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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.
Analogously, the model produced by SVR depends only on a subset of the training data, because the cost function for building the model ignores any training data close to the model prediction. Another SVM version known as least-squares support vector machine (LS-SVM) has been proposed by Suykens and Vandewalle. [39]
Consider a binary classification problem with a dataset (x 1, y 1), ..., (x n, y n), where x i is an input vector and y i ∈ {-1, +1} is a binary label corresponding to it. A soft-margin support vector machine is trained by solving a quadratic programming problem, which is expressed in the dual form as follows:
Empirically, for machine learning heuristics, choices of a function that do not satisfy Mercer's condition may still perform reasonably if at least approximates the intuitive idea of similarity. [6] Regardless of whether k {\displaystyle k} is a Mercer kernel, k {\displaystyle k} may still be referred to as a "kernel".
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 ...
The ranking SVM algorithm is a learning retrieval function that employs pairwise ranking methods to adaptively sort results based on how 'relevant' they are for a specific query. The ranking SVM function uses a mapping function to describe the match between a search query and the features of each of the possible results.
Associating each input datum with an RBF leads naturally to kernel methods such as support vector machines (SVM) and Gaussian processes (the RBF is the kernel function). All three approaches use a non-linear kernel function to project the input data into a space where the learning problem can be solved using a linear model.
The plot shows that the Hinge loss penalizes predictions y < 1, corresponding to the notion of a margin in a support vector machine. In machine learning, the hinge loss is a loss function used for training classifiers. The hinge loss is used for "maximum-margin" classification, most notably for support vector machines (SVMs). [1]