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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.
Thus, SVMs use the kernel trick to implicitly map their inputs into high-dimensional feature spaces, where linear classification can be performed. [3] Being max-margin models, SVMs are resilient to noisy data (e.g., misclassified examples). SVMs can also be used for regression tasks, where the objective becomes -sensitive.
SVM algorithms categorize binary data, with the goal of fitting the training set data in a way that minimizes the average of the hinge-loss function and L2 norm of the learned weights. This strategy avoids overfitting via Tikhonov regularization and in the L2 norm sense and also corresponds to minimizing the bias and variance of our estimator ...
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.
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 ...
Vladimir Naumovich Vapnik (Russian: Владимир Наумович Вапник; born 6 December 1936) is a computer scientist, researcher, and academic.He is one of the main developers of the Vapnik–Chervonenkis theory of statistical learning [1] and the co-inventor of the support-vector machine method and support-vector clustering algorithms.
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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.