Which statement about the kernel trick is correct?

• A. It maps data to a higher dimensional space explicitly to compute coordinates.
• B. It maps data into a higher-dimensional space implicitly to separate with a linear hyperplane; example: polynomial kernel.
• C. It makes the data linearly separable in the original space.
• D. It eliminates the need for regularization.

Answer: (B)

The kernel trick relies on mapping data into a higher-dimensional feature space so that a linear boundary can separate the data, but it does this implicitly. Instead of computing the coordinates in that new space, we use a kernel function K(x, z) = φ(x)·φ(z) that gives the inner product in the feature space directly from the original inputs. This lets algorithms like support vector machines find a linear separator in the transformed space without ever forming φ(x) explicitly. A polynomial kernel is a classic example: it corresponds to mapping into polynomial features without actually constructing them, so the decision boundary in the original space can become nonlinear after the implicit transformation.

So the correct statement captures that implicit mapping to a higher-dimensional space enables linear separation there, not in the original space, and that computations are done via kernels rather than explicit feature coordinates. It also acknowledges that regularization remains a separate consideration; the kernel trick itself doesn’t remove the need for regularization.