An incomplete QoS service recommendation method based on variational autoencoder and probability skyline

Abstract

The application provides an incomplete QoS service recommendation method based on a variational autoencoder and a probability Skyline, and relates to the technical field of service recommendation.The application adopts a trained HeteroVAE encoder and a heterogeneous decoupling decoder to process an input vector constructed based on an original incomplete data matrix and a missing indication matrix to obtain data after filling of QoS dimensions in an offline data generation stage.In an online probability recommendation stage, user preferences are perceived through input of each QoS dimension weight, a target quota of active dimensions is calculated, and active dimension partitions are divided, and finally, in combination with matrix probability Skyline, numerical values of target services in active dimensions are output, and services are screened and recommended.The application can guarantee efficient online recommendation operation, greatly meet user individualized needs, and ensure that the recommended services have significant global objective quality and stability in a multi-dimensional space.

Description

Technical Field

[0001] This invention relates to the field of service recommendation technology, specifically to an incomplete QoS service recommendation method based on variational autoencoders and probabilistic Skylines. Background Technology

[0002] In modern cloud computing and Service-Oriented Architecture (SOA), with the exponential growth in the number of functionally similar web services and cloud APIs, Quality of Service (QoS, such as response time, throughput, and reliability) has become a core non-functional standard for differentiating similar services and guiding users in their choices. However, in real-world distributed cloud environments, edge computing, and IoT scenarios, due to network fluctuations, privacy restrictions, or limited monitoring and detection range, the historical QoS call matrices collected by the system often exhibit extremely high data sparsity and incompleteness (i.e., a large number of missing values). How to perform accurate, personalized, and efficient service recommendations under highly incomplete QoS data is a key challenge in the current service computing field.

[0003] Currently, service recommendations based on incomplete QoS data mainly rely on the following three categories:

[0004] 1. QoS prediction technology based on single-point filling and collaborative filtering:

[0005] Most studies employ matrix factorization or latent semantic models to perform single imputation on incomplete QoS matrices, then rank and recommend based on the predicted deterministic scalar values. For example, a latent factor model integrating dual space and dual norm was proposed in the top international journal IEEE Transactions on Services Computing (2023) for high-precision Web service QoS prediction. Such methods reconstruct the missing matrix by extracting global latent features.

[0006] 2. Incomplete data recommendation techniques based on probabilistic skylines and spatial partitioning:

[0007] Skyline queries aim to select a set of Pareto optimal services from a large dataset that are not completely dominated by any other service across all dimensions. For incomplete data, the IQSrec algorithm was proposed in the top-tier journal IEEE Transactions on Services Computing (2023). IQSrec is the first to combine probabilistic Skyline queries with dimension-based spatial partitioning. This algorithm uses the empirical cumulative distribution function (CDF) of the original observation data to divide services into different dimensional sub-regions and calculates the probabilistic Skyline within each sub-region, thus operating directly on incomplete QoS data while ensuring the diversity of recommendation results.

[0008] 3. Multiple Imputation (MI) based on deep generative models:

[0009] In recent years, variational autoencoders (VAEs) have demonstrated excellent distribution fitting capabilities in handling missing values ​​in heterogeneous tabular data. Nazabal et al. proposed the HI-VAE framework in Pattern Recognition (2020), designing a variational inference model based on Masked ELBO for incomplete data containing heterogeneous attributes such as continuous, discrete, and categorical data. Ma et al. proposed the MIVAE model in Engineering Applications of Artificial Intelligence (2023), which achieves multiple imputation of incomplete data by extracting multiple samples from the learned posterior distribution, thereby capturing the cognitive uncertainty of missing values.

[0010] The aforementioned background technologies have the following significant drawbacks when processing service recommendations based on extremely incomplete QoS data:

[0011] 1. Single interpolation (SI) ignores the statistical uncertainty of the data:

[0012] Existing QoS prediction models (such as matrix factorization and graph neural networks) only output a single, absolutely deterministic QoS prediction scalar, completely ignoring the distribution variance caused by missing information. In multi-objective optimization Skyline queries, decisions are extremely sensitive to risk and extreme values. When faced with extremely sparse data, the bias based on the mean or single-point estimation is enormous, easily leading to the "false positive" rejection of high-variance (i.e., high-potential but also risky) high-quality services, or the misdirection of mediocre services to users.

[0013] 2. The existing probabilistic Skyline algorithm suffers from the "high missing rate partition disaster" and a sharp drop in recall under high missing rate conditions:

[0014] Recent technologies, such as the IQSrec algorithm, calculate dominance probabilities directly on incomplete data to avoid imputation errors. Its core logic is: during partitioning, partitioning is only performed on the effective QoS dimension of the current service. This heuristic rule works well when the missing data rate is low (…). It is effective when the matrix missing rate exceeds 100%. At this point, the system will generate a massive number of services that are missing in more than half of the dimensions, making partitioning based on effective dimensions extremely difficult. This will cause the candidate services within each partition to no longer represent the best service (or even the real skyline service) in the corresponding dimension. The algorithm will completely lose its discriminative power, resulting in a significant decrease in the proportion of real skyline services in the candidate set, a sharp drop in recall, and consequently, a decrease in the regression rate of real skyline services in IQSrec's partitioning method.

[0015] 3. Deep integration of generative model's lack of multiple imputation with multi-objective recommendation selection mechanism:

[0016] Existing VAE multiple imputation models (such as HI-VAE and MIVAE) only focus on data reconstruction errors or simple downstream classification tasks. If the multisamples generated by these models are directly averaged and fed into the Skyline recommendation system, the "mean smoothing effect" will also eliminate the peak potential of the service in a single dimension (i.e., "premature pruning"). In addition, existing recommendation systems often use simple linear weighting when processing user preference weights for different QoS dimensions, which can easily lead to the loss of dimension positions due to weight rounding, and cannot fairly reflect the diverse preferences of users at the underlying hardware partitioning logic. Summary of the Invention

[0017] To address the shortcomings of existing technologies, the present invention aims to propose an incomplete QoS service recommendation method based on variational autoencoders and probabilistic skylines, comprising:

[0018] Step 1: Obtain the original incomplete data matrix and its corresponding missing indicator matrix ;

[0019] Among them, the Includes n rows of web services and d columns of QoS, and elements in This represents the observed value of QoS in the j-th column corresponding to the web service in the i-th row. There are missing observations in the data; a missing observation indicator matrix is ​​defined. : A value of 0 indicates that the corresponding observation is missing, while a value of 1 indicates that a valid observation exists at the corresponding position.

[0020] Step 2: According to and Construct a normalized matrix ;

[0021] Step 3: Based on Constructing input vectors ,according to and The HeteroVAE encoder and heterogeneous decoupling decoder are trained to obtain the trained HeteroVAE encoder and heterogeneous decoupling decoder.

[0022] Step 4: Based on the trained HeteroVAE encoder and heterogeneous decoupling decoder, perform... The process yields the padded matrix, the multisampled 3D tensor Q, the expected CDF matrix, the padded expected mean matrix, the original CDF matrix, and the first matrix.

