# Addressing the Cold-Start Problem in Recommender Systems Based on Frequent Patterns
## 3 Proposed Methodology
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **Age** & **Sex** & **Occupation** & **Country** & **Wage (In \$)** \\ \hline \(u_{1}\) & **25–35** & F & **Pharmacist** & **Germany** & **3000** \\ \(u_{2}\) & 18–24 & M & Teacher & USA & 5000 \\ \(u_{3}\) & **36–45** & F & **Economist** & **France** & **2500** \\ \(u_{4}\) & **25–35** & F & **Doctor** & **UK** & **3000** \\ \(u_{5}\) & 46–55 & M & Engineer & USA & 8000 \\ \(u_{6}\) & 18–24 & M & Professor & USA & 6000 \\ \(u_{7}\) & 25–35 & M & Lawyer & USA & 8000 \\ \(u_{8}\) & 18–24 & F & Teacher & USA & 6000 \\ \(u_{\text{nofu-1}}\) & Over 55 & F & Teacher & Canada & 6000 \\ \(u_{\text{nofu}}\) & 46–55 & M & Assistant & China & 1500 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: User matrix UM. Figure 1: Proposed methodology. ### Clustering Procedure

Initially, during a preprocessing phase, users are clustered to certain clusters by applying a clustering algorithm to the user matrix. The selection of the clustering algorithm depends on the type of users' characteristics. Assume that a set \(C\) that contains \(n\)_clusters of users_\((c_{1},\ldots,\)\(c_{n})\) is extracted at the first phase. ### Extraction of Frequent Itemsets

Then, during Step 3, for each cluster \(c_{i}\in C\), an ARM algorithm is used to extract the frequent itemsets along with their frequencies. When the ARM algorithm is applied to the two-dimensional binary matrix, it extracts the frequent itemsets by taking as input for each row (i.e., transaction) the columns (i.e., items) containing the value 1, i.e., the products that the user purchased. The ARM algorithm is used to extract for each cluster \(c_{i}\in C\), the set of frequent itemsets \(FIS_{c_{i}}\). The choice of the ARM algorithm is not critical, and it depends on the size of the user-product matrix. For the cluster \(c_{i}\in C\), \(1\leq i\leq n\), the relative frequency of each frequent itemset \(fis_{c_{i}a}\in FIS_{c_{i}}\) is:

\[RFfis_{c_{i}a}=Ffis_{c_{i}a}/|c_{i}| \tag{1}\]

where \(c_{i}\in C\), \(1\leq i\leq n\) and \(fis_{c_{i}a}\in FIS_{c_{i}}\), \(1\leq a\leq m\), where \(m\) is the total number of frequent itemsets for the cluster \(c_{i}\). The relative frequency of an itemset represents how frequent this itemset is, in all the transactions, i.e., the number of transactions that contain this itemset. In the proposed methodology, the relative frequency is the total number of users (rows) that the cluster \(c_{i}\) contains, where \(c_{i}\subseteq U\). ### Extraction of Discriminant Itemsets

During Step 4, the discriminant itemsets are extracted for each user cluster. For each extracted frequent itemset \(fis_{c_{i}a}\), it is checked if it is included in other user clusters. Given that \(\theta>1\) and \(0<\varphi<\frac{1}{\theta}\) are user-specified thresholds, a frequent itemset \(fis_{c_{1}1}\) is discriminant in the cluster \(c_{1}\), iff the following hold [45]:

\[\left(n*RFfis_{c_{1}1}/\sum_{i=1}^{n}RFfis_{c_{i}1}\right)\geq\theta \tag{2}\]

\[RFfis_{c_{1}1}\geq\varphi*\theta\text{, where }0<\varphi<\frac{1}{\theta} \tag{3}\] \begin{table}
\begin{tabular}{c c c c c c c c} \hline  & **P1** & **P2** & **P3** & **P4** & **P5** & **Proof-1** & **Proof** \\ \hline \(\mathbf{u_{1}}\) & **1** & 0 & **1** & & & & **Not updated** \\ \hline \(u_{2}\) & 1 & & & 1 & 1 & & **Updated (*cold user)** \\ \hline \(\mathbf{u_{3}}\) & **1** & 1 & **1** & & 1 & & **Updated** \\ \hline \(\mathbf{u_{4}}\) & **1** & & **0** & 1 & 0 & 1 & **Not updated** \\ \hline \(u_{5}\) & 0 & 1 & 0 & & & 0 & \\ \hline \(u_{6}\) & 1 & & & 0 & & 1 & **Not updated** \\ \hline \(u_{7}\) & 1 & & & 1 & 1 & & **Not updated** \\ \hline \(u_{8}\) & 1 & & & 1 & 1 & & **Updated** \\ \hline \(u_{\text{nofu-1}}\) & & & & & 0 & 1 & \\ \hline \(u_{\text{nofu}}\) & 0 & 1 & 0 & 1 & & & \\ \hline \end{tabular}
\end{table} 
Table 2: User–product matrix UP. The use of these thresholds ensures that itemsets with extremely low frequencies are eliminated.