Support Vector Machines (SVMs) are a set of supervised learning methods that analyze data and recognize patterns, used for classification and regression analysis. Original SVM algorithm invented by Vladimir Vapnik and the current standard derivative (soft margin) was proposed by Corinna Cortes and Vladimir Vapnik (Cortes, C. and Vapnik, V, 1995).
Take the standard SVM input data set, and predicts, for any given input, the input is likely one of the members of the class of the two classes, which makes a linear SVM as a binary classifier nonprobabilistik. Since an SVM is a classifier, then given a set of training, each marked as belonging to one of two categories, an SVM training algorithm to build a model that predicts whether a new data fall into a category or the other. Intuitively, SVM models are representations of the data as points in space, mapped so that separate instances category divided by a clear gap as wide as possible.
The new data is then mapped into the same space and is expected to include a category based on which side of the gap data is located. More formally, construct Support Vector Machine hyperplane hyperplane or set in a high or infinite dimensions, which can be used for classification, regression or other tasks. Intuitively, a good separation is achieved by the hyperplane that has the largest distance to the nearest training data points of any class (so-called functional margin), since in general the larger the margin the lower the generalization error of the classifier. When the origin of the problem may be expressed in a finite-dimensional space, it often happens that in space, the set is not linearly separated. For this reason it is proposed that the finite-dimensional space are mapped into a space that is much higher dimension that might make the separation easier in that space.
SVM schemes use a mapping into a larger space so that the cross product can be easily calculated in terms of the variables in the original space making the computational load reasonable. Cross product in a larger space is defined in terms of the kernel function K (x, y) which can be selected according to the problem. Set of hyperplane in a large space that is defined as the set of points whose cross product with a constant vector in space. Vectors defining the hyperplanes can be chosen to be a linear combination with the parameters α i of image feature vectors that occur in the database. With this option a hyperplane at point x in the feature space is mapped to the hyperplane is determined by the relation:
Note that if K (x, y) becomes small when y grows further from x, each element in the sum of the degree of proximity measurement test point x to point xi in the corresponding database. In this way the number of kernels in the above can be used to measure the relative proximity of each test points to the data points that come in one or the other of the set to be clustered. Note the fact that the set of points x mapped into any hyperplane, can be quite complicated as a result of allowing a more complex separation between distant from the convex set in the original space.
Take the standard SVM input data set, and predicts, for any given input, the input is likely one of the members of the class of the two classes, which makes a linear SVM as a binary classifier nonprobabilistik. Since an SVM is a classifier, then given a set of training, each marked as belonging to one of two categories, an SVM training algorithm to build a model that predicts whether a new data fall into a category or the other. Intuitively, SVM models are representations of the data as points in space, mapped so that separate instances category divided by a clear gap as wide as possible.
The new data is then mapped into the same space and is expected to include a category based on which side of the gap data is located. More formally, construct Support Vector Machine hyperplane hyperplane or set in a high or infinite dimensions, which can be used for classification, regression or other tasks. Intuitively, a good separation is achieved by the hyperplane that has the largest distance to the nearest training data points of any class (so-called functional margin), since in general the larger the margin the lower the generalization error of the classifier. When the origin of the problem may be expressed in a finite-dimensional space, it often happens that in space, the set is not linearly separated. For this reason it is proposed that the finite-dimensional space are mapped into a space that is much higher dimension that might make the separation easier in that space.
SVM schemes use a mapping into a larger space so that the cross product can be easily calculated in terms of the variables in the original space making the computational load reasonable. Cross product in a larger space is defined in terms of the kernel function K (x, y) which can be selected according to the problem. Set of hyperplane in a large space that is defined as the set of points whose cross product with a constant vector in space. Vectors defining the hyperplanes can be chosen to be a linear combination with the parameters α i of image feature vectors that occur in the database. With this option a hyperplane at point x in the feature space is mapped to the hyperplane is determined by the relation:
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| SVM Calculation |
Note that if K (x, y) becomes small when y grows further from x, each element in the sum of the degree of proximity measurement test point x to point xi in the corresponding database. In this way the number of kernels in the above can be used to measure the relative proximity of each test points to the data points that come in one or the other of the set to be clustered. Note the fact that the set of points x mapped into any hyperplane, can be quite complicated as a result of allowing a more complex separation between distant from the convex set in the original space.
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