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A training example of SVM with kernel given by φ((a, b)) = (a, b, a 2 + b 2) Suppose now that we would like to learn a nonlinear classification rule which corresponds to a linear classification rule for the transformed data points ().
The alternative follows from Mercer's theorem: an implicitly defined function exists whenever the space can be equipped with a suitable measure ensuring the function satisfies Mercer's condition. Mercer's theorem is similar to a generalization of the result from linear algebra that associates an inner product to any positive-definite matrix .
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.
The hyperplane learned in feature space by an SVM is an ellipse in the input space. In machine learning , the polynomial kernel is a kernel function commonly used with support vector machines (SVMs) and other kernelized models, that represents the similarity of vectors (training samples) in a feature space over polynomials of the original ...
Here, K is some kernel function. Formally, a kernel function is a non-negative semidefinite kernel (see Mercer's condition), representing an inner product between samples in a high-dimensional space, as if the samples had been expanded to include additional features by a function Φ: K(x, x') = Φ(x) · Φ(x').
gretl is an example of an open-source statistical package. ADaMSoft – a generalized statistical software with data mining algorithms and methods for data management; ADMB – a software suite for non-linear statistical modeling based on C++ which uses automatic differentiation; Chronux – for neurobiological time series data; DAP – free ...
In machine learning, the radial basis function kernel, or RBF kernel, is a popular kernel function used in various kernelized learning algorithms. In particular, it is commonly used in support vector machine classification .
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 ]