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Dec isionT heory Dec isionsand Feature Space

Summary: Chapter 2
Dec isionT heory
Dec isionsand Feature Space
W e w illnow examine the processofclassifyingob servationsonthe b asisof
feature vectors.Let x2 Frepresent a feature vector vector that isprod uced
byanob servation.T he d ecisionsystem must thenselect a particular pattern
from the set P ofpossib le patterns.W e seeka system byw hich the d ecisions
canb e mad e that w illminimize the expected loss.
Assume that the feature vector containsthe numericalmeasurementsof
M features. T he featuresmight have particular namessuch asheight or
weight, or just listed symb olically asf1;f2 ;:::;fM .Inthe case ofsports
»guresw e used height and weight asfeatures,and that space had M = 2
d imensions.Ifw e had ad d ed another feature,such asshoe size,w e w ould
have had M = 3.T he numb er offeatures,and thusthe d imensionalityofF,
d epend sonprob lem mod el.A particular feature vector1
x= [x1;x2 ;:::xM ]
w illcontainnumericalvalues. W e permit allrealnumb ersfor the feature
values,although a particular mod elmay restrict the range.For example,a
feature such asheight or w eight must have a non-negative value.
Inallofour mod elsthe numb er ofpatternsw illb e »nite.W e w illrepresent


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


Collections: Computer Technologies and Information Sciences