agrupamento e classificação de padrões

EE-214/2011EE-214/2011

Agrupamento eClassificaçãode Padrões

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EE-214/2011EE-214/2011

0 vértices 4 vértices

Agrupamento:Característica = Número de Vértices

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EE-214/2011EE-214/2011

= 470 nm = 550 nm

Agrupamento:Característica = Cor (Comprimento de Onda)

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A > 3 cm2 A 3 cm2

Agrupamento:Característica = Área

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?

Classificação


EE-214/2011EE-214/2011


?

EE-214/2011EE-214/2011

Círculo

Reconhecimento de Padrões

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Quadrado


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Uh?


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Ventilador acionado por Motor DC

A

V

TACMOT

J,B

BAT

Imot

,

EE-214/2011EE-214/2011


R Bat Ia R a

Ea

J , B

VBatV

aBat

aBatmot

a

mot

2

RR

EVI

E

I

Bdt

dJ

aBat

2

BataBat

aBat

Bat

aBat

aBat

2

RRV

RR

RR

V

RR

EV

BA

V

TACMOT

J,B

BAT

Imot

,

EE-214/2011EE-214/2011


BataBat

VRR

aBat

2

RR

nom

nom

motIk

R Bat Ia R a

Ea

J , B

VBatV

aBat

2

BataBat

aBat

Bat

aBat

aBat

2

RRV

RR

RR

V

RR

EV

B

EE-214/2011EE-214/2011


BataBat

VRR

aBat

2

RR

nom

nom

BmotIk

R Bat Ia R a

Ea

J , B

VBatV

aBat

2

BataBat

aBat

Bat

aBat

aBat

2

RRV

RR

RR

V

RR

EV

B

EE-214/2011EE-214/2011


BataBat

VRR

aBat

2

RR

motIk

RBAT + Ra

EE-214/2011EE-214/2011


BataBat

VRR

aBat

2

RR

motIk

VBAT

EE-214/2011EE-214/2011


BataBat

VRR

motIk

Eixo Quebrado

EE-214/2011EE-214/2011


BataBat

VRR

aBat

2

RR

motIk

Curto-ciruito

Eixo-travado

EE-214/2011EE-214/2011

Imot

E

B

C

Q

T

TT

EE

EE

NN

N

N

N

BB B

B

C

Q QQ

Q

E – Escova com RN – NominalB – Bateria com VC – CurtoT – Eixo TravadoQ – Eixo Quebrado

EE-214/2011EE-214/2011

Imot

E

B

C

Q

T

TT

EE

EE

NN

N

N

N

BB B

B

C

Q QQ

Q

E – Escova com RN – NominalB – Bateria com VC – CurtoT – Eixo TravadoQ – Eixo Quebrado

Eixo Quebrado

Curto-circuito

Motor-travado

g( , Imot ) = 0

> 0< 0

Qnew

d

EE-214/2011EE-214/2011

0.2935 0.0151 1.0227 0.0016 0.2549 0.0121 0.2960 0.0131 0.2871 0.0151 1.0943 0.0021 0.3128 0.0138 0.3004 0.0143 0.2636 0.0122 0.3048 0.0140 0.3036 0.0131 0.3054 0.0139 0.9157 0.0023 0.3573 0.0155 0.2950 0.0131 0.3431 0.0155 0.3191 0.0135 0.3071 0.0143 0.2975 0.0140 0.3382 0.0159 0.2672 0.0122 0.3509 0.0159 0.3536 0.0149 0.2939 0.0142 0.3177 0.0134 0.2545 0.0123 0.2523 0.0127 0.3070 0.0147 0.3625 0.0165 0.2511 0.0120 0.3121 0.0134 0.3436 0.0148 0.2948 0.0140 0.3105 0.0133 0.2936 0.0143 0.9123 0.0019 0.2975 0.0136 0.2615 0.0125 0.9941 0.0021 0.9485 0.0022 0.2619 0.0116 0.3065 0.0135 0.3051 0.0135

