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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.
The SVM is only directly applicable for two-class tasks. Therefore, algorithms that reduce the multi-class task to several binary problems have to be applied; see the multi-class SVM section. Parameters of a solved model are difficult to interpret.
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 ...
The SVM learning code from both libraries is often reused in other open source machine learning toolkits, including GATE, KNIME, Orange [3] and scikit-learn. [4] Bindings and ports exist for programming languages such as Java, MATLAB, R, Julia, and Python. It is available in e1071 library in R and scikit-learn in Python.
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:
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.
The hinge loss is a convex function, so many of the usual convex optimizers used in machine learning can work with it.It is not differentiable, but has a subgradient with respect to model parameters w of a linear SVM with score function = that is given by