[0023] Step 5: Determine the active dimension in real time across all QoS levels, and then calculate the target quota for the active dimension. ;

[0024] Step 6: Construct a global candidate set based on the imputed mean matrix, the multisampled 3D tensor Q, and the expected CDF matrix, and then combine it with the original CDF matrix and the missing indicator matrix. Calculate the target probability for each candidate dimension in the global candidate set;

[0025] Step 7: Based on the target probability, target quota, and the first matrix, determine the target service corresponding to each active dimension, and then combine the padded matrix with the original incomplete data matrix. Output the value of the target service in the active dimension.

[0026] Optionally, step 2 specifically includes:

[0027] Step 2.1: Based on the QoS dimension type, Perform a nonlinear transformation to obtain the transformed observations. Specifically, it includes:

[0028] When the QoS dimension type is a long-tailed positive real number dimension, for A smooth logarithmic transformation is performed using the following formula:

[0029] ;

[0030] in, This is a preset constant;

[0031] When the QoS dimension type is percentage and probability dimension, for The Logit transformation is performed using the following formula:

[0032] ;

[0033] ;

[0034] ;

[0035] in, for The maximum value among all QoS values ​​in the j-th column. , As an intermediate variable;

[0036] Step 2.2: For Perform Z-Score standardization based on the standardized observations and the missing indicator matrix. Generate a normalized matrix Specifically, this is achieved through the following formula:

[0037] ;

[0038] ;

[0039] ;

[0040] ;

[0041] in, This represents the mean. Indicates standard deviation, As an intermediate variable, Missing indicator matrix The mask in Representing a normalized matrix The elements in.

[0042] Optionally, step 3 specifically includes:

[0043] Step 3.1: Normalize the matrix Each row in the vector is used as a zero-padding input vector. The row corresponding to the missing indicator matrix M is used as the mask vector. ,Will and The input vector is obtained by concatenating the features along their dimensions. ;

[0044] Step 3.2: Input vector Input the HeteroVAE encoder to obtain the mean vector. With log-variance vector ;

[0045] Specifically, the input vector Inputting the input layer of the HeteroVAE encoder yields nonlinear hidden layer features. Specifically, this is achieved through the following formula:

[0046] ;

[0047] in, The weight matrix of the input layer. Here, Tanh represents the bias vector of the input layer;

[0048] Nonlinear hidden layer features Input two parallel linear layers to obtain the mean vector. With log-variance vector , is represented as:

[0049] ;

[0050] ;

[0051] in, These are the weight matrices that control the mapping of mean and variance, respectively. This is the corresponding bias vector;

[0052] Build and The corresponding continuous latent space, and the latent feature vectors obtained by sampling in the continuous latent space. ;

[0053] according to and The posterior distribution of Web service i is generated using the following formula:

[0054] ;

[0055] in, Describes the posterior distribution of Web service i. Indicates a normal distribution. Indicates diagonal;

[0056] Step 3.3: Convert the latent feature vector Input the heterogeneous decoupling decoder to obtain the probability density function and distribution parameter set;

[0057] latent feature vectors Input a shared linear layer to obtain a joint representation , is represented as:

[0058] ;

[0059] in, To share the weight matrix of the linear layer, The bias vector for the shared linear layer;

[0060] When the QoS dimension type is a long-tailed positive real number dimension, the joint representation will be used. After passing through a linear layer, the expected mean is obtained. Sum of logarithmic variance Specifically, it is expressed by the following formula:

[0061] ;

[0062] ;

[0063] in, This is the weight matrix for the long-tailed distribution branch. , This is the bias vector for the long-tailed distribution branch. This is a numerical truncation function;

[0064] according to and Construct the probability density function, expressed as: ;

[0065] When the QoS dimension type is percentage, the Softplus function is used for joint representation. Processing is performed to obtain shape parameters. and Specifically, it is expressed by the following formula:

[0066] ;

[0067] ;

[0068] in, As a preset constant, Here is the weight matrix for the Beta distribution branch. , This is the bias vector for the Beta distribution branch;

[0069] According to shape parameters and Construct the probability density function, expressed as: ,in, Represents the Beta distribution;

[0070] Among them, the QoS of the long-tail positive real number dimension and and the shape parameters of QoS in the percentage dimension and Form a distributed parameter set;

[0071] Step 3.4: Calculate the reconstruction loss Specifically, this is achieved through the following formula:

[0072] ;

[0073] in, This represents a set of QoS values ​​with a long-tailed positive real number dimension. This represents a set of QoS values ​​with a percentage dimension.

[0074] Calculate total loss Specifically, this is achieved through the following formula:

[0075] ;

[0076] in, For dynamic weights, Denotes KL divergence, Represents a normal distribution;

[0077] Step 3.5: Based on the total loss The parameters of the HeteroVAE encoder and the heterogeneous decoupling decoder are updated until the HeteroVAE encoder and the heterogeneous decoupling decoder converge, thus obtaining the trained HeteroVAE encoder and the heterogeneous decoupling decoder.

[0078] Optionally, step 4 specifically includes:

[0079] Step 4.1: [The text appears to be incomplete and contains several grammatical errors. A more accurate translation would require Input the trained HeteroVAE encoder to obtain the posterior distribution of Web service i. Then, resample multiple times from the posterior distribution of Web service i to obtain... One latent variable sample ;

[0080] Step 4.2: For each latent variable sample Input a heterogeneous decoupling decoder to obtain a set of distributed parameters. Point sampling is performed on this set of parameters to obtain a prediction vector. Then, the normalized matrix is... For each missing observation in the i-th row, the corresponding predicted value is obtained from the prediction vector and inserted into the missing observation's position. After all rows are filled, the filled matrix is ​​obtained. Inverse standardization and inverse nonlinear transformation are then performed on the filled matrix to obtain the QoS estimation matrix in the physical space. Get from The observations with a value of 1 are used to replace the corresponding values ​​in the QoS estimation matrix, resulting in a padded observation matrix. This process yields ms padded observation matrices.

[0081] Step 4.3: Based on the QoS evaluation type, normalize each filled observation matrix using the following formula to obtain normalized observation values. All normalized observation values ​​form an intermediate matrix. The intermediate matrices of all the filled observation matrices form a multisampling 3D tensor Q. For all intermediate matrices... The average of the normalized observations corresponding to the i-th Web service and the j-th QoS is used to obtain the first matrix;

[0082] When the QoS evaluation type is benefit-based, normalization is performed using the following formula:

[0083] ;

[0084] in, These are the elements in the filled observation matrix. These are the normalized observations. Let be the minimum value in the j-th column of the filled observation matrix. This represents the maximum value in the j-th column of the filled observation matrix;

[0085] When the QoS evaluation type is cost-based, normalization is performed using the following formula:

[0086] ;

[0087] Step 4.4: For each QoS, obtain all normalized observations corresponding to the QoS in the multisampling three-dimensional tensor Q, and sort all normalized observations in ascending order to obtain the continuous empirical cumulative distribution function. For each web service, in the continuous experience cumulative distribution function In this process, the sequence number of the normalized observation corresponding to the Web service is determined, the ratio of each sequence number to the total number of Web services is calculated, and then the arithmetic mean of all ratios is calculated to obtain the representative score. Representative scores of all rows and columns Construct the expected CDF matrix;

[0088] Step 4.5: In the multisampling 3D tensor Q, obtain all normalized observations of the i-th Web service on the j-th QoS, and then calculate the mean of all normalized observations, using it as the sampling mathematical expectation. The mathematical expectations of all samples form the matrix that fills the expectation mean.

