Movatterモバイル変換


[0]ホーム

URL:


CN111881363B - Recommendation method based on graph interaction network - Google Patents

Recommendation method based on graph interaction network
Download PDF

Info

Publication number
CN111881363B
CN111881363BCN202010578943.8ACN202010578943ACN111881363BCN 111881363 BCN111881363 BCN 111881363BCN 202010578943 ACN202010578943 ACN 202010578943ACN 111881363 BCN111881363 BCN 111881363B
Authority
CN
China
Prior art keywords
user
node
interaction
module
network
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Active
Application number
CN202010578943.8A
Other languages
Chinese (zh)
Other versions
CN111881363A (en
Inventor
简萌
张宸林
毋立芳
邓斯诺
胡文进
卢哲
张恒
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Beijing University of Technology
Original Assignee
Beijing University of Technology
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Beijing University of TechnologyfiledCriticalBeijing University of Technology
Priority to CN202010578943.8ApriorityCriticalpatent/CN111881363B/en
Publication of CN111881363ApublicationCriticalpatent/CN111881363A/en
Application grantedgrantedCritical
Publication of CN111881363BpublicationCriticalpatent/CN111881363B/en
Activelegal-statusCriticalCurrent
Anticipated expirationlegal-statusCritical

Links

Classifications

Landscapes

Abstract

A recommendation method based on a graph interaction network is applied to the field of personalized recommendation of users. The rapid development of the internet industry and the continuous increase of network data volume, the traditional recommendation method and the deep learning method are difficult to meet the complex application environment, and have the defects in accuracy and space complexity. Therefore, the recommendation method based on the graph interaction network, provided by the invention, has the advantages that the personalized recommendation accuracy can be ensured, the model space complexity is reduced, and the application prospect is wide.

