## 3 The Closest Resemblance Algorithm
### Phase 1: Learning Phase
#### 3.1.2 Prototype-Based Classifiers with Percentile-Based Reference Intervals  
This approach modifies the previous method by using percentiles to define reference intervals for each feature within a class. For each class \(C^{h}\) and for each feature \(f_{j}\), calculate the lower quartile \(L_{j}^{h}\) and upper quartile \(U_{j}^{h}\) using the training dataset \(X\) (see Equation (3)). \[I_{j}(f_{j},C^{h})=[L_{j}^{h}(f_{j},C^{h}),U_{j}^{h}(f_{j},C^{h})] \tag{3}\]  
Percentiles capture the distribution of data points within a class for each feature. The \(L_{j}^{h}\) and \(U_{j}^{h}\) percentiles define an interval that encompasses a specific proportion \(L\%\) to \(U\%\) of the data points in that class for that feature. This method is robust to outliers as extreme values have less influence on percentiles compared to the mean and the standard deviation. This technique captures the central tendency and spread of feature values within each class, offering a robust representation of the distribution by focusing on the lower and upper quartiles. Using percentile intervals for each feature of each class to represent a profile of the class in a classification problem can offer several benefits: By calculating percentile intervals for each feature within each class, create distinct profiles that characterize each class. This can help in understanding the unique characteristics and behaviors associated with each class in classification problem. Percentile intervals highlight the range of values that are most representative of each class. Features with wider intervals or larger differences between classes may indicate greater importance in distinguishing between classes. Class profiles based on percentile intervals are intuitive and easy to interpret. They provide clear boundaries that define the typical range of feature values associated with each class, making it easier to understand the characteristics of each class. Class profiles based on percentile intervals can aid in feature selection by identifying features that are most discriminative between classes. Features with significant differences in percentile intervals across classes may be more informative for classification tasks. When presenting classification results to stakeholders or end-users, class profiles based on percentile intervals provide a transparent explanation of how features contribute to class prediction. This enhances the interpretability and trustworthiness of the classification model. Similar to using percentile intervals for the entire training set, calculating class profiles \"prototypes\" based on percentile intervals can make the classification model more robust to outliers within each class. Outliers have less influence on percentile intervals compared to other summary statistics like mean and standard deviation. Class profiles based on percentile intervals can be visually represented using box plots or similar visualization techniques. These visual representations can offer a concise summary of the distribution of feature values within each class, facilitating comparison and interpretation. Overall, using percentile intervals to represent class profiles in a classification problem can enhance model interpretability, aid in feature selection, and provide valuable insights into the characteristics of each class, thereby improving the overall performance and understanding of the classification model. These techniques serve as crucial steps in learning the _CR_ classification, offering different perspectives on how to define feature intervals. The mean and standard deviation technique presented in Equation (2) adapts to class-specific variations, and the percentile-based approach presented in Equation (3) provides a robust summary of the feature distributions within each class. Each technique contributes to the overall goal of capturing essential patterns and characteristics for the subsequent phases of the classification process. To learn the \(CR\) classifier, we follow the different steps of Algorithm 1.