[0089] Step 4.6: For each QoS, in the intermediate matrix Obtain all normalized observations corresponding to QoS, sort all normalized observations in ascending order, and obtain the original empirical cumulative distribution function. For each web service, the original empirical cumulative distribution function In this process, the index of the normalized observation corresponding to the Web service is determined, the ratio of each index to the total number of Web services is calculated, and the original score is obtained. The original scores of all Web services corresponding to all QoS are used to form the original CDF matrix.

[0090] Optionally, step 5 specifically includes:

[0091] Step 5.1: Obtain the importance weight assigned by the user to each QoS in real time, and designate QoS with importance weights greater than the threshold as active dimensions. All active dimensions form an active dimension subset. ;

[0092] Step 5.2: Set the target total number of recommendations The target quota is allocated to each active dimension using the maximum balance method. ;

[0093] Specifically, for Each active dimension is assigned a baseline quota, and then the first remaining quota R is calculated. Then calculate the additional quota for each active dimension. Specifically, this is achieved through the following formula:

[0094] ;

[0095] ;

[0096] in, Indicates the first The importance weight of each active dimension For intermediate parameters;

[0097] Subtract the additional quotas for all active dimensions from the first remaining quota to obtain the second remaining quota. For each active dimension, calculate and The differences are calculated, and the differences of all active dimensions are sorted in descending order. The second remaining quota is then allocated sequentially according to the sorted order to obtain the compensation quota, baseline quota, extra quota, and compensation quota for each active dimension, thus obtaining the target quota for each active dimension. .

[0098] Optionally, step 6 specifically includes:

[0099] Step 6.1: For each Web service, obtain the sampled mathematical expectation for each active dimension from the sampled mathematical expectations of all QoS values ​​that fill the expected mean matrix. Determined in the expected CDF matrix Corresponding representative score Among all the representative scores corresponding to the active dimensions, the active dimension with the largest representative score is obtained, and the Web service is assigned to the active dimension partition of the active dimension with the largest representative score.

[0100] Step 6.2: Partition for each active dimension In the multisampled 3D tensor Q, obtain the activity dimension u of Web service i. Each normalized observation value, in 95th quantile of the normalized observations Obtain from the expected CDF matrix The corresponding representative scores are then used to obtain the active dimension partitions. The representative scores of all Web services are obtained and sorted in descending order. The target quota of the activity dimension u is multiplied by a preset expansion coefficient to obtain the target number. All Web services with the target number are obtained in order from all Web services in descending order to form a candidate pool for the activity dimension.

[0101] Step 6.3: Merge the candidate pools of all active dimensions to obtain a global candidate set. For any two candidate services in the global candidate set, in the missing indicator matrix... In the above, we obtain the elements of the two candidate services on the active dimension u, denoted as: and ;

[0102] according to and Calculate the probability that candidate service a dominates candidate service b on the active dimension u. ;

[0103] exist At that time, the observations of two candidate services on the active dimension u are obtained from the original incomplete data matrix. and ,exist hour, ,exist hour, ;

[0104] exist hour, ;

[0105] exist At that time, obtain the observations of candidate service b on the active dimension u from the original incomplete data matrix. Then obtain from the original CDF matrix The corresponding raw score G b , ;

[0106] exist At that time, obtain the observations of candidate service a on the active dimension u from the original incomplete data matrix. Then obtain from the original CDF matrix The corresponding raw score G a , ;

[0107] Across all active dimensions, the probability that candidate service a dominates candidate service b is calculated using the following formula:

[0108] ;

[0109] Calculate the target probability of candidate service b The target probability The probability of candidate service b becoming an objective Skyline is represented by the following formula:

[0110] ;

[0111] Where C represents all Web services in the global candidate set. This refers to the web services in C other than b.

[0112] Optionally, step 7 specifically includes:

[0113] Sort the target probabilities of all candidate services included in the active dimension partition in descending order, and then obtain the top [probabilities] in the sorted order. Each candidate service is used as the target service. The numerical value of the target service on the active dimension u is obtained from the first matrix. If the numerical value of the target service on the active dimension u corresponds to a missing indicator matrix... If the mask is 0, the padded values ​​are denormalized, and the denormalized values ​​are output; if the target service has a missing indicator matrix corresponding to the value on the active dimension u. The middle mask is 1, which will transform the original incomplete data matrix. The numerical value of the target service on the active dimension u is directly output.

[0114] The beneficial effects of adopting the above technical solution are as follows:

[0115] In the offline data generation phase, WADrec utilizes a customized machine learning model (HeteroVAE) to capture potential physical associations in the QoS dimension to perform missing value imputation and quantifies the uncertainty of inference, statically materializing the results into a low-dimensional matrix to eliminate online computational overhead. In the online probabilistic recommendation phase, guided by user's personalized preferences, the system sequentially performs dimensional quota allocation and conditional posterior partitioning. Finally, it combines matrix-based probabilistic Skyline calculation and subjective utility rearrangement to select the final service layer by layer. Extensive experimental results demonstrate that, compared to existing state-of-the-art recommendation algorithms, WADrec ensures efficient online recommendation operations, greatly satisfies users' personalized needs, and guarantees that the recommended services possess significant global objective quality and stability in a multi-dimensional space. Attached Figure Description

[0116] Figure 1 This is a flowchart illustrating an incomplete QoS service recommendation method based on variational autoencoder and probabilistic Skyline in an embodiment of the present invention.

[0117] Figure 2 This is a flowchart illustrating the offline data generation stage in an embodiment of the present invention.

[0118] Figure 3 This is a schematic diagram of a multisampling three-dimensional tensor in an embodiment of the present invention;

[0119] Figure 4 This is a schematic diagram of the Boolean missing matrix in an embodiment of the present invention;

[0120] Figure 5 This is a flowchart illustrating the online probability recommendation stage in an embodiment of the present invention;

[0121] Figure 6 This is a schematic diagram of a dimension-based partitioning method in an embodiment of the present invention;

[0122] Figure 7 This is a schematic diagram of another dimension-based partitioning in an embodiment of the present invention. Detailed Implementation

[0123] The specific embodiments of the present invention will be described in further detail below with reference to the accompanying drawings and examples. The following examples are for illustrative purposes only and are not intended to limit the scope of the invention.

[0124] To address the problems of existing technologies, this invention provides an incomplete QoS service recommendation method based on variational autoencoders and probabilistic skylines. The aim is to overcome the shortcomings of existing technologies, such as insufficient representation of uncertainty in missing data, loss of discriminative power of probabilistic skylines under high missing rates, and the smooth elimination of potentially high-quality services due to mean-based evaluation. This invention proposes an incomplete QoS service recommendation method based on variational autoencoders and probabilistic skylines (WADrec). This invention aims to reconstruct the underlying probability distribution of missing data through VAE multisampling, pioneering multi-dimensional recommendation service allocation based on user weights. It combines strict Hare-Niemeyer quota allocation and expected utility partitioning strategies to ensure absolute diversity in recommendations, and uses an optimistic potential selection mechanism based on the "95th percentile" to combat uncertainty penalties. Finally, through matrix-based probability calculation, it achieves personalized service recommendations with microsecond-level response efficiency, high recall, and high accuracy even under high missing rates.

