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Based on Regularization framework kernel function selection

Author: WangXueYan
Tutor: ZhouShuiSheng
School: Xi'an University of Electronic Science and Technology
Course: Applied Mathematics
Keywords: Kernel function Regularization Supervised learning Hilbert space Greedy algorithm
CLC: TP181
Type: Master's thesis
Year: 2009
Downloads: 83
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Abstract


In the 1990s , the Vapnik et al 's efforts, data-based machine learning theory has been considerable development , formed a relatively complete statistical learning theory . The essence of statistical learning theory introduces a hypothetical function capacity control , in order to make the learning machine has better generalization ability , you need to assume that the function volume control and minimize the risk of experience as a good compromise between . Before the statistical learning theory , kernel function in machine learning was introduced too , which includes linear and nonlinear mapping function . Kernel function can effectively reduce the dimensionality of the data and avoid overfitting the data . Since statistical learning theory and nuclear technologies, nuclear plant caused the emergence and development of rapid success . Current nuclear plant technologies include support vector machines, multi-core learning , PAC framework and kernel Fisher classifier and other issues. This thesis is to expand on the above theoretical perspectives , including the following three aspects. First, the introduction of statistical learning theory and nature of the basic theorems on Hilbert space kernel learning and knowledge are summarized. Secondly, since the statistical learning theory and the effective integration of the kernel function , the resulting framework based on regularization kernel learning optimization problems, effectively solve the problem of solving a supervised learning . For regularization in combination with the kernel ridge regression and support vector machine application for a detailed derivation . Finally, in the regularized loss function based on the framework , we propose a new method of selecting kernel function , and gives the corresponding algorithm . The new algorithm is different from the greedy algorithm is: choose the minimum value of the objective function combination coefficients , the original optimization problem into a constrained linear programming problem, and use non-negative least squares method to solve it. After MNIST data with the results of the experiment show that the new method of classification superior to greedy algorithm classifier.

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