Which of the following correctly describes Support-Vector Machines (SVMs)?

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Question prompt: Which of the following correctly describes Support-Vector Machines (SVMs)?

Option 1: 'SVM can be applied only when the data are linearly separable.' This is a common misconception. In fact, SVMs can handle nonlinearly separable data using kernel functions to map inputs into higher-dimensional spaces where separation is possible. Therefore, this statement is incorrect.

Option 2: 'SVM uses a loss function that determines how much the penalty should be assigned to misclassified cases.' This aligns with the core idea of SVMs: they optimize a margin while penalizing misclassifications through a loss term (e.g., hinge loss) and a regularization parameter. The penalty controls how much misclassified points influence the optimization, making this statement correct in essence.

Option 3: 'SVMs are based on unsupervised learning.' This is false. SVMs are a supervised learning method that relies on labeled training data to find a decision boundary. There are unsupervised techniques like SVM variants (e.g., one-class SVM) but the standard SVM described here is supervised, so this option is incorrect.

Option 4: 'SVM chooses the linear classifier to minimize the margin between two classes.' This is misleading. SVMs aim to maximize the margin between classes, not minimize it. They select a hyperplane that has the largest distance to the nearest data points of any class (the support vectors). Moreover, when using kernels, the classifier need not be linear in the input space. Thus, this option is incorrect.

In summary, Option 2 correctly captures a central aspect of SVMs related to the loss-based penalty for misclassifications, while the other statements either misstate the role of kernels, the learning paradigm, or the margin objective.

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Which of the following correctly describes Support-Vector Machines (SVMs)?

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