of the promotion responsiveness F1 is set to 0.4, the weight coefficient of the product diversity preference F2 is set to 0.3, and the weight coefficient of the seasonal demand fluctuation F3 is set to 0.3. The prediction formula is as follows:

[0083] Prediction score = 0.4 × F1 + 0.3 × F2 + 0.3 × F3

[0084] If a customer's factor score is F1 = 0.8, F2 = 0.6, F3 = 0.5, then its predicted score is:

[0085] Prediction score = 0.4 × 0.8 + 0.3 × 0.6 + 0.3 × 0.5 = 0.32 + 0.18 + 0.15 = 0.65

[0086] The prediction score is 0.65, indicating that the customer is a high-potential customer and suitable for further promotional activities. On this basis, the supermarket integrates the factor analysis results into its decision support system to help formulate more precise marketing strategies, such as personalized coupons, customized advertising, and inventory replenishment recommendations, thereby improving customer satisfaction and sales.

[0087] In order to further improve the effect of data quantification, the supermarket decided to use the VAE model to model the latent space of customer behavior data. First, the customer transaction data accumulated by the supermarket in the past year (including purchase frequency, purchase amount, seasonal preference, promotion response, etc.) was used as the input data set. The data show obvious cyclical changes and skewed distribution, especially during holiday promotions, when there are obvious peaks.

[0088] The core of the VAE model is to learn the latent representation of data through the encoder and decoder structure. The encoder part converts the high-dimensional original customer data x into a low-dimensional representation z(x) in the latent space to capture the implicit patterns and features in the data. In the decoder part, VAE converts z(x) back to approximate original data, thereby ensuring that the captured data features can accurately reflect the real behavior of customers. The latent space representation of the VAE model can be described by the following formula:

[0089]

[0090] Among them, z(x) is the mapping of the data point x in the latent space, which represents the low-dimensional latent features after conversion by the VAE model. is the input dataset, which contains all customer transaction data points used for training. θ (z|x) is the conditional probability distribution, which represents the probability distribution of the latent variable z given a data point x. This reflects how the model learns the underlying pattern of customer behavior based on the input data. θ is the model parameter, including the weights of the encoder and decoder, which represents the structure of the latent space learned during the training process. dθ represents the integral of the model parameters, which is used to adjust the latent space representation by optimizing the training process to make the model more accurate.

[0091] Substitute actual data into the example calculation

[0092] In order to verify the effectiveness of the model, the supermarket chooses to analyze the purchasing behavior data of a specific customer group within a certain quarter. Set the input data set Contains the following information:

[0093] Customer A: The average number of purchases per month is 8, the purchase amount is between RMB 200-400, and the seasonal preference is concentrated in the summer and holiday promotions.

[0094] Customer B: The average number of purchases per month is 3, but the amount of each purchase is high, usually more than 600 yuan, and the response to promotions is low.

[0095] Customer C: His purchasing behavior is unstable, but there will be peak purchases during promotions, and he usually purchases a variety of product categories.

[0096] After modeling the latent space of these data through the VAE model, the following latent representation is obtained:

[0097] For customer A, the latent space representation z of the VAE model A (x) shows its high responsiveness to promotions and seasonal products and captures the cyclical changes in its purchase frequency. For customer B, the latent representation z B (x) shows that he prefers to buy high-value goods and is not sensitive to promotional activities. For customer C, the potential expression z C (x) reflects the instability of their purchasing behavior and their strong preference for different categories of goods.

[0098] After obtaining the latent space representation, the supermarket needs to optimize the data quantification standard based on the latent features in order to more accurately quantify customer behavior data. The quantification standard generated by VAE uses the following formula:

[0099]

[0100] Formula explanation:

[0101] The quantized data value is used to standardize customer behavior data to the range of 0,1.

[0102] σ(·): sigmoid function Used to normalize the integral result so that it falls between 0 and 1.

[0103] The integral represents the distribution density of the data point x in the quantization interval [a(x), b(x)], and f(t) is the probability density function of the data point in the latent space.

[0104] a(x), b(x): are the upper and lower limits of the quantization interval, respectively. These intervals are dynamically adjusted according to the distribution characteristics of customer data.

