## 3 Methodology
### User Affiliation Network
#### 3.3.2 User Affiliation Network  
The schematic diagram of the affiliation network is shown in Figure 5. For each user, their affiliated users include both indirect and virtual users. In Figure 5, the pink figure means the real user, and the gray figure is the affiliated user. If users buy an item that does not fit their age profile, a virtual person is built for them. The preference matrix of affiliated users is constructed for each real user node. When the user purchases items, the algorithm automatically identifies which node belongs to according to the item information. When making recommendations, in addition to recommending the user's own favorite items, users can also be recommended items in line with the preferences of other affiliated users. For example, if a middle-aged woman buys a children's dress, a daughter's affiliated user will be added to her affiliation network. The preference information of the affiliated user will be recorded according to the color and style of the dress, and recommend children's items with the same or similar style according to the purchased dress to the user. **Definition 1**. : _Virtual users. If a real user purchases an item that does not belong to him or her, a corresponding affiliated user is constructed, such as father, mother, child, friend, etc. sub represents the affiliated user node; then, the affiliated user node sub is:_  
\[sub=ext\{I|I\in(i_{b}-i_{u})\} \tag{8}\]  
_where \(ext\) is the extraction operation, \(i_{b}\) is all the items purchased by user \(u\), \(i_{u}\) is the items purchased by user \(u\) that conform to user identity information, and \(I\) is the set of items selected by the same affiliated user._  
**Definition 2**. : _Indirect user. For user \(u_{a}\), if there is another user \(u_{b}\) with the same or similar preferences as \(u_{a}\) in the category, color, and style of items, \(u_{b}\) is the indirect user of \(u_{a}\), represented by \(ind\); then, the indirect user node \(ind\) of user \(u_{a}\) is:_  
\[ind=\left\{u_{b}\right|A_{u_{b}}\sim A_{u_{a}}\} \tag{9}\]  
_where \(\sim\) indicates similar preferences._  
The preference relationship between the indirect and virtual user relative to the user itself is the affiliated relationships. The affiliated relationships of indirect users refer to the idea of collaborative filtering. If users have similar preferences and they have no  
Figure 5: User affiliation network. social relationship, they are indirect users of each other. The affiliation of virtual users is information about what the user has purchased for them. When making recommendations, the virtual user considers not only the user themself but also the affiliated relationships of the user as a part of the user data, and makes recommendations separately from the user preference. **Definition 3**. : _Increasing preference. The increasing preference pays attention to the changes in the interests of affiliated users, recommends items they continue to like in their historical preferences, and conducts interest testing with a small number of novel items that have never appeared, which is the key to interact and influence with the surrounding users._  
Whether between users or between users and affiliated users, purchase behavior is crucial to the generation and change in the relationship chain between users. the relationship chain means that real users have the same preference, real users buy items for affiliated users, and the identity of affiliated users is consistent with the algorithm judgment. Through the items purchased by users for different affiliated users, the preference information of affiliated users is obtained and, based on this, the user affiliation network is constructed to enhance the user preferences. **Definition 4**. : _Affiliated user preference attributes.