Which is the actual computational complexity of the learning phase of SVM (let's say, that implemented in LibSVM)?
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Training complexity of nonlinear SVM is generally between O(n^2) and O(n^3) with n the amount of training instances. The following papers are good references:
- Support Vector Machine Solvers by Bottou and Lin
- SVM-optimization and steepest-descent line search by List and Simon
PS: If you want to use linear kernel, do not use LIBSVM. LIBSVM is a general purpose (nonlinear) SVM solver. It is not an ideal implementation for linear SVM. Instead, you should consider things like LIBLINEAR (by the same authors as LIBSVM), Pegasos or SVM^perf. These have much better training complexity for linear SVM. Training speed can be orders of magnitude better than using LIBSVM.
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Marc Claesen
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Link 2 is dead, and for link 1 the document seems to have been removed – Carlos Pinzón Dec 20 '18 at 14:51
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And what is the complexity of liblinear svm? – Michael D Nov 04 '21 at 11:03
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This is going to be heavily dependent on svm type and kernel. There is a rather technical discussion http://www.csie.ntu.edu.tw/~cjlin/papers/libsvm.pdf. For a quick answer, http://www.csie.ntu.edu.tw/~cjlin/papers/libsvm.pdf, says expect it to be n^2.
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