[0105] Assume that the density function of customer A's purchase frequency in the latent space is f(t) = 0.7, and the integral interval is [a(x), b(x)] = [0.5, 1.5]. Then according to the formula:

[0106]

[0107] Then substitute the integral result into the sigmoid function:

[0108]

[0109] Therefore, after VAE modeling and quantification, the purchase frequency of customer A is 0.67, which indicates that his purchase frequency is close to the upper level of the overall customer base, and supermarkets can formulate more precise promotion strategies for such high-frequency customers.

[0110] Through the above data analysis, supermarkets can better identify the different characteristics of customer groups. For example, for customer A with a higher quantitative value, supermarkets can push promotional information in a targeted manner and recommend seasonal products that match his purchasing behavior. For customer B with a lower quantitative value, the frequency of his purchases can be increased by increasing the discount for single large purchases. In addition, for customer C, whose purchasing behavior is unstable but active during the promotion period, supermarkets can push advertisements in a concentrated manner before the promotion to increase his purchase conversion rate.

[0111] In the previous analysis, the supermarket has successfully quantified and analyzed customer behavior data through the variational autoencoder (VAE) model and extracted key factors to optimize marketing strategies. In order to further improve the accuracy of data quantification and more effectively capture the potential patterns of customer behavior, the supermarket decided to adopt a joint optimization method to combine the potential representation of VAE with the generation of quantitative standards.

[0112] First, the supermarket introduced a joint optimization method based on VAE to further optimize the data quantization process. In the previous step, the VAE model has modeled the latent space of customer behavior data and generated preliminary quantization standards. However, in order to ensure that the quantized data values ​​maintain a higher degree of similarity with the original data, the supermarket decided to minimize the quantization error by introducing calculus optimization methods. Specifically, the supermarket uses the following loss function for optimization:

[0113]

[0114] Formula explanation:

[0115] represents the loss function of joint optimization, which is used to measure the difference between the quantized data and the original data. By minimizing this loss function, the accuracy of data quantization can be ensured. N: The total number of data points. Here, N=1000 is set, which means that the supermarket randomly selected 1000 customers' purchase records from the customer data of the past year for analysis. i : The i-th data point represents the purchasing behavior data of each customer, such as monthly purchase frequency, purchase amount, and promotion responsiveness. The quantized data point value represents the customer behavior data after conversion through VAE and quantification criteria. The square of the quantization error represents the difference between the quantized data value and the original data value. This part is used to evaluate the information loss in the quantization process. dx: The integral of all data points represents the sum over the entire data set to minimize the overall quantization error.

[0116] Substitute actual data into the example calculation:

[0117] Before optimization, the supermarket randomly selected 1,000 customers’ purchase data for modeling, including:

[0118] Customer A: The monthly purchase frequency is 10 times, the average purchase amount is 350 yuan, and the promotion responsiveness is 0.75.

[0119] Customer B: The monthly purchase frequency is 4 times, the average purchase amount is 700 yuan, and the promotion responsiveness is 0.3.

[0120] Customer C: Monthly purchase frequency is 6 times, average purchase amount is 150 yuan, and promotion responsiveness is 0.5.

[0121] The supermarket first uses VAE to preliminarily quantify these customer data and obtains preliminary quantitative values:

[0122]

[0123] Next, we use the joint optimization method to further adjust the quantitative standard. By substituting the actual data into the loss function, we set the original data value of customer A to x A =0.7, then the quantization error is:

[0124]

[0125] For Customer B:

[0126]

[0127] For Customer C:

[0128]

[0129] Sum and calculate the average error over all customer data:

[0130]

[0131] The overall integral result is set to 0.005. By minimizing the loss function, the supermarket can adjust the parameter θ of the VAE model to further reduce the quantization error.

[0132] Through the above joint optimization, the supermarket not only reduces the error of data quantification, but also further improves the understanding of customer behavior. Based on the optimized customer data, the supermarket can more accurately predict the customer's future purchasing behavior. For example, according to the optimized quantitative value: Customer A has a higher purchase frequency and promotion responsiveness, so the supermarket can push personalized coupons to him and recommend seasonal products that match his preferences. Although customer B has a lower purchase frequency, the single purchase amount is higher, so he can be provided with discounts for large consumption to increase his repurchase rate. Customer C has a significant purchase peak during the promotion period, so advertisements can be pushed to him on the eve of holidays and promotional seasons to increase his purchase conversion rate.

