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A Large Dimensional Analysis of Least Squares Support Vector Machines

Abstract : In this article, a large dimensional performance analysis of kernel least squares support vector machines (LS-SVMs) is provided under the assumption of a two-class Gaussian mixture model for the input data. Building upon recent advances in random matrix theory, we show, when the dimension of data $p$ and their number $n$ are both large, that the LS-SVM decision function can be well approximated by a normally distributed random variable, the mean and variance of which depend explicitly on a local behavior of the kernel function. This theoretical result is then applied to the MNIST and Fashion-MNIST datasets which, despite their non-Gaussianity, exhibit a convincingly close behavior. Most importantly, our analysis provides a deeper understanding of the mechanism into play in SVM-type methods and in particular of the impact on the choice of the kernel function as well as some of their theoretical limits in separating high dimensional Gaussian vectors.
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Submitted on : Tuesday, May 19, 2020 - 1:55:09 PM
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Zhenyu Liao, Romain Couillet. A Large Dimensional Analysis of Least Squares Support Vector Machines. IEEE Transactions on Signal Processing, Institute of Electrical and Electronics Engineers, 2019, 67 (4), pp.1065-1074. ⟨10.1109/TSP.2018.2889954⟩. ⟨hal-02048984⟩



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