Description

Recommendation method based on graph interaction network
Technical Field
The invention is applied to the field of recommendation systems based on U-I relations, and particularly relates to data mining and deep learning technologies such as a graph depth network, an attention mechanism, user preference information and item attribute information feature extraction, U-I interaction information modeling and the like.
Background
Personalized recommendation is a comprehensive analysis task, and is widely applied to the fields of social networks, music stations, electronic commerce, personalized advertisements, movies, video websites and the like, so that the personalized recommendation is paid attention to. With the rapid development of the internet industry and the continuous increase of network data volume, recommendation systems face increasingly complex recommendation tasks and application environments. Particularly, since the Web 2.0 era, with the advent of the dismilitary of social networking media, the internet people are consumers of network information and producers of network content, and the amount of information in the internet has increased exponentially. Because of the limited discrimination capability of users, users often feel unproductive when faced with huge and complex internet information, so that the cost of searching useful information in the internet is huge, and the information overload problem arises. Thus, it is a very important and challenging matter for users how to quickly and accurately locate their own desired content in exponentially growing resources. It is also a very difficult matter for merchants to present the appropriate items to users in time, thereby promoting increases in transaction volume and economy. The advent of recommendation systems has greatly alleviated this difficulty.
Collaborative filtering algorithm plays an important role in the early recommended scenario as the most classical traditional recommendation algorithm. The collaborative filtering algorithm can naturally model the higher-order relation between the user and the object, and has low model complexity and easy deployment. These advantages make it the most widely used recommended method to date. However, with the explosive growth of internet users, the variety and properties of the articles are more and more complete, and the increasing richness of internet resources makes the preference information of users progress toward diversification and refinement. Under such an environment, the recommendation accuracy of the algorithm has a great disadvantage, and the conventional recommendation algorithm represented by the collaborative filtering algorithm is difficult to meet the personalized requirements of users.
In recent years, deep learning techniques have been rapidly developed. Deep learning is increasingly used in the field of computer vision, natural language processing and recommendation systems. The deep learning technology is used for deep mining of user preference information and article attribute information by constructing a deep network. The model architecture of the recommendation system is innovated, and various defects of the traditional model are overcome. The recommendation accuracy is greatly improved, and a more effective solution is provided for the problems of system cold start and the like, so that the recommendation accuracy is widely paid attention to. Conventional deep learning techniques do not naturally combine user and item information. Generally, the method for stacking multiple models only extracts better quality characteristics of users and articles by utilizing a deep network according to the interaction relation between the users and the articles, and predicts the preference degree of the users to the articles to be recommended through other models or another deep network.
In recent years, the analysis and processing of non-European data becomes a hot topic in academia and industry, and a graph depth network can naturally integrate interaction relationship between users and articles. The method effectively extracts the graph data characteristics and the node characteristics, naturally mines the user preference and the article attribute information expression, and provides a brand-new direction for personalized recommendation tasks. In recent years, the research of the graph depth network has greatly developed, thomas Kpif in 2017 proposes the concept of the graph convolution network, which provides a brand-new idea for processing graph structure data and applies the convolutional neural network in the deep learning to the graph structure data. The graph convolution method based on the spatial domain takes any node as a convolution object, and gathers information of neighbor nodes to construct a graph convolution layer, so that the graph convolution method based on the spatial domain is more widely applied compared with the graph convolution method based on the frequency domain due to flexibility and high efficiency. Meanwhile, hamilton provides a generalized learning mode suitable for a large-scale network, so that node characteristics can be quickly generated for newly added nodes without additional training, and the problem of expandability of the graph convolution neural network is greatly relieved. The rapid development of graph depth networks indicates directions for the construction of personalized recommendation systems.
Disclosure of Invention
In order to realize a personalized recommendation system of a user, a personalized recommendation scheme based on a graph interaction network is provided. The process flow is shown in fig. 1. According to the method, a U-I interaction relation diagram is used as input data, all modules finish feature extraction and feature analysis processing on user preference and object attributes, and finally, the prediction score of a user on a target object is output. Specifically, the method firstly carries out graph structure modeling on the interactive relation data of the user and the article, and the data sets are all from the public data sets in the industry. After the graph structuring process is completed, the characteristic distribution of the user and the object is optimized by stacking a plurality of average convolution layers. After the U-I feature optimization is completed, there may be a greater similarity between the user features and the item features that meet the user's preferences. And then, utilizing an attention mechanism, fusing the node characteristics of the target user and the node characteristics of the object to be recommended to obtain an implicit characteristic expression of the graph interaction network, namely an interaction vector of the U-I relation pair, and finally, modeling a high-order nonlinear relation among U-I through a multi-layer graph full-connection layer network learning interaction characteristic vector distribution rule to obtain a prediction score of the user on the target object. And finally, realizing personalized recommendation tasks for the user through a top-N recommendation mechanism. The overall block diagram of the method is shown in fig. 1.
The invention content of each main module of the method is as follows:
1. User preference information and item attribute information optimization
