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Low-rank matrix approximations are essenti … Low-rank matrix approximations are essential tools in the application of kernel methods to large-scale learning problems. Kernel methods (for instance, support vector machines or Gaussian processes) project data points into a high-dimensional or infinite-dimensional feature space and find the optimal splitting hyperplane. In the kernel method the data is represented in a kernel matrix (or, Gram matrix). Many algorithms can solve machine learning problems using the kernel matrix. The main problem of kernel method is its high computational cost associated with kernel matrices. The cost is at least quadratic in the number of training data points, but most kernel methods include computation of matrix inversion or eigenvalue decomposition and the cost becomes cubic in the number of training data. Large training sets cause large storage and computational costs. Despite low rank decomposition methods (Cholesky decomposition) reduce this cost, they continue to require computing the kernel matrix. One of the approaches to deal with this problem is low-rank matrix approximations. The most popular examples of them are Nyström method and the random features. Both of them have been successfully applied to efficient kernel learning.ully applied to efficient kernel learning.
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| rdfs:comment |
Low-rank matrix approximations are essenti … Low-rank matrix approximations are essential tools in the application of kernel methods to large-scale learning problems. Kernel methods (for instance, support vector machines or Gaussian processes) project data points into a high-dimensional or infinite-dimensional feature space and find the optimal splitting hyperplane. In the kernel method the data is represented in a kernel matrix (or, Gram matrix). Many algorithms can solve machine learning problems using the kernel matrix. The main problem of kernel method is its high computational cost associated with kernel matrices. The cost is at least quadratic in the number of training data points, but most kernel methods include computation of matrix inversion or eigenvalue decomposition and the cost becomes cubic in the number of training datecomes cubic in the number of training dat
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| rdfs:label |
Low-rank matrix approximations
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