# A High-Level Representation of the Navigation Behavior of Website Visitors
## 2 Identification of Rules in Each Class of Visitors
### Rule Extraction
#### 2.3.2 Inter-Class Analysis  
The objective of the inter-class analysis is to find out (1) if the rules are different for each class of visitors, and (2) if those rules are relevant. To this aim, we computed two metrics:  
* Percentage of rules found in sessions: given a set of rules, it measures the percentage of those rules that are found in a group of sessions. It allows us to find out if a set of rules describes a specific class of visitors or not. A result of 100% in all classes of visitors for a given set of rules would mean that all those rules were found in the four classes of visitors. Thus, that set of rules would not describe a specific class of visitors.
* Inverse frequency of a rule: it measures the percentage of sessions in which a rule is found at least once. A high percentage indicates that the rule is relevant for describing the navigation behavior of visitors. As an example of the inter-class analysis, in Table 3, we show the metrics of the rules found in visitors from the class \"Made payment\". Below, we summarize the interpretation of this table.
* A total of 100% of the rules were found in \"Made payment\" sessions because rules were extracted from those sessions. We can see that this percentage decreases to approximately 50% for the classes of visitors \"Started payment\" and \"Other conversions\". For the visitors from the class \"No conversion\", it reduces to 6%. These results indicate that approximately 50% of the rules specifically describe the navigation behavior of the visitors that belong to the class \"Made payment\".
* The highest inverse frequency indicates that one rule was found in up to 91% of sessions that belong to the class of visitors \"Made payment\". This metric is lower for the other three classes of visitors. Since we use this metric to measure the rule relevance, we can say that this set of rules is more relevant for the visitors that belong to the class \"Made payment\".  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Metric** & **Made Payment** & \
\begin{tabular}{c} **Started** \\ **Payment** \\ \end{tabular} &
\begin{tabular}{c} **Other** \\ **Conversions** \\ \end{tabular} & **No Conversion** \\ \hline Percentage of visitors & 7\% & 10\% & 32\% & 52\% \\ Number of rules & 764 & 704 & 997 & 92 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Rules obtained in each class of visitors. Columns 2 to 5 indicate the class of visitor. Seven percent of the sessions are visitors from the class Made payment, where we found 764 rules. Conversely, fifty-two percent of the sessions are visitors from the class No conversion, where we found only 92 rules.  
We made the inter-class analysis for the other three classes of visitors. Both metrics are higher when the set of rules and the sessions belong to the same class of visitors. Nevertheless, it was remarkable that the highest inverse frequency of No conversion rules was only 14% in the sessions of the same class. This indicates that the behavior of the visitors that belong to the class No conversion is less homogeneous.  
The inter-class analysis confirmed that there are relevant and specific rules for each class of visitors. The next step was to select the best rules for describing the navigation behavior of visitors.