The first module is a user preference and article attribute feature optimization module, and the purpose of user preference information modeling is to obtain accurate user feature representation according to user interaction behaviors so as to fully mine the interest and hobby information of a user. The object attribute information modeling is used for obtaining perfect relation attributes and content characteristics, further accurately finding out audience groups of objects, and completing personalized recommendation of the objects. User and item feature expressions are quickly obtained by using two mean convolution layers. Where the characteristics between U-I, where the user preferences and item attributes are consistent, are more similar. The user and article feature extraction is an important component for constructing a recommendation system, and plays a key role in personalized recommendation.
Firstly, carrying out graph structural modeling on the U-I interaction data, and establishing a connection relationship between user items with interaction behaviors. After the structured modeling of the graph is completed, initializing user preference characteristics and item attribute characteristics, and then accurately modeling the user item characteristics, so that user preference information and item attribute information are fully mined. The method optimizes the characteristics of users and articles through two average convolution layers, wherein each layer of target node characteristic learning is obtained by carrying out averaging treatment on the basis of one layer of neighbor node characteristics and the node characteristics on the node. After the modeling of the user and the article features is finished, the user features and the article features have stronger distribution regularity, and then the user preference and the article attribute information are preliminarily extracted. The mean convolution processing greatly reduces the space complexity of the model while ensuring the feature accuracy. The module flow framework is shown in fig. 2.
U-I interaction feature extraction module
The second module is a U-I interaction feature extraction module, and the function of this module is to extract the interaction feature expression between the user item pairs. The U-I interactive feature extraction module is used for directly fusing user features and article features on the graphic neural network to learn interactive feature expression of the user features and the article features after the user preference information and the article attribute information are extracted. The U-I interaction characteristics are input characteristics of the interaction speculation module.
Firstly, splicing user characteristics and first-order neighbor node characteristics of a user, splicing characteristics of articles to be recommended and first-order neighbor node characteristics of the articles to be recommended, and inputting the spliced characteristics into a self-attention network to obtain attention coefficients of the module, wherein the self-attention network adopts multi-layer full-connection layer network modeling. And finally, aggregating the U-I target node characteristics and the neighbor node characteristics thereof through the attention coefficients obtained through learning to obtain the final interaction characteristic expression. The specific flow of the module is shown in fig. 3.
3. Interactive speculation module
The third module is an interaction presumption module, and the function of the module is to learn the distribution rule of the interaction characteristics after the U-I interaction characteristic extraction module extracts the interaction characteristics between the user and the target object, so as to obtain the presumption score of the user on the target object. The interactive speculation module is an indispensable step for building recommendation, and the design method of the interactive speculation module is quite many, such as traditional feature inner products, logistic regression algorithms and the like, but the traditional algorithms cannot well model the high-dimensional feature relation between the user and the object, so that the invention adopts the classical DNN algorithm to fuse the feature information of the user and the object and obtain a more accurate speculation result.
After the interactive feature expression of the user and the target object is obtained, the interactive vector is directly input into the DNN network, and the preliminary prediction of the model is obtained. And then, carrying out normalization processing on the module predicted value through a sigmoid function, and modeling the predicted score of the target object by the user into a preference probability expression. The flow of this module is shown in fig. 4.
Top-N recommendation module
The last module of the invention is a top-N recommendation module, and a top-N recommendation mechanism is also the most commonly used mechanism for constructing a recommendation system. And after the evaluation value prediction of all the articles of the list to be recommended by the target user is obtained. And sorting all the articles in a descending order according to the scores, recommending the first N articles to the user, and realizing personalized recommendation of the user.
Drawings
FIG. 1 is a general block diagram of an interaction graph based neural network;
FIG. 2 is a user preference information and item attribute information modeling module framework;
FIG. 3 is a U-I interaction feature extraction module framework
FIG. 4 is an interactive speculation module framework
Detailed Description
The invention provides a personalized recommendation method based on an interaction graph neural network. The specific implementation steps of the invention are as follows:
Step one: selecting a public recommended data set, arranging serial numbers for all users and articles, randomly selecting 90% of the articles interacted by each user as a training set, and remaining 10% of the articles as a test set. Each training set and test set consists of three parts: user, article, label. The item with interactive behavior with the user has a label of 1, otherwise the label is 0. And carrying out undirected graph structural expression through all pieces of data with the labels of 1 in the training set, and establishing a connection relationship for users with interactive behaviors and articles.
Step two: after the training set undirected graph is structured, randomly initializing high-dimensional feature expression of all user nodes and object nodes in the graph, namely randomly initializing user preference information and object attribute information. And then, building two layers of mean value convolution layer networks according to the node connection relation of the undirected graph, wherein all node characteristics in each layer of mean value convolution layer network are obtained by polymerizing the node characteristics and first-order neighbor node characteristics in the previous layer of network, the polymerization mode is an averaging treatment, and the mathematical expression is as follows:
Wherein the method comprises the steps ofFeatures of user node u representing the K-th mean convolution layer. N (u) represents a first-order item neighbor node of the user node u. N (v) represents a first-order user neighbor node of item node v. /(I)Features of the item node v representing the K-th mean convolution layer. MEAN represents the averaging process, i.e. averaging the relevant U-I features for each dimension. After the multi-layer mean convolution layer processing, all node characteristics in the undirected graph have larger distribution regularity, and user nodes with similar preference and attribute and object node characteristics are similar. User preference information and item attribute information are initially modeled.
