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In machine learning, kernel methods are a class of algorithms for pattern analysis, whose best known member is the support vector machine (SVM). The general task of pattern analysis is to find and study general types of relations (for example clusters, rankings, principal components, correlations, classifications) in datasets. 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 pairs of data points in raw representation. Kernel methods owe their name to the use of kernel functions, which enable them to operate in a high-dimensional, ''implicit'' feature space without ever computing the coordinates of the data in that space, but rather by simply computing the inner products between the images of all pairs of data in the feature space. This operation is often computationally cheaper than the explicit computation of the coordinates. This approach is called the "kernel trick". Kernel functions have been introduced for sequence data, graphs, text, images, as well as vectors. Algorithms capable of operating with kernels include the kernel perceptron, support vector machines (SVM), Gaussian processes, principal components analysis (PCA), canonical correlation analysis, ridge regression, spectral clustering, linear adaptive filters and many others. Any linear model can be turned into a non-linear model by applying the kernel trick to the model: replacing its features (predictors) by a kernel function. Most kernel algorithms are based on convex optimization or eigenproblems and are statistically well-founded. Typically, their statistical properties are analyzed using statistical learning theory (for example, using Rademacher complexity). ==Motivation and informal explanation== Kernel methods can be thought of as instance-based learners: rather than learning some fixed set of parameters corresponding to the features of their inputs, they instead "remember" the -th training example and learn for it a corresponding weight . Prediction for unlabeled inputs, i.e., those not in the training set, is treated by the application of a similarity function , called a kernel, between the unlabeled input and each of the training inputs . For instance, a kernelized binary classifier typically computes a weighted sum of similarities :, where * is the kernelized binary classifier's predicted label for the unlabeled input whose hidden true label is of interest; * is the kernel function that measures similarity between any pair of inputs ; * the sum ranges over the labeled examples in the classifier's training set, with ; * the are the weights for the training examples, as determined by the learning algorithm; * the sign function determines whether the predicted classification comes out positive or negative. Kernel classifiers were described as early as the 1960s, with the invention of the kernel perceptron.〔 Cited in 〕 They rose to great prominence with the popularity of the support vector machine (SVM) in the 1990s, when the SVM was found to be competitive with neural networks on tasks such as handwriting recognition. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「kernel method」の詳細全文を読む スポンサード リンク
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