Seonglae ChoThe Kernel Trick is different from Kernel lol. The strategy is to embed the data into a space where the patterns can be discovered as linear relations.
- Kernel function that maps the data into the embedding or feature space
- Learning algorithm designed to discover linear patterns in that space
The input data is mapped to a higher-dimensional space to enable modeling with linear functions, using inner product operations in the mapped space to calculate linear functions. By doing this, non-linear problems are solved. For Non-separable case, kernel mapping increase the likelihood to find linearly separable but cannot guarantee it.
The algorithms are implemented in such a way that the coordinates of the embedded points are not needed, only their pairwise inner products. The pairwise inner products can be computed efficiently directly from the original points using a kernel function. i.e. Theoretically Feature Map is required. However, calculations are possible by just knowing the Kernel Function. Gram Matrix is used with valid kernel functions.
Kernel Method Notion
Kernel Methods
Kernel method
In machine learning, kernel machines are a class of algorithms for pattern analysis, whose best known member is the support-vector machine (SVM). These methods involve using linear classifiers to solve nonlinear problems.[1] The general task of pattern analysis is to find and study general types of relations (for example clusters, rankings, principal components, correlations, classifications) in datasets. For many algorithms that solve these tasks, the data in raw representation have to be explicitly transformed into feature vector representations via a user-specified feature map: in contrast, kernel methods require only a user-specified kernel, i.e., a similarity function over all pairs of data points computed using inner products. The feature map in kernel machines is infinite dimensional but only requires a finite dimensional matrix from user-input according to the Representer theorem. Kernel machines are slow to compute for datasets larger than a couple of thousand examples without parallel processing.
https://en.wikipedia.org/wiki/Kernel_method