[0125] Online service recommendations have high requirements for response time. Complex deep generative model inference, probability distribution fitting, and Monte Carlo integration would result in significant latency if performed online. Therefore, the WADrec architecture principle is: detailed offline inference caching and lightweight online decision-making. The offline phase focuses on utilizing known QoS data from existing datasets to train a HeteroVAE model that understands the heterogeneous distributions and implicit correlations among various QoS attributes, and then statically materializes the inference results.

[0126] Combination Figure 1 The incomplete QoS service recommendation method based on variational autoencoder and probabilistic Skyline provided by this invention may include the following steps:

[0127] Step 1: Combining Figure 2 In the offline data generation phase, the raw, incomplete data matrix is ​​obtained. and its corresponding missing indicator matrix For example, obtaining the raw, incomplete data matrix from a service X dimension (different types of QoS metrics, such as response time, feasibility, throughput, reliability, etc.) like the QWS dataset. ;

[0128] Among them, the Includes n rows of web services and d columns of QoS, and elements in This represents the observed value of QoS in the j-th column corresponding to the web service in the i-th row. There are missing observations in the data; a missing observation indicator matrix is ​​defined. : A value of 0 indicates that the corresponding observation is missing, while a value of 1 indicates that a valid observation exists at the corresponding position.

[0129] Step 2: According to and Construct a normalized matrix ;

[0130] Step 2.1: Based on the QoS dimension type, Perform a nonlinear transformation to obtain the transformed observations. Specifically, it includes:

[0131] Traditional VAE models theoretically rely on Gaussian priors and Gaussian likelihood assumptions. However, the physical distribution of real-world QoS exhibits strong heterogeneity. Directly applying simple linear normalization to these distributions is highly likely to distort the model. Therefore, to overcome the variance collapse caused by the forced fitting of a Gaussian distribution in conventional VAEs, WADrec, based on the distribution heterogeneity theory of HI-VAEs, performs specific nonlinear transformations on different QoS groups:

[0132] When the QoS dimension is a long-tailed positive real number dimension (e.g., response time, network latency, concurrent throughput), the physical lower bound of these metrics is 0 (no negative numbers), but numerically they often exhibit a right-skewed long-tail distribution. A small subset of poor-performing samples elongates the tail of the distribution. To map this to an approximately Gaussian distribution, ... A smooth logarithmic transformation is performed using the following formula:

[0133] ;

[0134] in, This is a preset constant;

[0135] When the QoS dimension type is percentage or probability (e.g., service availability, API call success rate, SLA compliance rate), the theoretical and physical limits of these metrics are restricted to... or Within such a closed interval, in actual cloud services, values ​​often cluster near 100% (forming a left-skewed Beta distribution). To project this onto an unbounded space of real numbers ( To adapt the output mapping of VAE, for The Logit transformation is performed using the following formula:

[0136] ;

[0137] ;

[0138] ;

[0139] in, for The maximum value among all QoS values ​​in the j-th column. , As an intermediate variable;

[0140] It is worth noting that if a service achieves a perfect 100% success rate ( The denominator of the formula will be 0. Therefore, before the transformation, the formula should be... implement Boundary truncation operation.

[0141] Step 2.2: The above operations stretch the data distribution type into a regular continuous state. Perform Z-Score standardization based on the standardized observations and the missing indicator matrix. Generate a normalized matrix Specifically, this is achieved through the following formula:

[0142] ;

[0143] ;

[0144] ;

[0145] ;

[0146] in, This represents the mean. Indicates standard deviation, As an intermediate variable, Missing indicator matrix The mask in Representing a normalized matrix Elements in;

[0147] Step 3: Based on the normalized matrix Constructing input vectors According to the input vector and missing indicator matrix The HeteroVAE encoder and heterogeneous decoupling decoder are trained to obtain the trained HeteroVAE encoder and heterogeneous decoupling decoder.

[0148] Step 3.1: Normalize the matrix Each row in the vector is used as a zero-padding input vector. The row corresponding to the missing indicator matrix M is used as the mask vector. ,Will and The input vector is obtained by concatenating the features along their dimensions. ;

[0149] Step 3.2: Input vector Input the HeteroVAE encoder to obtain the mean vector. With log-variance vector ;

[0150] Traditional VAE models strongly assume that all features follow a single Gaussian distribution, which leads to severe prediction distortion and variance collapse on heterogeneous QoS data. To address this, this invention constructs HeteroVAE, which accurately captures cross-dimensional joint correlations through deep joint representations and multi-branch heterogeneous decoders.

[0151] Specifically, the input vector The input layer of the HeteroVAE encoder, which uses a multilayer perceptron (MLP), is used to obtain nonlinear hidden layer features. Specifically, this is achieved through the following formula:

[0152] ;

[0153] in, The weight matrix of the input layer. Let Tanh be the bias vector of the input layer, and let tangent be the hyperbolic tangent function. This invention uses the hyperbolic tangent function as a nonlinear activation function. The theoretical motivation for this is that the standardized input data exhibits a zero-mean distribution, and Tanh can smoothly and symmetrically map the features to tangent. The interval effectively prevents gradient vanishing in deep networks and provides a stable continuous manifold for latent space projection;

[0154] Nonlinear hidden layer features Input two parallel linear layers to obtain the mean vector. With log-variance vector , is represented as:

[0155] ;

[0156] ;

[0157] in, These are the weight matrices that control the mapping of mean and variance, respectively. This is the corresponding bias vector;

[0158] Build and The corresponding continuous latent space, and the latent feature vectors obtained by sampling in the continuous latent space. Specifically, sampling is achieved through reparameterization techniques. This operation makes the variational inference process differentiable. The variational prior is forced to assume a standard normal distribution. (in (where the identity matrix is ​​used), this assumption mathematically requires that the latent features of different dimensions in the latent space be independent of each other and have zero mean and unit variance, so as a strong regularization term to enable the model to learn decoupled service representations.

[0159] according to and The posterior distribution of Web service i is generated using the following formula:

[0160] ;

[0161] in, Describes the posterior distribution of Web service i. Indicates a normal distribution. Indicates diagonal;

[0162] Step 3.3: Convert the latent feature vector Input the heterogeneous decoupling decoder to obtain the probability density function and distribution parameter set;

[0163] To address the representation failure problem of a single likelihood function, latent feature vectors are... Input a shared linear layer to obtain a joint representation , is represented as:

[0164] ;

[0165] in, To share the weight matrix of the linear layer, The bias vector for the shared linear layer;

[0166] When the QoS dimension type is a long-tailed positive real number dimension, the joint representation will be used. After passing through a linear layer, the expected mean is obtained. Sum of logarithmic variance Specifically, it is expressed by the following formula:

[0167] ;

[0168] ;

[0169] in, This is the weight matrix for the long-tailed distribution branch. , This is the bias vector for the long-tailed distribution branch. This is a numerical truncation function; unconstrained exponentiation is used when inferring high polarity variance. This can easily lead to gradient explosion, resulting in NaN (Not a Number) errors. The Clamp operation strictly limits the linear output to... Within the safety threshold, it ensures robustness against extreme values ​​during the backpropagation process.

[0170] according to and Construct the probability density function, expressed as: ;

[0171] During inference, samples are obtained from this distribution. Afterwards, inverse normalization and inverse logarithmic transformation must be performed sequentially to map the response time or absolute throughput value with physical meaning. The Clamp operation strictly limits the hidden layer output to... The internal design aims to prevent gradient explosion during exponential reduction.

