Which method's basis for calculating worth involves the sum of squared proportions across classes?

The Gini Index is a measure often used in decision tree algorithms and classification tasks to assess the impurity or richness of a dataset in terms of class distributions. The basis for calculating the Gini Index involves the sum of squared proportions of classes, which helps quantify the likelihood of misclassification of a randomly chosen element from the dataset.

When you compute the Gini Index for a node within a decision tree, you consider the probabilities of each class at that node. The formula takes into account the sum of the squared proportions of each class. By subtracting this value from one, you effectively capture how mixed the classes are at that node. A lower Gini Index indicates a node that primarily contains one class and is therefore "purer," while a higher value indicates a more mixed node.

This method is particularly effective in guiding the splitting criteria in decision trees, as it helps in selecting the attribute that can best separate the classes, leading to more accurate predictions. Thus, the Gini Index's unique approach of utilizing the sum of squared proportions extends its capability to measure and guide decision-making based on the class distribution within the data.