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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 ...
Sequential minimal optimization (SMO) is an algorithm for solving the quadratic programming (QP) problem that arises during the training of support-vector machines (SVM). It was invented by John Platt in 1998 at Microsoft Research. [1] SMO is widely used for training support vector machines and is implemented by the popular LIBSVM tool.
In a typical document classification task, the input to the machine learning algorithm (both during learning and classification) is free text. From this, a bag of words (BOW) representation is constructed: the individual tokens are extracted and counted, and each distinct token in the training set defines a feature (independent variable) of each of the documents in both the training and test sets.
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.
Schölkopf developed SVM methods achieving world record performance on the MNIST pattern recognition benchmark at the time. [2] With the introduction of kernel PCA, Schölkopf and coauthors argued that SVMs are a special case of a much larger class of methods, and all algorithms that can be expressed in terms of dot products can be generalized to a nonlinear setting by means of what is known ...
where is the kernel function (usually Gaussian), are the variances of the prior on the weight vector (,), and , …, are the input vectors of the training set. [ 4 ] Compared to that of support vector machines (SVM), the Bayesian formulation of the RVM avoids the set of free parameters of the SVM (that usually require cross-validation-based ...