[0172] When the QoS dimension type is percentage, the Softplus function is used for joint representation. Processing is performed to obtain shape parameters. and Specifically, it is expressed by the following formula:

[0173] ;

[0174] ;

[0175] in, As a preset constant, , Here is the weight matrix for the Beta distribution branch. , This is the bias vector for the Beta distribution branch;

[0176] Unlike the traditional approach of using the ReLU function to truncate negative values, this invention uses the Softplus function (defined as...). Since the shape parameter of the Beta distribution must be a real number strictly greater than 0 by mathematical definition, Softplus provides a smooth and globally differentiable positive nonlinear mapping, perfectly matching the parameter domain validity requirement of the probability density function. To prevent the distribution from degenerating into a minimum constant of singular points.

[0177] According to shape parameters and Construct the probability density function, expressed as: ,in, Represents a Beta distribution; the result sampled from this Beta distribution during inference. Only after inverse normalization and Sigmoid function mapping can it be represented as the percentage of availability or success rate in physical space.

[0178] Among them, the QoS of the long-tail positive real number dimension and and the shape parameters of QoS in the percentage dimension and Form a distributed parameter set;

[0179] Step 3.4: Calculate the reconstruction loss Specifically, this is achieved through the following formula:

[0180] ;

[0181] in, This represents a set of QoS values ​​with a long-tailed positive real number dimension. This represents a set of QoS values ​​with a percentage dimension.

[0182] Calculate total loss Specifically, this is achieved through the following formula:

[0183] ;

[0184] in, For dynamic weights, Denotes KL divergence, Represents a normal distribution;

[0185] Step 3.5: Based on the total loss The parameters of the HeteroVAE encoder and the heterogeneous decoupling decoder are updated until the HeteroVAE encoder and the heterogeneous decoupling decoder converge, thus obtaining the trained HeteroVAE encoder and the heterogeneous decoupling decoder.

[0186] In this invention, the AdamW optimizer is used (learning rate set to...). Weight decay Parameter updates are performed. To prevent the model from getting trapped in local minima in the early stages of training due to extremely sparse data (i.e., posterior collapse by directly minimizing KL divergence while ignoring mutual information), the system strictly implements the KL annealing strategy: during the first 30% of training iterations (Epochs), dynamic weights are updated. Locking the value to 0 forces the network's computing power to be fully devoted to fitting the extremely complex heterogeneous reconstruction error; after this... The iteration count increases linearly up to 1 with each iteration round.

[0187] In addition, to prevent gradient explosion caused by heterogeneous likelihood functions (especially exponential and beta partial derivatives) under extreme residuals, global gradient clipping (with a maximum norm of 5.0) is performed on the network layer after each backpropagation gradient calculation.

[0188] The convergence of the HeteroVAE encoder and heterogeneous decoupling decoder does not depend on a set maximum number of epochs (e.g., 800 epochs), but instead employs an early stopping mechanism based on the reconstruction error of the observation set. At the end of each iteration, the model is evaluated... The root mean square error (RMSE) on the set. If the observation error does not show marginal improvement within 50 consecutive training results (the rate of improvement is...). If the model's latent space manifold is fully fitted, training is terminated and a snapshot of the model with the best generalization weights is saved, thus transitioning to the offline static materialization stage.

[0189] Step 4: Based on the trained HeteroVAE encoder and heterogeneous decoupling decoder, process the input vector... The process yields the padded matrix, the multisampled 3D tensor Q, the expected CDF matrix, the padded expected mean matrix, the original CDF matrix, and the first matrix.

[0190] Step 4.1: [The text appears to be incomplete and contains several grammatical errors. A more accurate translation would require Input the trained HeteroVAE encoder to obtain the posterior distribution of Web service i. Then, resample multiple times from the posterior distribution of Web service i to obtain... One latent variable sample ;

[0191] Step 4.2: For each latent variable sample Input a heterogeneous decoupling decoder to obtain a set of distributed parameters. Point sampling is performed on this set of parameters to obtain a prediction vector. Then, the normalized matrix is... For each missing observation in the i-th row, the corresponding predicted value is obtained from the prediction vector and inserted into the missing observation's position. After all rows are filled, the filled matrix is ​​obtained. Inverse standardization and inverse nonlinear transformation are then performed on the filled matrix to obtain the QoS estimation matrix in the physical space. Get from The observations with a value of 1 are used to replace the corresponding values ​​in the QoS estimation matrix, resulting in a padded observation matrix. This process yields ms padded observation matrices.

[0192] Step 4.3: Based on the QoS evaluation type, normalize each filled observation matrix using the following formula to obtain normalized observation values. All normalized observation values ​​form an intermediate matrix. The intermediate matrices of all the filled observation matrices form the multisampling three-dimensional tensor Q, such as Figure 3 For all intermediate matrices The average of the normalized observations corresponding to the i-th Web service and the j-th QoS is used to obtain the first matrix;

[0193] QoS attributes have different dimensions, and the polarity of desired attributes varies. For benefit attributes (such as throughput), higher values ​​are better; for cost attributes (such as response time), lower values ​​are better. This invention first performs a unified Min-Max normalization on the observation data across all dimensions.

[0194] When the QoS evaluation type is benefit-based, normalization is performed using the following formula:

[0195] ;

[0196] in, These are the elements in the filled observation matrix. These are the normalized observations. Let be the minimum value in the j-th column of the filled observation matrix. This represents the maximum value in the j-th column of the filled observation matrix;

[0197] When the QoS evaluation type is cost-based, normalization is performed using the following formula:

[0198] ;

[0199] Step 4.4: For each QoS, obtain all normalized observations corresponding to the QoS in the multisampling three-dimensional tensor Q, and sort all normalized observations in ascending order to obtain the continuous empirical cumulative distribution function. For each web service, in the continuous experience cumulative distribution function In this process, the sequence number of the normalized observation corresponding to the Web service is determined, the ratio of each sequence number to the total number of Web services is calculated, and then the arithmetic mean of all ratios is calculated to obtain the representative score. Representative scores of all rows and columns Construct the expected CDF matrix;

[0200] Step 4.5: In the multisampling 3D tensor Q, obtain all normalized observations of the i-th Web service on the j-th QoS, and then calculate the mean of all normalized observations, using it as the sampling mathematical expectation. The mathematical expectations of all samples form the matrix that fills the expectation mean.

[0201] Step 4.6: For each QoS, in the intermediate matrix Obtain all normalized observations corresponding to QoS, sort all normalized observations in ascending order, and obtain the original empirical cumulative distribution function. For each web service, the original empirical cumulative distribution function In the process, the index of the normalized observation corresponding to the Web service is determined, the ratio of each index to the total number of Web services is calculated, and the raw score is obtained. The raw scores of all Web services corresponding to all QoS are used to form the original CDF matrix.

