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What is the main objective of Support Vector Machine (SVM) regarding hyperplanes?

To minimize the number of data points misclassified

To choose the hyperplane that maximizes the smallest distance to data points

To ensure all data points lie on the hyperplane

To represent the largest margin between the two classes

Support Vector Machines (SVM) aim to find the hyperplane that maximizes the margin between different classes in the data. The principal goal is to effectively differentiate between the classes by creating a clear boundary that not only separates the classes but does so with the greatest possible distance from the nearest data points of either class. This distance, known as the margin, is critical as it contributes to the SVM's robustness and generalization ability on unseen data.

The rationale behind maximizing this margin is that a larger margin implies greater confidence in the classification. Thus, if new data points are introduced, the SVM model is less likely to misclassify them. By focusing on this aspect, SVM inherently discourages overfitting and ensures that the model remains reliable across variations in input data.

Choosing a hyperplane that simply minimizes the number of misclassified points, ensuring all points lie on it, or maximizing the smallest distance to data points does not provide the same balance of performance and generalization that maximizing the margin does. Therefore, the main objective of SVM is indeed to represent the largest margin between the two classes efficiently, resulting in a more effective decision boundary.

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