[0133] Embodiment 2:

[0134] Combined with Figure 3 In Example 1, the supermarket has previously processed the customer's purchase behavior data through variational autoencoders (VAE) and quantitative analysis methods, and extracted relevant factors for marketing decisions. However, in order to more accurately predict customer behavior, the supermarket management decided to adopt a multi-task learning (MTL) framework to achieve joint optimization of data quantification and factor analysis through an alternating optimization mechanism. The core of this method is to make the generation of quantitative standards and factor extraction mutually constrained in the same process, so as to more accurately reflect the potential characteristics of the data.

[0135] S1: Joint Optimization via Multi-Task Learning (MTL)

[0136] Under the multi-task learning framework, the supermarket first inputs the historical purchase data of all customers into the system, including monthly purchase frequency, purchase amount, promotion responsiveness, seasonal preferences, etc. To ensure the accuracy of data analysis, the system adjusts the quantitative standards and factor extraction process through an alternating optimization strategy.

[0137] In each training iteration, the parameters of the quantization module are first updated to generate the latest quantization standard. Specifically, for each data point x, its quantization value is calculated using the following formula:

[0138]

[0139] Formula explanation:

[0140] is the adjusted quantization value, which represents the discretization of the data point x generated by the optimized quantization standard. φ: nonlinear adjustment function, used to map the integral result to the quantization space. For example, The sigmoid function normalizes the result to the range of 0,1. h(t): The distribution weight function of the latent factor, which indicates the influence of the latent factor on the data quantification at time t. The value range is 0.1, 0.9, indicating the weight of the factor on the data. g(x): The influencing factor of the data feature, which reflects the influence of the input data x on the quantitative standard. The value range is usually 0.5, 2.0, which is used to adjust the contribution of different features to the quantitative results. c(x) and d(x): The upper and lower limits of the quantification interval of the data point x. For example, for the feature of monthly purchase frequency, set c(x) = 5 times / month and d(x) = 20 times / month. It indicates the contribution of the accumulated potential factors to the data within the quantitative interval and is used to dynamically adjust the quantitative standard.

[0141] Suppose the supermarket analyzes the data of the following three customers:

[0142] Customer A: Monthly purchase frequency is 12 times, purchase amount is RMB 300, and promotion responsiveness is 0.6.

[0143] Customer B: Monthly purchase frequency is 8 times, purchase amount is 500 yuan, and promotion responsiveness is 0.4.

[0144] Customer C: Monthly purchase frequency is 15 times, purchase amount is RMB 200, and promotion responsiveness is 0.7.

[0145] In order to optimize the quantitative standard, the supermarket first calculates the quantitative value

[0146] 1. For customer A, let h(t) = 0.7, g(x) = 1.5, and the quantization intervals be c(x) = 5, d(x) = 20. Calculate the integral term:

[0147]

[0148] Then a nonlinear adjustment function φ is applied:

[0149]

[0150] 2. For customer B, let h(t) = 0.5, g(x) = 1.2, and the quantization intervals be c(x) = 5, d(x) = 20. Calculate the integral term:

[0151]

[0152] Then a nonlinear adjustment function φ is applied:

[0153]

[0154] 3. For customer C, let h(t) = 0.8, g(x) = 1.8, and the quantization intervals be c(x) = 5, d(x) = 20. Calculate the integral term:

[0155]

[0156] Then a nonlinear adjustment function φ is applied:

[0157]

[0158] S2: Factor extraction and dynamic adjustment of quantitative standards

[0159] After completing the data quantification, the quantified data is input into the factor analysis module to extract potential factors. The supermarket found that:

[0160] The latent factors of customer A show that they have a higher responsiveness to seasonal promotions.

[0161] The factor analysis results of customer B show that he prefers high-priced goods and is not easily influenced by promotional activities.

[0162] Customer C's factor reflects a preference for low-priced promotional items, especially during holidays when purchase frequency increases.

[0163] Based on the results of factor analysis, the system dynamically adjusts the quantitative criteria. For example, when the system identifies that customer C is highly sensitive to promotions, the quantitative interval is adjusted to a more detailed range to capture his purchase fluctuations within a specific time period.