Step three: after the modeling of the user object features is completed, aiming at a target user and an object node to be recommended in the undirected graph, a graph attention mechanism is fused, and the interaction feature expression between the U-I pair is obtained by aggregating the user and the first-order neighbor features thereof and the object and the first-order neighbor features thereof. And splicing the user characteristics and the first-order neighbor node characteristics of the user, splicing the characteristics of the articles to be recommended and the first-order neighbor node characteristics thereof, inputting the spliced characteristics into the attention network, and obtaining attention coefficients corresponding to the user and the article characteristics. And carrying out softmax normalization treatment on the obtained attention coefficients. The method for the graph annotation force network adopts two full-connection layers for modeling. The advantage of constructing the self-attention mechanism network by adopting the multi-layer full-connection layer is obvious, the number of the first-order neighbor nodes of the undirected graph node can be self-adapted, and the importance of the first-order neighbors of the node to the node can be effectively modeled. And thus a more accurate attention coefficient. Wherein attention coefficient modeling mathematical expression is:
Wherein W1,W2 represents the parameter matrix of the first layer and the second layer of the two-layer attention network, b1,b2 represents the deviation coefficient of the first layer and the second layer of the two-layer attention network, sigma represents a nonlinear activation function, and Relu activation function is adopted in the invention.Represented is a node characteristic of the target user ui in the undirected graph. ha denotes the characteristics of node a, which is any node in the set of user ui and its first-order neighbors N (i). N (i) represents the first-order item neighbor set for user ui.Representing the stitching process. /(I)Represented is a node characteristic of the item vj to be recommended. hb is a feature of node b, which is any node in the set of item vj and its first order neighbors N (j). N (j) represents a first-order set of user neighbors of item vj. /(I)AndAnd (5) representing the weight coefficient which is preliminarily obtained by the characteristics obtained by splicing through attention networks. And then carrying out softmax normalization processing to obtain attention coefficients alphaia of the target user and the first-order neighbors thereof and attention coefficients betajb of the articles to be recommended and the first-order neighbors thereof.
And after attention coefficients of the user, the first-order neighbors of the user and the target object and the first-order neighbors of the target object are obtained, the attention coefficient weighting target node characteristics are fused to obtain the final interaction characteristic expression. The mathematical expression is as follows:
zij is the interactive feature expression of the obtained target user ui and the item vj to be recommended.
Step four: after the interactive feature expression of the user and the target object is obtained, the model learns the distribution rule of the interactive feature through the interactive presumption module, and further the accurate object scoring of the user on the object is obtained. Interaction speculation module the method uses classical DNN networks. The DNN network can effectively learn the characteristic distribution and model the nonlinear relationship between the user and the article. The interaction presumption module directly inputs the interaction characteristics into the DNN network to obtain the predictive score of the user on the object, and then models the predictive score of the model into the probability expression of the user on the target object through sigmoid normalization processing. The mathematical expression is as follows:
g1=zij (8)
g2=σ(W1·g1+b1) (9)
g3=σ(W2·g2+b2) (10)
r′ij=sigmoid(W3·g3) (11)
Wherein W1,W2,W3 represents a parameter matrix of the DNN network, b1,b2 represents a deviation coefficient in the DNN network, sigma represents a nonlinear activation function, and Relu activation function is adopted in the method. g1,g2,g3 is the interaction vector expression output by each layer of the DNN network. r'ij is the final probability prediction evaluation value expression obtained after sigmoid normalization.
Step five: to optimize the parameters of the model and the user item node feature expression. According to the method, the fitting degree of the cross entropy loss function modeling model is constructed, and the loss function value is minimized through a random gradient descent algorithm, so that the effect of optimizing the model parameters and node characteristics is achieved. Wherein, the mathematical expression of the cross entropy loss function is:
Where |O| represents all user item node pairs extracted from the undirected graph during model training, and rij represents the tag values of the target user ui and the item vj to be recommended, and the value range is {0,1}. A label of 0 indicates that the item vj attribute information does not conform to the preference information of the user ui as a negative sample of model training. A label of 1 indicates that user ui has interactive behavior with item vj, which is positive sample data for model training. r'ij represents the predictive score of the model. The difference between r'ij and the actual label rij is minimized through a random gradient descent algorithm, so that the loss function value is optimized, the parameter matrix of the model is optimized, and the user preference information and the article attribute information are effectively extracted.
Step six: after model training is completed, the algorithm of the present invention was tested on dataset huaban and Amazon-Book in order to verify the effectiveness of the present invention. After model training is completed, the predictive rating of the negative-sample participation model is randomly acquired at a ratio of 1:100 for the test set of each data set. Meanwhile, in order to ensure the effectiveness of model evaluation, the negative samples collected by the test set do not participate in training in the training set. After the predictive evaluation values of the model on all the articles of each user are obtained, sorting the articles participating in the evaluation from large to small according to the output value of the model, and recommending the top N articles after sorting to the target user through a top-N recommendation machine. And the effectiveness of the method is compared through effective evaluation indexes. Tables 1 and 2 show the algorithm of the present invention in comparison to the partial front recommendation algorithm recall, which can be seen to be superior to the other recommendation algorithms shown.
Table 1: performance comparison on Amazon-book dataset
Table 2: performance contrast on huaban dataset

