# Re-Enrichment Learning: Metadata Saliency for the Evolutive Personalization of a Recommender System
## 3 Re-Enrichment Learning
### Metadata Saliency  
A user's behavioral history can be used not only as primary cumulative data, but also as information from which secondary features are extracted. Metadata saliency is one of the secondary features that can play an important role, especially in leveraging implicit logged feedback data. A few interesting items usually account for the majority of interest fixation, and they can be quantified by extracting metadata saliency from the logged feedback. Among the various types of feedback, we focus on the ones that contain the retention data of a user, and we start with the simplest type: the clicks on recommended items. The metadata saliency of the \(i_{d}^{th}\) category in the transferred domain at time \(t\), \(v_{k,t}(i_{d})\), is computed based on the \(i_{d}^{*}\)\({}^{th}\) clicked category, as in Equation (10). A Gaussian fixation model has been adopted [21, 41, 42, 4], of which the average and standard deviation are \(i^{*}\) and \(1\), respectively, in order to reinforce the metadata saliency of the \(i_{d}^{th}\) category, but also to enrich its nearest neighbors with respect to the transferred domain. The Gaussian fixation is also scaled based on the metadata saliency of the \(i_{d}^{th}\) category at time \(t-1\), \(v_{k,t-1}(i_{d})\), and the influence factor \(\alpha\) (see Equation (11)). The very first metadata saliency, \(v_{k,0}\), can be set by a preference survey for new users for the cold start (discussed in Section 4.2.1). Otherwise, for users who refuse the survey, the average of the metadata saliencies of many random users can be an alternative for \(v_{k,0}\) (discussed in Section 4.2.2).  
\[v_{k,t}(i_{d})=v_{k,t-1}(i_{d})+\frac{A\big{|}_{i_{d}^{*}}}{\sqrt{2\pi}}\cdot e ^{-\frac{1}{2}(i_{d}-i_{d}^{*})^{2}} \tag{10}\]  
\[A\big{|}_{i_{d}^{*}}=\frac{1}{e^{v_{k,t-1}^{*}(i_{d}^{*})^{2}+\alpha}} \tag{11}\]  
Figure 1: Adjacency matrix \(E_{k,t}\).  
Suppose that a graph has been built to represent the metadata saliencies of movie genres for a user (see Figure 2). A node is presented as a circle, of which the radius indicates its attribute level. An edge is drawn as a line, of which the thickness is proportional to its attribute level. The user must mostly have preferences for Action movies, as well as Sci-Fi movies, because the two nodes corresponding to those genres are the two biggest circles, as shown in Figure 2. Provided that the user clicked an item that belongs to the Action category at time \(t\), not only does the metadata saliency of Action node get larger at time \(t+1\), but that of the Sci-Fi node also benefits from it to a certain extent due to the connection of the edge to the two nodes and the Gaussian fixation effect. Moreover, the Fantasy and Adventure nodes also deserve a small benefit from the feedback. Because of the new feedback, the attributes of the nodes and edges change simultaneously and incrementally create a new condition in the graph representation. As such, the metadata saliency naturally changes over time by means of the newly collected feedback. The change in metadata saliency is promptly reflected in a user's graph and, by extension, also in the universal domain, which is built upon many users' graphs. Consequently, the evolutive characteristic based on the mutual interaction in the graph makes re-enrichment learning prompt and flexible.