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M ultivariate NormalM od el 3.1 Introd uc tion

Summary: Chapter 3
M ultivariate NormalM od el
3.1 Introd uc tion
Inthislecture w e w illexamine the use ofthe multivariate normalmod eland
itsuse inpatternclassi¯cation.A point infeature space w illb e represented
by a row vector xofM d imensions.x= x1;:::;xM ,w here xi isthe value
offeature numb er i.P articular pointsinfeature space may b e referred to
asx1,x2 and so on.W e w illillustrate some ofthe conceptsbyusing¯gures
b ased onM = 2 ; b ut realprob lemsoftenuse much larger valuesofM :T he
mathematicsisthe same inhigher d imensions,b ut w e can't d raw the ¯gures.
T he multivariate normald istrib utionhasa relatively simple expression
that isalmost ind epend ent ofthe numb er ofd imensions. T hisand other
propertiesmake it very °exib le asa mod elingtool.T he expressionis
pN (x) =
(2 ¼)M =2 j§ j1=2
e¡ 1
2 [(x¡¹)§ ¡1(x¡¹)0
] (3.1)
W e w illuse the notationpN (x;¹;§ ) to refer to the ab ove expressionw hen


Source: Anderson, Peter G. - Department of Computer Science, Rochester Institute of Technology


Collections: Computer Technologies and Information Sciences