[0164] Through joint optimization analysis, supermarkets have obtained more accurate customer classification and prediction models. For example:

[0165] For customer A who makes frequent purchases and is highly responsive to promotions, personalized holiday promotion coupons can be pushed.

[0166] For customer B, the supermarket can recommend high-value products to him to increase the customer's single purchase amount.

[0167] For customer C, a limited-time discount notification can be sent on the eve of the promotion to increase his purchase conversion rate.

[0168] Through a multi-task learning framework and alternating optimization strategies, the supermarket has significantly improved the accuracy of data analysis, thereby improving the effectiveness of marketing campaigns and the efficiency of inventory management.

[0169] In the above analysis, the supermarket has successfully optimized the quantification and analysis of customer behavior data through multi-task learning (MTL) and latent factor extraction methods. However, the management hopes to further improve the accuracy of the model, especially in the coordinated optimization of data quantification and factor analysis. Therefore, the supermarket decided to introduce a joint loss function to integrate the data quantification error and the reconstruction error of factor analysis to further improve the accuracy of data processing.

[0170] In this optimization, the supermarket combines customer behavior data quantification with factor analysis, with the goal of minimizing the difference between the quantified data and the original data while improving the accuracy of the factor analysis. To this end, the supermarket introduces the following joint loss function:

[0171]

[0172] Formula explanation:

[0173] The joint loss function is used to measure the overall optimization goal of data quantization and factor analysis. By minimizing this loss function, the accuracy of quantization and factor extraction can be optimized simultaneously.

[0174] α: weight coefficient of quantization error, ranging from 0.3 to 0.7, used to adjust the impact of quantization error in overall optimization. Data quantization error, indicating the quantized data value The absolute difference between the original data x and the original data x, used to measure the accuracy of the quantization process. β: The weight coefficient of the factor analysis error, ranging from 0.5 to 1.0, is used to adjust the importance of factor extraction in optimization. z(x): The latent factor extracted by the factor analysis module, representing the implicit features extracted from the quantitative data. y(x): The target factor representation, used to measure the difference between the factor analysis results and the actual data structure. |z(x)-y(x)| 2 : Factor reconstruction error, which represents the Euclidean distance between the extracted latent factors and the target factors, is used to ensure the accuracy of factor extraction. dx: represents the integral of all data points, ensuring the sum of the loss function over the entire data set.

[0175] Suppose the supermarket chooses to analyze the data of the following three customers to further optimize its marketing strategy:

[0176] Customer A: Monthly purchase frequency is 12 times, average purchase amount is 400 yuan, and promotion responsiveness is 0.8.

[0177] Customer B: Monthly purchase frequency is 5 times, average purchase amount is RMB 600, and promotion responsiveness is 0.3.

[0178] Customer C: Monthly purchase frequency is 8 times, average purchase amount is RMB 250, and promotion responsiveness is 0.5.

[0179] The supermarket first processed the customer data through the VAE and factor analysis modules and obtained the following preliminary results:

[0180] Quantitative value of customer A Original data value x A =0.8, extract factor z(x A )=0.6,the target factor y(x A )=0.7.

[0181] Quantitative value of customer B Original data value x B =0.35, extract factor z(x B )=0.5,the target factor y(x B )=0.45.

[0182] Quantitative value of customer C Original data value x C =0.65, extract factor z(x C )=0.7,the target factor y(x C )=0.6.

[0183] The weight coefficients are set to α = 0.5 and β = 0.8. The supermarket calculates the loss function by substituting customer data.

[0184] 1. Quantization error and factor reconstruction error of customer A:

[0185]

[0186] |z(x A )-y(x A )| 2 =(0.6-0.7) 2 =0.01

[0187]

[0188] 2. Quantization error and factor reconstruction error of customer B:

[0189]

[0190] |z(x B )-y(x B )| 2 =(0.5-0.45) 2 =0.0025

[0191]

[0192] 3. Quantization error and factor reconstruction error of customer C:

[0193]

[0194] |z(x C )-y(x C )| 2 =(0.7-0.6) 2 =0.01

[0195]

[0196] Calculation of comprehensive loss:

[0197] In order to optimize the accuracy of overall data quantification and factor analysis, the supermarket performs a joint loss summation on all customer data:

[0198]

[0199] The supermarket adjusts the model parameters θ by minimizing the joint loss function, so that the quantization error and factor reconstruction error are further reduced.

