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4931

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. )z(f=x

: )x=X(P

x t = }sessoT{#/}sdaeH{ # = op3

N / t

:: : low risk High risk

Input: x = [x1,x2]T ,Output: C {0,1}

: high risk(C=1) or low risk(C=0)

4

classification

otherwise 0

)|()|( if 1 choose

or

otherwise 0

)|( if 1 choose

C

C

C

C

,xxCP ,xxCP

. ,xxCP

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01

501

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x . )x|C(P

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eluR seyaB

x x

xp

PpP

CCC

| |

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011

CCCC

CC

ppPpP

PP

xxx

roiretsop

roirpdoohilekil ssalC

ecnedive

x . C

C . x

()...

6

pattern recognition using neural networks theory and algorithms for

engineers and scientists, by Carl G. Looney

xx

xp

pPP

CCC

| |

7

xx

xp

pPP iii

CCC

| |

x Ci

Class likelihood

K

kpP

pP

p

pPP

1|

| | |

ii

iiiii

CC

CCCCC

x

x

x

xx

xx |max| ki CC PPk

Ci .

. iC i

. i ki

. k ksir detcepxe

:

8

sksiR dna sessoL

1

| |K

k ki i

k

C P R

x x

x x R Rk k i i| nim | fi esoohc

ssoL 1/0

9

ik

ikki

fi

fi

1

0

x

x

xx

|

|

||

i

kik

K

kikik

PC

PC

RPC

1

1

.

. 1+k :)tcejer ( :

01

1

dna | | fi esoohc

k i| |

i k R R Ck i i

R R

x x

x x

x x k, , , i R Ri k | | tcejer2 1 1

()... :

11

otherwise reject

| and || if choose 1xxx ikii CPikCPCPC

10

1

1

0

otherwise

if

if

,Ki

ki

ik

xxx

xx

|||

||

iik

ki

K

kkK

CPCPR

CPR

1

1

1

12

Kigi ,, , 1x xx kkii ggC max if choose

xxx kkii gg max| R

ii

i

i

i

CPCp

CP

R

g

|

|

|

x

x

x

x

K decision regions R1,...,RK

Dichotomizer g(x) = g1(x) g2(x)

otherwise

if choose

2

1 0

C

gC x

Discriminant Functions

13

Equal losses

Unequal losses

With reject

x )x|kS( P : kS

: k i kiU

41

xx

xx

esoohC fi |xam |

||

jj

ii

kikik

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Y X Y X

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sremotsuc sremotsucohw thguob dna

#

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XY PXY

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X

XY

PX

PXYPYX

sremotsucohw thguob

sremotsucohw thguob dna

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tfil -

:)Y X( tseretni/tfiL

1=tfiL . Y X

1>tfiL . Y X

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tesmeti . tesrepus

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