[0202] Furthermore, this invention constructs a Boolean missing matrix based on M. ,like Figure 4 The Boolean missing matrix The elements in are represented as ,and ;

[0203] Step 5: Combining Figure 5 During the online probabilistic recommendation phase, the active dimension is determined in real time among all QoS levels, and then the target quota for the active dimension is calculated. ;

[0204] Step 5.1: In the online probabilistic recommendation stage, obtain the importance weight assigned to each QoS by the user in real time, and use the QoS with an importance weight greater than the threshold as the active dimension. All active dimensions form an active dimension subset. ;

[0205] Step 5.2: Set the target total number of recommendations The target quota is allocated to each active dimension using the maximum balance method. ;

[0206] Specifically, for Each active dimension is assigned a baseline quota, and then the first remaining quota R is calculated. Then calculate the additional quota for each active dimension. Specifically, this is achieved through the following formula:

[0207] ;

[0208] ;

[0209] in, Indicates the first The importance weight of each active dimension For intermediate parameters;

[0210] Subtract the additional quotas for all active dimensions from the first remaining quota to obtain the second remaining quota. For each active dimension, calculate and The differences are calculated, and the differences of all active dimensions are sorted in descending order. The second remaining quota is then allocated sequentially according to the sorted order to obtain the compensation quota, baseline quota, extra quota, and compensation quota for each active dimension, thus obtaining the target quota for each active dimension. ;

[0211] Step 6: Construct a global candidate set based on the imputed mean matrix, the multisampled 3D tensor Q, and the expected CDF matrix, and then combine it with the original CDF matrix and the missing indicator matrix. Calculate the target probability for each candidate dimension in the global candidate set;

[0212] Step 6.1: For each Web service, obtain the sampled mathematical expectation for each active dimension from the sampled mathematical expectations of all QoS values ​​that fill the expected mean matrix. Determined in the expected CDF matrix Corresponding representative score Among all the representative scores corresponding to the active dimensions, the active dimension with the highest representative score is selected, and the web service is assigned to the active dimension partition of the active dimension with the highest representative score, such as... Figure 6 and Figure 7 ;

[0213] Step 6.2: Partition for each active dimension In the multisampled 3D tensor Q, obtain the activity dimension u of Web service i. Each normalized observation value, in 95th quantile of the normalized observations Obtain from the expected CDF matrix The corresponding representative scores are then used to obtain the active dimension partitions. The representative scores of all Web services are obtained and sorted in descending order. The target quota of the activity dimension u is multiplied by a preset expansion coefficient to obtain the target number. All Web services with the target number are obtained in order from all Web services in descending order to form a candidate pool for the activity dimension.

[0214] Step 6.3: Merge the candidate pools of all active dimensions to obtain a global candidate set. For any two candidate services in the global candidate set, in the missing indicator matrix... In the above, we obtain the elements of the two candidate services on the active dimension u, denoted as: and ;

[0215] according to and Calculate the probability that candidate service a dominates candidate service b on the active dimension u. ;

[0216] exist At that time, the observations of two candidate services on the active dimension u are obtained from the original incomplete data matrix. and ,exist hour, ,exist hour, ;

[0217] exist hour, ;

[0218] exist At that time, obtain the observations of candidate service b on the active dimension u from the original incomplete data matrix. Then obtain from the original CDF matrix The corresponding raw score G b , ;

[0219] exist At that time, obtain the observations of candidate service a on the active dimension u from the original incomplete data matrix. Then obtain from the original CDF matrix The corresponding raw score G a , ;

[0220] Across all active dimensions, the probability that candidate service a dominates candidate service b is calculated using the following formula:

[0221] ;

[0222] Calculate the target probability of candidate service b The target probability The probability of candidate service b becoming an objective Skyline is represented by the following formula:

[0223] ;

[0224] Where C represents all Web services in the global candidate set. This refers to the web services in C other than b.

[0225] Step 7: Based on the target probability, target quota, and the first matrix, determine the target service corresponding to each active dimension, and then combine the padded matrix with the original incomplete data matrix. Output the value of the target service in the active dimension;

[0226] Sort the target probabilities of all candidate services included in the active dimension partition in descending order, and then obtain the top [probabilities] in the sorted order. Each candidate service is used as the target service. The numerical value of the target service on the active dimension u is obtained from the first matrix. If the numerical value of the target service on the active dimension u corresponds to a missing indicator matrix... If the mask is 0, the padded values ​​are denormalized, and the denormalized values ​​are output; if the target service has a missing indicator matrix corresponding to the value on the active dimension u. The middle mask is 1, which will transform the original incomplete data matrix. The numerical value of the target service on the active dimension u is directly output;

[0227] In summary, the key points of this invention are:

[0228] (1) Multiple interpolation mechanism of masked Gaussian mixture latent variable VAE:

[0229] This approach overcomes the limitations of traditional matrix factorization for single-point estimation by introducing a mask-based ELBO deep generative model. Through a forced hard-coverage strategy and 20 Monte Carlo sampling iterations, it reconstructs the potential probability distribution and cognitive uncertainty boundary of missing QoS data, thus overcoming the theoretical bottleneck of loss of discriminative power caused by mechanically determining 0.5 for probabilistic Skyline data under dual missing conditions.

[0230] (2) Optimistic potential candidate selection mechanism based on the 95th percentile:

[0231] By leveraging the variance information inherent in the multiple sampling of the generative model, the conservative "mean evaluation" was abandoned in the partitioned preliminary selection stage. Instead, the 95th percentile was used as the upper limit for potential detection. This maximized the implementation of Skyline's "presumption of guilt" principle to prevent wrongful elimination. Unknown services with highly volatile but potentially top-performing performance were included in the global competition, greatly improving the true recall rate of the candidate set.

[0232] (3) Absolute diversity control that integrates user weights, Hare-Niemeyer quotas, and expected utility:

[0233] Innovatively, user weights are set for each QoS dimension, and the maximum balance method from the field of election physics is introduced into the service quota calculation to eliminate weight rounding errors. Furthermore, a smooth CDF is used to construct the expected utility surface, which strictly and physically isolates the multi-dimensional service space. This ensures that the final recommendation list is not "winner-takes-all" by an absolute dominant force in any one dimension, and enforces high diversity coverage across dimensions in terms of geometric topology.

[0234] (4) Matrix-based global probability Skyline computation (MSPC) strategy:

[0235] The extremely time-consuming pointwise integration and nested loop logic in traditional probabilistic Skyline are decoupled and mapped to a four-element scenario lookup table operation guided by a Boolean state matrix. By constructing a high-throughput threat matrix and accelerating it with underlying vectorized multiplication, the time barrier of complex probabilistic inference on incomplete data is completely broken down.

[0236] Through rigorous theoretical derivation and computational complexity analysis of large-scale real-world datasets (such as QWS, CloudServiceQoS), this invention offers the following significant advantages over existing technologies:

[0237] (1) Recommendation of high precision under relatively incomplete data:

[0238] Theoretical analysis shows that traditional probabilistic Skyline algorithms (such as IQSrec) experience an exponential drop in accuracy when the missing rate exceeds 50%, due to the large number of invalid tie probabilities generated by collisions. This invention benefits from the "distributed memory and restoration" effect of VAE multiple imputation, using resampling to fill in the gaps in the accuracy. It is expected to maintain a Skyline accuracy of over 60% even with a high missing rate, achieving high robustness.

