Based on the figure provided, a decision tree would have the highest recall with respect to the fraudulent class. Recall is a model evaluation metric that measures the proportion of actual positive instances that are correctly classified by the model. Recall is calculated as follows:
Recall = True Positives / (True Positives + False Negatives)
A decision tree is a type of machine learning model that can perform classification tasks by splitting the data into smaller and purer subsets based on a series of rules or conditions. A decision tree can handle both linear and non-linear data, and can capture complex patterns and interactions among the features. A decision tree can also be easily visualized and interpreted1
In this case, the data is not linearly separable, and has a clear pattern of seasonality. The fraudulent class forms a large circle in the center of the plot, while the normal class is scattered around the edges. A decision tree can use the transaction month and the age of account as the splitting criteria, and create a circular boundary that separates the fraudulent class from the normal class. A decision tree can achieve a high recall for the fraudulent class, as it can correctly identify most of the black dots as positive instances, and minimize the number of false negatives. A decision tree can also adjust the depth and complexity of the tree to balance the trade-off between recall and precision23
The other options are not valid or suitable for achieving a high recall for the fraudulent class. A linear support vector machine (SVM) is a type of machine learning model that can perform classification tasks by finding a linear hyperplane that maximizes the margin between the classes. A linear SVM can handle linearly separable data, but not non-linear data. A linear SVM cannot capture the circular pattern of the fraudulent class, and may misclassify many of the black dots as negative instances, resulting in a low recall4 A naive Bayesian classifier is a type of machine learning model that can perform classification tasks by applying the Bayes’ theorem and assuming conditional independence among the features. A naive Bayesian classifier can handle both linear and non-linear data, and can incorporate prior knowledge and probabilities into the model. However, a naive Bayesian classifier may not perform well when the features are correlated or dependent, as in this case. A naive Bayesian classifier may not capture the circular pattern of the fraudulent class, and may misclassify many of the black dots as negative instances, resulting in a low recall5 A single perceptron with sigmoidal activation function is a type of machine learning model that can perform classification tasks by applying a weighted linear combination of the features and a non-linear activation function. A single perceptron with sigmoidal activation function can handle linearly separable data, but not non-linear data. A single perceptron with sigmoidal activation function cannot capture the circular pattern of the fraudulent class, and may misclassify many of the black dots as negative instances, resulting in a low recall.
