▁with ▁the ▁ordering ▁of ▁the ▁points ▁as ▁processed ▁by ▁OP T IC S ▁on ▁the ▁x - axis ▁and ▁the ▁reach ability ▁distance ▁on ▁the ▁y - axis . ▁Since ▁points ▁belonging ▁to ▁a ▁cluster ▁have ▁a ▁low ▁reach ability ▁distance ▁to ▁their ▁nearest ▁neighbor , ▁the ▁clusters ▁show ▁up ▁as ▁valle ys ▁in ▁the ▁reach ability ▁plot . ▁The ▁deeper ▁the ▁valley , ▁the ▁dens er ▁the ▁cluster . ▁ ▁The ▁image ▁above ▁illustr ates ▁this ▁concept . ▁In ▁its ▁upper ▁left ▁area , ▁a ▁synth etic ▁example ▁data ▁set ▁is ▁shown . ▁The ▁upper ▁right ▁part ▁visual izes ▁the ▁sp anning ▁tree ▁produced ▁by ▁OP T IC S , ▁and ▁the ▁lower ▁part ▁shows ▁the ▁reach ability ▁plot ▁as ▁computed ▁by ▁OP T IC S . ▁Colors ▁in ▁this ▁plot ▁are ▁labels , ▁and ▁not ▁computed ▁by ▁the ▁algorithm ; ▁but ▁it ▁is ▁well ▁visible ▁how ▁the ▁valle ys ▁in ▁the ▁plot ▁correspond ▁to ▁the ▁clusters ▁in ▁above ▁data ▁set . ▁The ▁yellow ▁points ▁in ▁this ▁image ▁are ▁considered ▁noise , ▁and ▁no ▁valley ▁is ▁found ▁in ▁their ▁reach ability ▁plot . ▁They ▁are ▁usually ▁not ▁assigned ▁to ▁clusters , ▁except ▁the ▁om ni present ▁" all ▁data " ▁cluster ▁in ▁a ▁hier arch ical ▁result . ▁ ▁Ext ract ing ▁clusters ▁from ▁this ▁plot ▁can ▁be ▁done ▁manually ▁by ▁selecting ▁a ▁range ▁on ▁the ▁x - axis ▁after ▁visual ▁ins pection , ▁by ▁selecting ▁a ▁threshold ▁on ▁the ▁y - axis ▁( the ▁result ▁is ▁then ▁similar ▁to ▁a ▁DB