Claims (1)

Firstly, carrying out graph structural modeling on user and article relation data; the user preference information and article attribute information optimizing module extracts user characteristics and article characteristic expression by stacking two average convolution layers; the U-I interaction feature extraction module utilizes a graph attention mechanism to fuse target user features and to-be-recommended object features to obtain implicit feature expression on a graph interaction network, namely interaction vectors of the U-I relation pairs; the interaction presumption module learns the distribution rule of the interaction feature vector through the DNN network, models the nonlinear relation among U-I, and obtains the prediction score of the user on the target object; finally, sorting the target objects through a top-N recommendation module to realize personalized recommendation tasks for users;
Wherein W1,W2 represents the parameter matrix of the first layer and the second layer of the two-layer attention network, b1,b2 represents the deviation coefficient of the first layer and the second layer of the two-layer attention network, sigma represents a nonlinear activation function, and Relu activation function is adopted; the node characteristics of a target user ui in the undirected graph are shown; ha is a feature of a node a, where a node a is any node in the set of the user ui and its first-order neighbor N (i); n (i) represents a first-order set of article neighbors for user ui; /(I)Representing a splicing process; /(I)Representing the node characteristics of the item vj to be recommended; hb is the feature of node b, which is any node in the set of item vj and its first-order neighbor N (j); n (j) represents a first-order set of user neighbors of item vj; /(I)AndRepresenting a weight coefficient preliminarily obtained by the characteristics obtained by splicing through attention networks; then carrying out softmax normalization processing to obtain attention coefficients alphaia of the target user and the first-order neighbors thereof and attention coefficients betajb of the articles to be recommended and the first-order neighbors thereof;
CN202010578943.8A2020-06-232020-06-23Recommendation method based on graph interaction networkActiveCN111881363B (en)

Priority Applications (1)

Application NumberPriority DateFiling DateTitle
CN202010578943.8ACN111881363B (en)2020-06-232020-06-23Recommendation method based on graph interaction network

Applications Claiming Priority (1)

Application NumberPriority DateFiling DateTitle
CN202010578943.8ACN111881363B (en)2020-06-232020-06-23Recommendation method based on graph interaction network

Publications (2)

Publication NumberPublication Date
CN111881363A CN111881363A (en)2020-11-03
CN111881363Btrue CN111881363B (en)2024-06-25

Family

ID=73158034

Family Applications (1)

Application NumberTitlePriority DateFiling Date
CN202010578943.8AActiveCN111881363B (en)2020-06-232020-06-23Recommendation method based on graph interaction network

Country Status (1)

CountryLink
CN (1)CN111881363B (en)

Families Citing this family (10)

* Cited by examiner, † Cited by third party
Publication numberPriority datePublication dateAssigneeTitle
CN112445981A (en)*2020-11-042021-03-05西安电子科技大学Social and consumption joint recommendation system, method, storage medium and computer equipment
CN112347362B (en)*2020-11-162022-05-03安徽农业大学 A Personalized Recommendation Method Based on Graph Autoencoder
CN112486467B (en)*2020-11-272022-04-29武汉大学Interactive service recommendation method based on dual interaction relation and attention mechanism
CN112559864B (en)*2020-12-142023-03-31西安电子科技大学Bilinear graph network recommendation method and system based on knowledge graph enhancement
CN113377656B (en)*2021-06-162023-06-23南京大学 A Crowd Test Recommendation Method Based on Graph Neural Network
CN115631008B (en)*2021-07-162024-02-13腾讯科技(深圳)有限公司Commodity recommendation method, device, equipment and medium
CN113590976A (en)*2021-07-172021-11-02郑州大学Recommendation method of space self-adaptive graph convolution network
CN113722583A (en)*2021-07-312021-11-30华为技术有限公司Recommendation method, recommendation model training method and related products
CN114254102B (en)*2022-02-282022-06-07南京众智维信息科技有限公司Natural language-based collaborative emergency response SOAR script recommendation method
CN114817751B (en)*2022-06-242022-09-23腾讯科技(深圳)有限公司Data processing method, data processing apparatus, electronic device, storage medium, and program product

