Pour dénir l’objectif correspondant à une marge souple, nous devons introduire
une variable ressort (en anglais, slack variable) ζ
(i)
≥ 0 pour chaque observation
76
: ζ
(i)
mesure de combien la i
ième
observation est autorisée à empiéter sur la marge. Nous
avons maintenant deux objectifs contradictoires: diminuer autant que possible les
variables ressort pour réduire les empiétements de marge, et minimiser ½w
T
w pour
accroître la marge. C’est là qu’intervient l’hyperparamètre C: il permet de dénir un
compromis entre ces deux objectifs. Ceci conduit au problème d’optimisation ...
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