[0200] By introducing the joint loss function, the supermarket can better optimize the results of data quantification and factor analysis at the same time. For example, according to the optimized factor analysis results:

[0201] For customer A, the system recognizes that he is highly responsive to promotions, so more frequent personalized coupons can be pushed. For customer B, because he prefers high-priced items and is not sensitive to promotions, the supermarket can recommend high-end items to him and reduce the interruption of promotional information. For customer C, the purchase fluctuations during the promotion period are identified, and the supermarket can send discount notifications in batches before the promotion season to improve the purchase conversion rate.

[0202] In the above optimization process, the supermarket has successfully integrated the data quantification and factor analysis modules through the joint loss function, thereby improving the accuracy of customer behavior analysis. However, in order to further optimize the performance of the model and ensure that data quantification and factor analysis can be adaptively adjusted in a dynamic environment, the supermarket decided to adopt an alternating training strategy. By alternating the optimization of the quantification task and the factor analysis module, the system can capture data features more efficiently and dynamically adjust the quantification criteria during the training process to better reflect the customer's behavioral characteristics.

[0203] The supermarket first inputs all customers' purchase data into the system, including monthly purchase frequency, purchase amount, seasonal preference, and promotion responsiveness. Under the multi-task learning (MTL) framework, the coordinated optimization of data quantification and factor analysis is ensured through an alternating training strategy. In each training cycle, the system first optimizes the parameters of the quantification task, then fixes the quantification parameters, and then optimizes the parameters of the factor analysis module. This alternating training strategy not only ensures that the two modules are independently optimized in the shared feature space, but also allows the adjustment of one task to directly affect the other task, thereby improving the overall analysis effect.

[0204] To implement this strategy, the supermarket uses the following formula to dynamically adjust the quantitative standards:

[0205]

[0206] Formula explanation:

[0207] Indicates the update increment of the quantization standard, which is used to adjust the parameters of the quantization task in each iteration. γ: Learning rate, which controls the step size of the quantization standard update. The value range is 0.01, 0.1, which is used to ensure the stability of the model during training. f(z): Latent factor feedback function, which indicates the feedback effect of factor z on the quantization standard. The value range is 0.5, 1.5, which is used to adjust the influence of the factor on the quantization adjustment. The partial derivative of the quantization standard with respect to the input data x is used to measure the sensitivity of the data features to the quantization standard. The integral represents the cumulative feedback effect on the entire dataset, ensuring that the quantification criterion is dynamically adjusted according to the data characteristics.

[0208] Substitute actual data into the example calculation

[0209] In this optimization, the supermarket selected the following three types of typical customers for testing:

[0210] Customer A: The monthly purchase frequency is 10 times, the average purchase amount is 300 yuan, and the promotion responsiveness is 0.7.

[0211] Customer B: Monthly purchase frequency is 6 times, average purchase amount is 500 yuan, and promotion responsiveness is 0.4.

[0212] Customer C: Monthly purchase frequency is 15 times, average purchase amount is RMB 200, and promotion responsiveness is 0.8.

[0213] Step 1: Optimize the parameters of the quantization task

[0214] First, the system optimizes the parameters of the quantization module to generate a new quantization standard. Set the current learning rate γ = 0.05, and the potential factor feedback function f(z A)=1.2. The system adjusts the quantification standard through the following formula:

[0215] 1. Calculate the update increment of the quantitative standard:

[0216]

[0217] 2. Update the quantitative value of customer A:

[0218] Original quantization value After adjustment:

[0219]

[0220] Step 2: Optimize the parameters of the factor analysis module

[0221] After adjusting the parameters of the quantification module, the system fixes the quantification standard and then optimizes the factor analysis module. For customer B, the result of the potential factor extraction is z(x B )=0.5, and the target factor is y(x B )=0.55. The system readjusts the factor analysis module based on the optimized quantitative data, making the potential factors more consistent with the actual data.

[0222] 1. Calculate the factor analysis error:

[0223] |z(x B )-y(x B )| 2 =(0.5-0.55) 2 =0.0025

[0224] 2. Adjust the parameters of the factor analysis model:

[0225] The system retrains the model based on the factor error, so that the extracted latent factors are more closely matched with the actual data, while also inversely affecting the adjustment of the quantitative standards.

