Kernel Trick

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The word "kernel" is used in mathematics to denote a weighting function for a weighted sum or integral.

functions that approximate the feature mappings that correspond to certain kernels, as they are used for example in Support Vector Machine (SVM). The feature functions perform non-linear transformations of the input, which can serve as a basis for linear classification or other algorithms. The advantage of using approximate explicit feature maps compared to the kernel trick, which makes use of feature maps implicitly, is that explicit mappings can be better suited for online learning and can significantly reduce the cost of learning with very large datasets. Standard kernelized Support Vector Machine (SVM)s do not scale well to large datasets, but using an approximate kernel map it is possible to use much more efficient linear Support Vector Machine (SVM)s. Kernel Approximation | Scikit-Learn

"Kernel Trick"

The kernel trick avoids the explicit mapping that is needed to get linear learning algorithms to learn a nonlinear function or decision boundary.