[0239] (2) Prevent "premature pruning" and maintain a high candidate recall rate:

[0240] Traditional evaluation systems based on single imputation or mean values ​​can maliciously suppress the peak potential of high-uncertainty data. This invention provides the highest-level trial-and-error channel for unexplored services with extremely high variance through an "optimistic potential quantile (95%)" mechanism. Mathematically, this ensures that true Pareto optimal entities will not be excluded in early partitioning filtering, and is expected to increase the candidate recall rate of underlying real Skyline objects by 15% to 20% compared to the conservative mean method.

[0241] (3) Accurately respond to personalized preferences and service diversity:

[0242] The Hare-Niemeyer-based computational power allocation and expected utility partitioning completely isolate numerical involution on a single dimension. Theoretical predictions show that, in terms of the diversity scores of Preference Achievement Degree (PAD) and Euclidean distance mapping, the projection volume of this invention far exceeds that of traditional schemes using global blind clustering, providing the healthiest and most comprehensive decision reference for scheduling various industrial microservices and cloud APIs.

[0243] (4) Linearly overcome time bottlenecks and achieve online second-level scheduling:

[0244] In terms of computational complexity, traditional interpolation-based composite probabilistic recommendation (such as MIFCM-DQCSR) takes tens of minutes to complete at a service scale of hundreds of thousands. This invention significantly reduces the time complexity of online recommendation by implementing a pre-built VAE offline solidification (eliminating recomputational power), a strict quota truncation coefficient (compressing submitted samples), and a high-speed MSPC matrix lookup engine. Theoretically, in a sandbox with 200,000 (200K) concurrent services, the end-to-end response time on a single CPU core can be strictly controlled to sub-second levels (<1 second), perfectly meeting the industrial deployment requirements of modern high-frequency cloud-native environments.

[0245] The above description is merely a preferred embodiment of this disclosure and an explanation of the technical principles employed. Those skilled in the art should understand that the scope of the invention involved in the embodiments of this disclosure is not limited to technical solutions formed by specific combinations of the above-described technical features, but should also cover other technical solutions formed by arbitrary combinations of the above-described technical features or their equivalents without departing from the above-described inventive concept. For example, technical solutions formed by substituting the above-described features with (but not limited to) technical features with similar functions disclosed in the embodiments of this disclosure.

Claims

1. An incomplete QoS service recommendation method based on variational autoencoder and probabilistic Skyline, characterized in that, include: Step 1: Obtain the original incomplete data matrix and its corresponding missing indicator matrix ; Among them, the Includes n rows of web services and d columns of QoS, and elements in Indicates the first i The first corresponding web service j The observed values ​​of QoS, the There are missing observations in the data; a missing observation indicator matrix is ​​defined. : A value of 0 indicates that the corresponding observation is missing, while a value of 1 indicates that a valid observation exists at the corresponding position. Step 2: According to and Construct a normalized matrix ; Step 3: Based on Constructing input vectors ,according to and The HeteroVAE encoder and heterogeneous decoupling decoder are trained to obtain the trained HeteroVAE encoder and heterogeneous decoupling decoder. Step 4: Based on the trained HeteroVAE encoder and heterogeneous decoupling decoder, perform... The process yields the padded matrix, the multisampled 3D tensor Q, the expected CDF matrix, the padded expected mean matrix, the original CDF matrix, and the first matrix. Step 5: Determine the active dimension in real time across all QoS levels, and then calculate the target quota for the active dimension. ; Step 6: Construct a global candidate set based on the imputed mean matrix, the multisampled 3D tensor Q, and the expected CDF matrix, and then combine it with the original CDF matrix and the missing indicator matrix. Calculate the target probability for each candidate dimension in the global candidate set; Step 7: Based on the target probability, target quota, and the first matrix, determine the target service corresponding to each active dimension, and then combine the padded matrix with the original incomplete data matrix. Output the value of the target service in the active dimension.

2. The incomplete QoS service recommendation method based on variational autoencoder and probabilistic Skyline according to claim 1, characterized in that, Step 2 specifically includes: Step 2.1: Based on the QoS dimension type, Perform a nonlinear transformation to obtain the transformed observations. Specifically, it includes: When the QoS dimension type is a long-tailed positive real number dimension, for A smooth logarithmic transformation is performed using the following formula: ； in, This is a preset constant; When the QoS dimension type is percentage and probability dimension, for The Logit transformation is performed using the following formula: ； ； ； in, for The Middle j The maximum value among all QoS values. , As an intermediate variable; Step 2.2: For Perform Z-Score standardization based on the standardized observations and the missing indicator matrix. Generate a normalized matrix Specifically, this is achieved through the following formula: ； ； ； ； in, This represents the mean. Indicates standard deviation, As an intermediate variable, Missing indicator matrix The mask in Representing a normalized matrix The elements in.

3. The incomplete QoS service recommendation method based on variational autoencoder and probabilistic Skyline according to claim 2, characterized in that, Step 3 specifically includes: Step 3.1: Normalize the matrix Each row in the vector is used as a zero-padding input vector. Missing indicator matrix M The corresponding row in the middle is used as the mask vector. ,Will and The input vector is obtained by concatenating the features along their dimensions. ; Step 3.2: Input vector Input the HeteroVAE encoder to obtain the mean vector. With log-variance vector ; Specifically, the input vector Inputting the input layer of the HeteroVAE encoder yields nonlinear hidden layer features. Specifically, this is achieved through the following formula: ； in, The weight matrix of the input layer. Here, Tanh represents the bias vector of the input layer; Nonlinear hidden layer features Input two parallel linear layers to obtain the mean vector. With log-variance vector , is represented as: ； ； in, These are the weight matrices that control the mapping of mean and variance, respectively. This is the corresponding bias vector; Build and The corresponding continuous latent space, and the latent feature vectors obtained by sampling in the continuous latent space. ; according to and Generate Web Services i The posterior distribution is obtained through the following formula: ； in, Indicates Web service i The posterior distribution, Indicates a normal distribution. Indicates diagonal; Step 3.3: Convert the latent feature vector Input the heterogeneous decoupling decoder to obtain the probability density function and distribution parameter set; latent feature vectors Input a shared linear layer to obtain a joint representation , is represented as: ； in, To share the weight matrix of the linear layer, The bias vector for the shared linear layer; When the QoS dimension type is a long-tailed positive real number dimension, the joint representation will be used. After passing through a linear layer, the expected mean is obtained. Sum of logarithmic variance Specifically, it is expressed by the following formula: ； ； in, This is the weight matrix for the long-tailed distribution branch. , This is the bias vector for the long-tailed distribution branch. This is a numerical truncation function; according to and Construct the probability density function, expressed as: ; When the QoS dimension type is percentage, the Softplus function is used for joint representation. Processing is performed to obtain shape parameters. and Specifically, it is expressed by the following formula: ； ； in, Here is the weight matrix for the Beta distribution branch. , This is the bias vector for the Beta distribution branch; According to shape parameters and Construct the probability density function, expressed as: ,in, Represents the Beta distribution; Among them, the QoS of the long-tail positive real number dimension and and the shape parameters of QoS in the percentage dimension and Form a distributed parameter set; Step 3.4: Calculate the reconstruction loss Specifically, this is achieved through the following formula: ； in, This represents a set of QoS values ​​with a long-tailed positive real number dimension. This represents a set of QoS values ​​with a percentage dimension. Calculate total loss Specifically, this is achieved through the following formula: ； in, For dynamic weights, Denotes KL divergence, Represents a normal distribution; Step 3.5: Based on the total loss The parameters of the HeteroVAE encoder and the heterogeneous decoupling decoder are updated until the HeteroVAE encoder and the heterogeneous decoupling decoder converge, thus obtaining the trained HeteroVAE encoder and the heterogeneous decoupling decoder.