[0226] After multiple rounds of alternating training, the supermarket successfully optimized the quantitative task and the factor analysis module and obtained higher analysis accuracy. For example:

[0227] The quantitative value of customer A increased to 0.736, indicating that he is more sensitive to promotional activities. Therefore, supermarkets can push more personalized promotional information to him. The factor analysis results of customer B show that he prefers high-priced goods. Supermarkets can increase the recommendation of high-end goods in his frequently purchased goods and reduce unnecessary promotional interruptions. The quantitative value of customer C is adjusted to show that his purchasing behavior is more driven by seasonal promotions. Therefore, supermarkets can lock in his demand in advance and increase sales through holiday promotions.

[0228] Through the alternating training strategy, the supermarket not only improved the accuracy of data quantification, but also optimized the effect of factor extraction. This collaborative optimization method enables supermarkets to flexibly adjust their marketing strategies and inventory management in a dynamically changing market environment. For example, before the promotion season arrives, supermarkets can more accurately predict which customers will increase their purchase frequency during the promotion period based on the optimized model, and prepare goods in advance, thereby reducing inventory pressure and improving sales performance. Ultimately, through this data-driven optimization strategy, supermarkets can have more advantages in a highly competitive market environment and achieve higher customer satisfaction and business growth.

[0229] The above shows and describes the basic principles, main features and advantages of the present invention. It should be understood by those skilled in the art that the present invention is not limited to the above embodiments, and the above embodiments and descriptions are only for explaining the principles of the present invention. Without departing from the spirit and scope of the present invention, the present invention may have various changes and improvements, which fall within the scope of the present invention to be protected. The scope of protection of the present invention is defined by the attached claims and their equivalents.

Claims

1. Data quantitative analysis and factor analysis method, characterized by The following steps are involved: S1. Adaptive data quantization: S1.

1. First, classify the original data and identify uniform distribution, skewed distribution, and periodic distribution; S1.

2. Generate dynamic quantization standards through the variational autoencoder VAE model according to data distribution; S1.3, quantize the data according to the generated standard so that each data point is mapped to a quantitative value that meets the characteristics; S2. Data dimensionality reduction and feature extraction based on factor analysis: S2.1, take the data quantized in S1.3 as input; S2.

2. Establish a model that captures the nonlinear factor relationship in the data by introducing deep neural networks; S2.3, extracting latent factors from data through optimization algorithms; S3. Jointly optimized factor analysis and data quantification model: S3.

1. First, the output of the adaptive data quantization method and the input of the factor analysis method are combined, and the two share learning information through collaborative learning; S3.2, adopting the multi-task learning MTL algorithm, so that data quantification and factor analysis constrain each other during the training process; S3.

3. By alternately optimizing the quantitative criteria and factor extraction, the two complement each other in the entire analysis process; S3.

4. After joint optimization, the model outputs the quantified data and extracted factors, and uses the factor analysis results to adjust the quantification criteria; S4. Quantitative expression of factor analysis results and decision support: S4.

1. Convert the factors extracted from factor analysis into quantifiable indicators and standardize them to meet the decision-making needs of specific fields; S4.

2. Construct a quantitative prediction model based on the transformed factors and use regression analysis to predict decision results; S4.

3. Integrate the quantified factor analysis results into the decision support system to form a complete decision-making basis and provide intelligent decision support based on data quantification and factor analysis.

2. The data quantitative analysis and factor analysis method according to claim 1 is characterized in that The adaptive data quantization method comprises: The VAE model is used to model the latent space of the data and learn the distribution characteristics of the data. The VAE captures the latent factors of the data through the encoder, maps them to the latent space, and then generates the corresponding quantization standard through the decoder. The quantization standard is generated dynamically during the process, and the quantization standard generation formula is as follows: in: represents the value obtained after quantizing the data point x; value represents the new value of the data point x after transformation, ranging from 0 to 1; σ(·) is the sigmoid function, that is, Used to map quantized values ​​to a standardized range; It is the integral from the data point x to the quantization standard boundaries a(x) and b(x), where f(t) is the probability density function of the data point x in the latent space; the size of the quantization interval corresponding to the data point x; a(x) and b(x) are the lower and upper bounds of the data point x in the quantization process, respectively.

