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Kernel classifiers were described as early as the 1960s, with the invention of the kernel perceptron. [3] They rose to great prominence with the popularity of the support-vector machine (SVM) in the 1990s, when the SVM was found to be competitive with neural networks on tasks such as handwriting recognition.
The kernel trick, where dot products are replaced by kernels, is easily derived in the dual representation of the SVM problem. This allows the algorithm to fit the maximum-margin hyperplane in a transformed feature space .
Kernel trick is also applicable when kernel based classifier is used, such as SVM. Pyramid match kernel is newly developed one based on the BoW model. The local feature approach of using BoW model representation learnt by machine learning classifiers with different kernels (e.g., EMD-kernel and kernel) has been vastly tested in the area of ...
Since the value of the RBF kernel decreases with distance and ranges between zero (in the infinite-distance limit) and one (when x = x'), it has a ready interpretation as a similarity measure. [2] The feature space of the kernel has an infinite number of dimensions; for =, its expansion using the multinomial theorem is: [3]
Least-squares support-vector machines (LS-SVM) for statistics and in statistical modeling, are least-squares versions of support-vector machines (SVM), which are a set of related supervised learning methods that analyze data and recognize patterns, and which are used for classification and regression analysis.
For degree-d polynomials, the polynomial kernel is defined as [2](,) = (+)where x and y are vectors of size n in the input space, i.e. vectors of features computed from training or test samples and c ≥ 0 is a free parameter trading off the influence of higher-order versus lower-order terms in the polynomial.
AdaTron uses the fact that the corresponding quadratic optimization problem is convex. The perceptron of optimal stability, together with the kernel trick, are the conceptual foundations of the support-vector machine. The -perceptron further used a pre-processing layer of fixed random weights, with thresholded output units.
Many (most?) people are introduced to the "Kernel Trick" because it is used by SVM, which is popular. I think having a dedicated topic for Kernel Trick is useful and should be MOTIVATED BY CLEAR EXAMPLE. The Mathematical principles should be in the Kernel Models page. my 2 cents.