Citations (1)

* Cited by examiner, † Cited by third party
Publication numberPriority datePublication dateAssigneeTitle
CN110162706A (en)*2019-05-222019-08-23南京邮电大学A kind of personalized recommendation method and system based on interaction data cluster

Family Cites Families (4)

* Cited by examiner, † Cited by third party
Publication numberPriority datePublication dateAssigneeTitle
US8463295B1 (en)*2011-12-072013-06-11Ebay Inc.Systems and methods for generating location-based group recommendations
CN110633421B (en)*2019-09-092020-08-11北京瑞莱智慧科技有限公司Feature extraction, recommendation, and prediction methods, devices, media, and apparatuses
CN110866145B (en)*2019-11-062023-10-31辽宁工程技术大学 A deep single-class collaborative filtering recommendation method assisted by common preferences
CN110910218B (en)*2019-11-212022-08-26南京邮电大学Multi-behavior migration recommendation method based on deep learning

Patent Citations (1)

* Cited by examiner, † Cited by third party
Publication numberPriority datePublication dateAssigneeTitle
CN110162706A (en)*2019-05-222019-08-23南京邮电大学A kind of personalized recommendation method and system based on interaction data cluster

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
推荐系统研究综述;周万珍;曹迪;许云峰;刘滨;;河北科技大学学报(第01期);全文*

Also Published As

Publication numberPublication date
CN111881363A (en)2020-11-03

Similar Documents

PublicationPublication DateTitle
CN111881363B (en)Recommendation method based on graph interaction network
CN111881342B (en) A recommendation method based on graph twin network
Liu et al.Contextualized graph attention network for recommendation with item knowledge graph
CN110674407B (en) Hybrid recommendation method based on graph convolutional neural network
CN112232925A (en)Method for carrying out personalized recommendation on commodities by fusing knowledge maps
CN113918832B (en) Graph convolution collaborative filtering recommendation system based on social relations
CN114117142A (en) A label-aware recommendation method based on attention mechanism and hypergraph convolution
CN113918833B (en)Product recommendation method realized through graph convolution collaborative filtering of social network relationship
CN113918834B (en)Graph convolution collaborative filtering recommendation method fusing social relations
CN113378048A (en)Personalized recommendation method based on multi-view knowledge graph attention network
Zarzour et al.RecDNNing: a recommender system using deep neural network with user and item embeddings
CN117313841A (en)Knowledge enhancement method based on deep migration learning and graph neural network
Wang et al.An enhanced multi-modal recommendation based on alternate training with knowledge graph representation
CN112149734B (en) A Cross-Domain Recommendation Method Based on Stacked Autoencoders
Zhou et al.Rank2vec: Learning node embeddings with local structure and global ranking
Lv et al.DSMN: An improved recommendation model for capturing the multiplicity and dynamics of consumer interests
Yu et al.A graph convolutional network based on object relationship method under linguistic environment applied to film evaluation
Li et al.Parallel recursive deep model for sentiment analysis
CN115204967A (en)Recommendation method integrating implicit feedback of long-term and short-term interest representation of user
Chen et al.Gaussian mixture embedding of multiple node roles in networks
Zhang et al.Knowledge Graph Driven Recommendation System Algorithm
Yuan et al.Matching recommendations based on siamese network and metric learning
CN119917707A (en) Data recommendation method and device, data recommendation model processing method and device
Lu et al.Product recommendation system based on deep learning
CN116108229A (en) A service recommendation method based on knowledge graph

Legal Events

DateCodeTitleDescription
PB01Publication
PB01Publication
SE01Entry into force of request for substantive examination
SE01Entry into force of request for substantive examination
GR01Patent grant
GR01Patent grant

[8]ページ先頭

©2009-2025 Movatter.jp