’ s ▁( 1 9 3 6 ) ▁canonical ▁vari ate ▁analysis ▁( also ▁called ▁the ▁canonical ▁correlation ▁analysis ), ▁designed ▁to ▁obtain ▁maximum ▁( can on ical ) ▁correl ations ▁between ▁the ▁predict or ▁and ▁criter ion ▁canonical ▁vari ates . ▁The ▁difference ▁between ▁the ▁canonical ▁vari ate ▁analysis ▁and ▁canonical ▁analysis ▁is ▁analog ous ▁to ▁the ▁difference ▁between ▁the ▁principal ▁components ▁analysis ▁and ▁factor ▁analysis , ▁each ▁with ▁its ▁characteristic ▁set ▁of ▁common al ities , ▁eigenvalues ▁and ▁eigen ve ctors . ▁ ▁Can on ical ▁analysis ▁( simple ) ▁ ▁Can on ical ▁analysis ▁is ▁a ▁mult ivari ate ▁technique ▁which ▁is ▁concerned ▁with ▁determ ining ▁the ▁relationships ▁between ▁groups ▁of ▁variables ▁in ▁a ▁data ▁set . ▁The ▁data ▁set ▁is ▁split ▁into ▁two ▁groups ▁X ▁and ▁Y , ▁based ▁on ▁some ▁common ▁characteristics . ▁The ▁purpose ▁of ▁canonical ▁analysis ▁is ▁then ▁to ▁find ▁the ▁relationship ▁between ▁X ▁and ▁Y , ▁i . e . ▁can ▁some ▁form ▁of ▁X ▁represent ▁Y . ▁It ▁works ▁by ▁finding ▁the ▁linear ▁combination ▁of ▁X ▁variables , ▁i . e . ▁X 1 , ▁X 2 ▁etc ., ▁and ▁linear ▁combination ▁of ▁Y ▁variables , ▁i . e . ▁Y 1 , ▁Y 2 ▁etc ., ▁which ▁are ▁most ▁highly ▁correl ated . ▁This ▁combination ▁is ▁known ▁as ▁the ▁" first ▁canonical ▁vari ates " ▁which ▁are ▁usually ▁denoted ▁U 1 ▁and ▁V 1 , ▁with ▁the ▁pair ▁of ▁U 1 ▁and ▁V 1 ▁being ▁called ▁a ▁" can on ical ▁function ".