# Recommendation Framework Combining User Interests with Fashion Trends in Apparel Online Shopping
## 3 Proposed Method
### Rating Item Clusters  
Rating the user's preference for item clusters is performed in three steps: Generating implicit ratings, clustering items, and rating item clusters by CF. We first suggest a weighting scheme that computes an implicit rating by the combination of three types of user activities, i.e., click, cart, and order, from user log data. The click activity implies browsing a webpage of a product and viewing its detailed information. Although the click represents an initial interest in an item, the cart activity shows more interest than the click. A user finally makes a choice by the order activity, which is an even stronger representation of interest in an item. Because these types of activities--click, cart, and order--are applied to almost all types of e-commerce [22; 36], we decide to use them in our study in order to preserve the generality of the proposed method. Note that although cart and order are one-time activities, a user can visit the webpage of a specific product multiple times, which means that k clicks can executed by a user. Setting the rating for order activity, \(w_{\mathit{order}}\), to the highest value of one (1 if ordered, 0 otherwise), the proportion of cart or click activity to order activity is assigned to its rating, which can be interpreted as the degree of purchase intention when an item is clicked or placed in cart. The rating of cart activity is then computed by  
\[w_{\mathit{cart}}=\frac{N(\mathit{CART}\cap\mathit{ORDER})}{N(\mathit{CART})}, \tag{1}\]  
where \(N(\mathit{CART})\) is the number of cart activities and \(N(\mathit{CART}\cap\mathit{ORDER})\) is the number of co-occurrences of both cart and order activities in the log data. Accordingly, \(N(\mathit{CART})-N(\mathit{CART}\cap\mathit{ORDER})\) is the number of activities by which a user placed an item in her/his cart but did not purchase it. Owing to the small size, \(N(\mathit{CART})=1\) and \(N(\mathit{CART}\cap\mathit{ORDER})=0\) in our example dataset in Table 1. The real dataset used in our experiments shows that approximately 18 percent of cart activities finally resulted in ordering the items in the cart (See Figure 7 in Section 4.3). We now evaluate the click activity, using the fact that more clicks on an item by a user imply her/his stronger interest in it and vice versa. Suppose that a user finally purchased an item after \(k\) clicks on it. We count the number of these activities from the log data, which is denoted by \(N(\mathit{CLICK}(k)\cap\mathit{ORDER})\). Notice that a user may purchase an item by one click and the user may do so after multiple clicks (\(k=1,\ 2,\ 3,\cdots\)). We then count the number of activities by which a user clicked \(k\) times on a certain item, which is denoted by \(N(\mathit{CLICK}(k))\). From the example in Table 1, we can obtain \(N(\mathit{CLICK}(1))=7\) (\(u_{1}\) clicked \(i_{3}\), \(i_{4}\), and \(i_{7}\) once each, \(u_{2}\) clicked \(i_{3}\) and \(i_{5}\) once each, and \(u_{3}\) clicked \(i_{8}\) and \(i_{9}\) once each), \(N(\mathit{CLICK}(2))=1\) (\(u_{1}\) clicked \(i_{1}\) twice), and \(N(\mathit{CLICK}(3))=1\) (\(u_{2}\) clicked \(i_{2}\) three times). Because \(u_{1}\) purchased \(i_{3}\) after one