Support Vector Classifiers in scikit-learn: Mathematical Detail, Part III

Abstract

We present mathematical detail pertaining to the theory of the soft-margin support vector classifier ν-SVC, as used in scikit-learn. We construct the primal problem, from which we derive the dual problem. We also show how the primal problem can be derived from the dual problem. We analyze the effect of the parameter ν, and we discuss the relationship between ν-SVC and C-SVC. We include an interesting numerical example. The paper is the third in a series and is intended to be educational in nature. Tunawasilisha maelezo ya hisabati yanayohusiana na nadharia ya kiainishi cha vekta ya usaidizi wa ukingo laini ν-SVC, kama inavyotumika katika kujifunza-scikit. Tunaunda shida ya msingi, ambayo tunapata shida mbili. Pia tunaonyesha jinsi shida ya msingi inaweza kutolewa kutoka kwa shida mbili. Tunachambua athari za parameta ν, na tunajadili uhusiano kati ya ν-SVC na C-SVC. Tunajumuisha mfano wa nambari unaovutia. Karatasi ni ya tatu katika mfululizo na inakusudiwa kuwa ya elimu kwa asili. (The translation into Swahili was provided by Google Translate).