Episode 551
Kernel method Tue, 2018Nov06 01:11 UTC Length  2:49
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The random article for Tuesday, 6 November 2018 is Kernel method.
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 userspecified feature map: in contrast, kernel methods require only a userspecified 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 highdimensional, 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 nonlinear 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 wellfounded. Typically, their statistical properties are analyzed using statistical learning theory (for example, using Rademacher complexity).
This recording reflects the Wikipedia text as of 01:11 UTC on Tuesday, 6 November 2018.
For the full current version of the article, go to http://en.wikipedia.org/wiki/Kernel_method.
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