# Re-Enrichment Learning: Metadata Saliency for the Evolutive Personalization of a Recommender System
## 3 Re-Enrichment Learning
### Summary  
In summary, we provide Figure 3 to depict a diagram that connects all the steps of the process, and the process can be listed as follows:  
* Step 1: Obtain the user's implicit logged feedback \(i_{d}^{*}\) at time \(t\) from the recommender
* Step 2: Update nodes \(V_{k,t-1}\to V_{k,t}\): Calculate node attribute \(v_{k,t}(i_{d})\) at time \(t\) using the universal domain \(\mathbf{D_{t-1}}\) and the node attribute \(v_{k,t-1}(i_{d})\) at time \(t-1\) (as shown in Equation (10)).
* Step 3: Update edges \(E_{k,t-1}\to E_{k,t}\): Calculate the edge attribute \(e_{k,t}(i,j)\) at time \(t\) using the node attribute \(v_{k,t}(i_{d})\) at time \(t\) (as in Equation (4), which consists of the two following terms).
* Compute the likelihood of influence of the node: \(\sigma\big{(}\alpha\cdot v_{k,t}^{\prime}(i)\big{)}\) (see Equation (5)).
* Compute the weight for the similarity between two nodes: \(1-\overset{\triangle}{v_{k,t}^{\prime}}(i,j)\) (see Equation (7)).
* Step 4: Update the universal domain \(D_{t-1}\to D_{t}\) (as in Equation (9)): Sort domain \(D_{t}(h)\) by edge attribute.
* Step 5: Apply the node attribute \(v_{k,t}(i_{d})\) at time \(t\), i.e., the metadata saliency, to the recommender.  
Figure 2: Conceptual visualization of a graph (node: circle radius, edge: line thickness).  
Furthermore, we provide a pseudocode to effectively present how the different steps of our proposed approach are organized (see Table 1).  
\begin{table}
\begin{tabular}{l} \hline \hline
**Pseudocode** \\ \hline
**Input** : Implicit logged feedback \(i_{d}^{s}\), Nodes \(V_{k,t-1}\), Edges \(E_{k,t-1}\), Universal domain \(\mathbf{D_{t-1}}\) \\
**Output** : Nodes \(V_{k,t}\), Edges \(E_{k,t}\), Universal domain \(\mathbf{D_{t}}\) \\
**Parameter** : Influence factor \(\alpha\) \\  /* _Update Nodes_\(V_{k,t-1}\to V_{k,t}\)\(*\)/ \\  **for**\(k=1:N\)**do** \\  **for**\(i_{d}=1:M\)**do** \\
**1** : Calculate Metadata saliency \(v_{k,t}(i_{d})\) \\  **end for** \\
* : Construct Nodes \(V_{k,t}=\{v_{k,t}(1)\), \(v_{k,t}(2)\),..., \(v_{k,t}(M)\}\) \\
**end for** \\  /* _Update Edges_\(E_{k,t-1}\to E_{k,t}\)\(*\)/ \\  **for**\(k=1:N\)**do** \\  **for**\(i=1:M\)**do** \\
**1** : Calculate Likelihood for influence of node \(\sigma\big{(}\alpha\cdot v_{k,t}^{\prime}(i)\big{)}^{\prime}\) \\
**2** : Calculate Weight for similarity between two nodes \(1-v_{k,t}^{\bigtriangleup}\)\((i,j)\) \\
**3** : Calculate Edge attribute \(e_{k,t}(i,j)=\sigma\big{(}\alpha\cdot v_{k,t}^{\prime}(i)\big{)}\cdot\big{(}1-v _{k,t}^{\bigtriangleup}(i,j)\big{)}\) \\
**end for** \\  * : Construct Edges \(E_{k,t}=\{e_{k,t}(1,2)\), \(e_{k,t}(1,2)\),..., \(e_{k,t}(M-1,M)\}\) \\
**end for** \\  **end for** \\  /* _Update Universal domain_\(D_{t-1}\to D_{t}\)\(*\)/ \\
**for**\(h=1:M\)**do** \\
**1** : Calculate Domain \(D_{t}(h)\) by sorting nodes _w.r.t._ edge attribute \\
**end for** \\  * : Construct Universal domain \(D_{t}=\{D_{t}(1)\), \(D_{t}(2)\),..., \(D_{t}(M)\}\) \\ \hline \hline \end{tabular}
\end{table}
Table 1: The pseudocode for re-enrichment learning.  
Figure 3: The process of re-enrichment learning.