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For many algorithms that solve these tasks, the data in raw representation have to be explicitly transformed into feature vector representations via a user-specified feature map: in contrast, kernel methods require only a user-specified kernel, i.e., a similarity function over all pairs of data points computed using inner products.
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 ...
Kernel trick is also applicable when kernel based classifier is used, such as SVM. Pyramid match kernel is newly developed one based on the BoW model. The local feature approach of using BoW model representation learnt by machine learning classifiers with different kernels (e.g., EMD-kernel and kernel) has been vastly tested in the area of ...
In a typical document classification task, the input to the machine learning algorithm (both during learning and classification) is free text. From this, a bag of words (BOW) representation is constructed: the individual tokens are extracted and counted, and each distinct token in the training set defines a feature (independent variable) of each of the documents in both the training and test sets.
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.
full expansion of the kernel prior to training/testing with a linear SVM, [5] i.e. full computation of the mapping φ as in polynomial regression; basket mining (using a variant of the apriori algorithm) for the most commonly occurring feature conjunctions in a training set to produce an approximate expansion; [6] inverted indexing of support ...
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Since the value of the RBF kernel decreases with distance and ranges between zero (in the infinite-distance limit) and one (when x = x'), it has a ready interpretation as a similarity measure. [2] The feature space of the kernel has an infinite number of dimensions; for =, its expansion using the multinomial theorem is: [3]