▁a ▁non - linear ▁approach ▁as ▁the ▁mapping ▁cannot ▁be ▁represented ▁as ▁a ▁linear ▁combination ▁of ▁the ▁original ▁variables ▁as ▁possible ▁in ▁techniques ▁such ▁as ▁principal ▁component ▁analysis , ▁which ▁also ▁makes ▁it ▁more ▁difficult ▁to ▁use ▁for ▁classification ▁applications . ▁ ▁Den ote ▁the ▁distance ▁between ▁it h ▁and ▁j th ▁objects ▁in ▁the ▁original ▁space ▁by ▁, ▁and ▁the ▁distance ▁between ▁their ▁pro jections ▁by ▁. ▁Sam mon ' s ▁mapping ▁a ims ▁to ▁minim ize ▁the ▁following ▁error ▁function , ▁which ▁is ▁often ▁referred ▁to ▁as ▁Sam mon ' s ▁stress ▁or ▁Sam mon ' s ▁error : ▁ ▁The ▁minim ization ▁can ▁be ▁performed ▁either ▁by ▁gradient ▁descent , ▁as ▁proposed ▁initially , ▁or ▁by ▁other ▁means , ▁usually ▁involving ▁iter ative ▁methods . ▁The ▁number ▁of ▁iterations ▁needs ▁to ▁be ▁experiment ally ▁determined ▁and ▁conver gent ▁solutions ▁are ▁not ▁always ▁guaranteed . ▁Many ▁implementations ▁prefer ▁to ▁use ▁the ▁first ▁Princi pal ▁Com ponents ▁as ▁a ▁starting ▁configuration . ▁ ▁The ▁Sam mon ▁mapping ▁has ▁been ▁one ▁of ▁the ▁most ▁successful ▁non linear ▁metric ▁mult id im ensional ▁scaling ▁methods ▁since ▁its ▁advent ▁in ▁ 1 9 6 9 , ▁but ▁effort ▁has ▁been ▁focused ▁on ▁algorithm ▁improvement ▁rather ▁than ▁on ▁the ▁form ▁of ▁the ▁stress ▁function . ▁The ▁performance ▁of ▁the ▁Sam mon ▁mapping ▁has ▁been ▁improved ▁by ▁extending ▁its ▁stress ▁function ▁using ▁left ▁B reg man ▁diver gence ▁▁ ▁and ▁right ▁B reg man ▁diver gence . ▁ ▁References ▁ ▁External ▁links ▁ ▁Hi See ▁– ▁an