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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. The transformation may be nonlinear and the transformed space high-dimensional; although the classifier is a hyperplane in ...
H 2 does, but only with a small margin. H 3 separates them with the maximum margin. In machine learning, the margin of a single data point is defined to be the distance from the data point to a decision boundary. Note that there are many distances and decision boundaries that may be appropriate for certain datasets and goals.
Many boosting algorithms rely on the notion of a margin to assign weight to samples. If a convex loss is utilized (as in AdaBoost or LogitBoost, for instance) then a sample with a higher margin will receive less (or equal) weight than a sample with a lower margin. This leads the boosting algorithm to focus weight on low-margin samples.
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]
There are many hyperplanes that might classify (separate) the data. One reasonable choice as the best hyperplane is the one that represents the largest separation, or margin, between the two sets. So we choose the hyperplane so that the distance from it to the nearest data point on each side is maximized.
In machine learning, kernel machines are a class of algorithms for pattern analysis, whose best known member is the support-vector machine (SVM). These methods involve using linear classifiers to solve nonlinear problems. [1]
LIBSVM and LIBLINEAR are two popular open source machine learning libraries, both developed at the National Taiwan University and both written in C++ though with a C API. LIBSVM implements the sequential minimal optimization (SMO) algorithm for kernelized support vector machines (SVMs), supporting classification and regression. [1]
Some active learning algorithms are built upon support-vector machines (SVMs) and exploit the structure of the SVM to determine which data points to label. Such methods usually calculate the margin , W , of each unlabeled datum in T U,i and treat W as an n -dimensional distance from that datum to the separating hyperplane.