4. The incomplete QoS service recommendation method based on variational autoencoder and probabilistic Skyline according to claim 3, characterized in that, Step 4 specifically includes: Step 4.1: [The text appears to be incomplete and contains several grammatical errors. A more accurate translation would require Input the trained HeteroVAE encoder to obtain the web service. i The posterior distribution in Web services i Multiple resampling in the posterior distribution yields One latent variable sample ; Step 4.2: For each latent variable sample Input a heterogeneous decoupling decoder to obtain a set of distributed parameters. Point sampling is performed on this set of parameters to obtain a prediction vector. Then, the normalized matrix is... For each missing observation in the i-th row, the corresponding predicted value is obtained from the prediction vector and inserted into the missing observation's position. After all rows are filled, the filled matrix is ​​obtained. Inverse standardization and inverse nonlinear transformation are then performed on the filled matrix to obtain the QoS estimation matrix in the physical space. Get from The observations with a value of 1 are used to replace the corresponding values ​​in the QoS estimation matrix, resulting in a padded observation matrix. This process yields ms padded observation matrices. Step 4.3: Based on the QoS evaluation type, normalize each filled observation matrix using the following formula to obtain normalized observation values. All normalized observation values ​​form an intermediate matrix. The intermediate matrices of all the filled observation matrices form a multisampling 3D tensor Q. For all intermediate matrices... The average of the normalized observations corresponding to the i-th Web service and the j-th QoS is used to obtain the first matrix; When the QoS evaluation type is benefit-based, normalization is performed using the following formula: ； in, These are the elements in the filled observation matrix. These are the normalized observations. Let be the minimum value in the j-th column of the filled observation matrix. This represents the maximum value in the j-th column of the filled observation matrix; When the QoS evaluation type is cost-based, normalization is performed using the following formula: ； Step 4.4: For each QoS, obtain all normalized observations corresponding to the QoS in the multisampling three-dimensional tensor Q, and sort all normalized observations in ascending order to obtain the continuous empirical cumulative distribution function. For each web service, in the continuous experience cumulative distribution function In this process, the sequence number of the normalized observation corresponding to the Web service is determined, the ratio of each sequence number to the total number of Web services is calculated, and then the arithmetic mean of all ratios is calculated to obtain the representative score. Representative scores of all rows and columns Construct the expected CDF matrix; Step 4.5: In the multisampling 3D tensor Q, obtain all normalized observations of the i-th Web service on the j-th QoS, and then calculate the mean of all normalized observations, using it as the sampling mathematical expectation. The mathematical expectations of all samples form the matrix that fills the expectation mean. Step 4.6: For each QoS, in the intermediate matrix Obtain all normalized observations corresponding to QoS, sort all normalized observations in ascending order, and obtain the original empirical cumulative distribution function. For each web service, the original empirical cumulative distribution function In this process, the index of the normalized observation corresponding to the Web service is determined, the ratio of each index to the total number of Web services is calculated, and the original score is obtained. The original scores of all Web services corresponding to all QoS are used to form the original CDF matrix.

5. The incomplete QoS service recommendation method based on variational autoencoder and probabilistic Skyline according to claim 1, characterized in that, Step 5 specifically includes: Step 5.1: Obtain the importance weight assigned by the user to each QoS in real time, and designate QoS with importance weights greater than the threshold as active dimensions. All active dimensions form an active dimension subset. ; Step 5.2: Set the target total number of recommendations The target quota is allocated to each active dimension using the maximum balance method. ; Specifically, for Each active dimension is assigned a baseline quota, and then the first remaining quota is calculated. R , Then calculate the additional quota for each active dimension. Specifically, this is achieved through the following formula: ； ； in, Indicates the first The importance weight of each active dimension For intermediate parameters; Subtract the additional quotas for all active dimensions from the first remaining quota to obtain the second remaining quota. For each active dimension, calculate and The differences are calculated, and the differences of all active dimensions are sorted in descending order. The second remaining quota is then allocated sequentially according to the sorted order to obtain the compensation quota, baseline quota, extra quota, and compensation quota for each active dimension, thus obtaining the target quota for each active dimension. .

6. The incomplete QoS service recommendation method based on variational autoencoder and probabilistic Skyline according to claim 4, characterized in that, Step 6 specifically includes: Step 6.1: For each Web service, obtain the sampled mathematical expectation for each active dimension from the sampled mathematical expectations of all QoS values ​​that fill the expected mean matrix. Determined in the expected CDF matrix Corresponding representative score Among all the representative scores corresponding to the active dimensions, the active dimension with the largest representative score is obtained, and the Web service is assigned to the active dimension partition of the active dimension with the largest representative score. Step 6.2: Partition for each active dimension Obtain Web services from the multisampled 3D tensor Q. i In the active dimension u On Each normalized observation value, in 95th quantile of the normalized observations Obtain from the expected CDF matrix The corresponding representative scores are then used to obtain the active dimension partitions. The representative scores of all Web services are obtained and sorted in descending order. The target quota of the activity dimension u is multiplied by a preset expansion coefficient to obtain the target number. All Web services with the target number are obtained in order from all Web services in descending order to form a candidate pool for the activity dimension. Step 6.3: Merge the candidate pools of all active dimensions to obtain a global candidate set. For any two candidate services in the global candidate set, in the missing indicator matrix... In the process, two candidate services are obtained in terms of activity. u The element on is represented as and ; according to and Calculate in the active dimension u On-the-spot service a Dominate candidate services b probability ; exist At that time, two candidate services are obtained from the original incomplete data matrix in terms of their activity dimension. u Observations on and ,exist hour, ,exist hour, ; exist hour, ; exist At that time, candidate services are obtained from the original incomplete data matrix. b In the active dimension u Observations on Then obtain from the original CDF matrix corresponding raw score G b , ; exist At that time, candidate services are obtained from the original incomplete data matrix. a In the active dimension u Observations on Then obtain from the original CDF matrix corresponding raw score G a , ; Calculate candidate services across all active dimensions a Dominate candidate services b The probability of is specifically achieved through the following formula: ； Computational candidate services b Target probability The target probability Characterization Candidate Service b The probability of becoming an objective Skyline is specifically calculated using the following formula: ; Where C represents all Web services in the global candidate set. This refers to the web services in C other than b.

7. The incomplete QoS service recommendation method based on variational autoencoder and probabilistic Skyline according to claim 6, characterized in that, Step 7 specifically includes: Sort the target probabilities of all candidate services included in the active dimension partition in descending order, and then obtain the top [probabilities] in the sorted order. Each candidate service is used as the target service, and the target service's activity dimension is obtained in the first matrix. u The values ​​above indicate that the target service is active. u The missing indicator matrix corresponding to the values ​​on If the mask is 0, the padded values ​​are denormalized, and the denormalized values ​​are output; if the target service is in the active dimension u The missing indicator matrix corresponding to the values ​​on The middle mask is 1, which will transform the original incomplete data matrix. In terms of the activity dimension of the target service u The values ​​are output directly.

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