3. The data quantitative analysis and factor analysis method according to claim 2 is characterized in that The adaptive data quantization method comprises: The VAE model learns the potential representation of the input data, identifies patterns in the data distribution including peaks, skewness, or periodic changes, and optimizes the quantization criteria so that the quantization process captures the details of the data. The representation of the latent space is given by the following formula: Where: z(x) is the mapping of data point x in the latent space; through the VAE model, the data point x is transformed into a representation z(x) in the latent space, which captures the potential characteristics of the data; is the input dataset, which contains all the original data points used to train the model; P θ (z|x) is the conditional probability distribution, which represents the probability distribution of the latent variable z given a data point x; here, θ is the model parameter including the weights of the encoder and decoder, which represents the structure of the latent space learned based on the input data x; dθ is the integration of the model parameters θ, which represents the adjustment of the latent space representation by optimizing the training process.

4. The data quantitative analysis and factor analysis method according to claim 3 is characterized in that The adaptive data quantization method comprises: A joint optimization approach is adopted to combine the potential representation of VAE with the generation of quantization standards, so that the quantization value of each data point conforms to the characteristics of the latent space and adapts to changes in the data distribution. The following calculus optimization method is introduced to form an adaptive feedback mechanism between the learning of the latent space and the minimization of the quantization error.

5. The data quantitative analysis and factor analysis method according to claim 1 is characterized in that The method for establishing the jointly optimized factor analysis and data quantification model: Using the multi-task learning MTL framework, through the mechanism of alternating optimization, the generation of quantitative standards and factor extraction are mutually constrained in the same process; In each training iteration, the parameters of the quantization module are first updated to generate a new quantization standard; The updated quantitative data were then fed into the factor analysis module to extract latent factors; According to the results of factor analysis, the quantitative standards are adjusted dynamically in turn.

6. The data quantitative analysis and factor analysis method according to claim 5 is characterized in that The method for establishing the jointly optimized factor analysis and data quantification model: By introducing a joint loss function, the data quantization error and the reconstruction error of factor analysis are integrated for collaborative optimization; the goal of data quantization is to map the original data to discrete values, and the joint loss function contains two main parts: data quantization error and factor reconstruction error; the quantization error measures the difference between the quantized data and the original data, while the factor reconstruction error evaluates the degree of match between the potential factors extracted by the factor analysis module and the original data structure; the formula is described as: in, is a joint loss function that measures the overall optimization goal of data quantization and factor analysis; by minimizing this loss function, the simultaneous optimization of data quantization and factor analysis is achieved; α is the weight coefficient of the quantization error, which is used to adjust the importance of data quantization and factor analysis in optimization; |Q(x)-x| is the data quantization error, which represents the data value after quantization The absolute difference between β and the original data x; β is the weight coefficient of factor analysis error, which controls the influence of factor extraction accuracy on overall optimization; z(x) is the potential factor extracted by the factor analysis module; y(x) is the target factor representation, which is used to measure the difference between the factor analysis result and the actual data structure; ||z(x)-y(x)|| 2 is the factor reconstruction error, which represents the Euclidean distance between the extracted latent factors and the original factors.

7. The data quantitative analysis and factor analysis method according to claim 6 is characterized in that The method for establishing the jointly optimized factor analysis and data quantification model: An alternating training strategy is adopted. In each training cycle, the parameters of the quantization task are optimized first, and then the quantization parameters are fixed and the parameters of the factor analysis module are optimized. The alternating optimization strategy controls each task to be optimized independently in the shared feature space, while benefiting from the adjustment of the other. The update of the quantization task will directly affect the factor analysis module, and the result of the factor analysis will in turn guide the adjustment of the quantization standard. The formula is described as: in, is the update increment of the quantization standard, which is used to adjust the parameters of the quantization process in each iteration; γ is the learning rate, which controls the step size of the quantization standard update; f(z) is the potential factor feedback function, which represents the feedback effect of factor z on the quantization standard; is the partial derivative of the quantization standard with respect to the input data x; The integral represents the cumulative feedback effect on the entire data set and is used to adjust the quantification standard.

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