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

We present mathematical detail pertaining to the theory of soft-margin support vector classifiers, designated C-SVC, as used in scikit-learn. We discuss the character of C-SVC, particularly with regard to the penalty term. We construct the primal problem and, thereafter, derive the dual problem. We introduce the notion of nonlinear classifiers and describe the so-called kernel trick. Additionally, we show how the primal problem can be derived from the dual problem. The paper is the second in a series and is intended to be educational in nature.Tunawasilisha maelezo ya hisabati yanayohusiana na nadharia ya viainishaji vya vekta vya usaidizi wa ukingo laini, iliyoteuliwa C-SVC, kama inavyotumiwa katika kujifunza kwa scikit. Tunajadili tabia ya C-SVC, hasa kuhusu muda wa adhabu. Tunaunda shida ya msingi na, baada ya hapo, tunapata shida mbili. Tunatanguliza wazo la viainishaji visivyo vya mstari na kuelezea kinachojulikana kama hila ya kernel. Zaidi ya hayo, tunaonyesha jinsi shida ya msingi inaweza kupatikana kutoka kwa shida mbili. Karatasi ni ya pili katika mfululizo na inakusudiwa kuwa ya elimu kwa asili.(The translation into Swahili was provided by Google Translate).