0.3065 0.0135 0.9897 0.0021 0.2523 0.0127 0.3147 0.0141 0.2646 0.0120 0.3470 0.0158 0.3005 0.0138 0.2939 0.0142 0.3279 0.0177 0.3470 0.0158 0.2882 0.0143 0.3382 0.0159 0.2997 0.0150 0.3068 0.0140 0.3061 0.0142 0.3001 0.0132 0.2871 0.0151 0.3095 0.0140 0.2523 0.0127 0.2975 0.0136 0.3128 0.0148 0.3463 0.0162 0.3279 0.0177 0.2975 0.0136 0.2975 0.0136 0.3175 0.0130 0.3417 0.0164 0.3121 0.0134 0.2887 0.0148 0.3356 0.0167 0.2669 0.0114 0.2754 0.0122 0.3038 0.0131 0.2997 0.0150 0.2927 0.0149 0.2938 0.0135 0.3082 0.0146 0.2580 0.0123 0.2632 0.0120 0.3194 0.0138 1.0943 0.0021 0.2995 0.0135 0.2935 0.0151

EE-214/2011EE-214/2011

0.2935 0.0151 1.0227 0.0016 0.2549 0.0121 0.2960 0.0131 0.2871 0.0151 1.0943 0.0021 0.3128 0.0138 0.3004 0.0143 0.2636 0.0122 0.3048 0.0140 0.3036 0.0131 0.3054 0.0139 0.9157 0.0023 0.3573 0.0155 0.2950 0.0131 0.3431 0.0155 0.3191 0.0135 0.3071 0.0143 0.2975 0.0140 0.3382 0.0159 0.2672 0.0122 0.3509 0.0159 0.3536 0.0149 0.2939 0.0142 0.3177 0.0134 0.2545 0.0123 0.2523 0.0127 0.3070 0.0147 0.3625 0.0165 0.2511 0.0120 0.3121 0.0134 0.3436 0.0148 0.2948 0.0140 0.3105 0.0133 0.2936 0.0143 0.9123 0.0019 0.2975 0.0136 0.2615 0.0125 0.9941 0.0021 0.9485 0.0022 0.2619 0.0116 0.3065 0.0135 0.3051 0.0135

0.3065 0.0135 0.9897 0.0021 0.2523 0.0127 0.3147 0.0141 0.2646 0.0120 0.3470 0.0158 0.3005 0.0138 0.2939 0.0142 0.3279 0.0177 0.3470 0.0158 0.2882 0.0143 0.3382 0.0159 0.2997 0.0150 0.3068 0.0140 0.3061 0.0142 0.3001 0.0132 0.2871 0.0151 0.3095 0.0140 0.2523 0.0127 0.2975 0.0136 0.3128 0.0148 0.3463 0.0162 0.3279 0.0177 0.2975 0.0136 0.2975 0.0136 0.3175 0.0130 0.3417 0.0164 0.3121 0.0134 0.2887 0.0148 0.3356 0.0167 0.2669 0.0114 0.2754 0.0122 0.3038 0.0131 0.2997 0.0150 0.2927 0.0149 0.2938 0.0135 0.3082 0.0146 0.2580 0.0123 0.2632 0.0120 0.3194 0.0138 1.0943 0.0021 0.2995 0.0135 0.2935 0.0151

Clusters?

EE-214/2011EE-214/2011

Observou-se = 0

No passado, a causa de motor parado tem sido:

- 70% casos = curto-circuito- 30 % casos = eixo-travado

Sem dados adicionais

Curto-circuito é a causa mais provável

Critério Utilizado: P(curto) > P(travado)

EE-214/2011EE-214/2011

Observou-se = 0 e mediu-se a corrente Imot = 21 A

Dados Históricos

Como aproveitar a informação de que

Imot = 21A ?

+10 20 30

[A]

+++ ++ +

+ = eixo-travado

+ +++ ++

+ = curto-circuito

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1122 p|xpp|xp decide

P(x| 2)P(2) > P(x| 1)P(1)

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1122 p|xpp|xp decide

iii p|xp)x(g

)x(g)x(g 12 decide

0)x(g)x(g 12 decide

)x(g)x(g)x(g 12

0

0

)x(g

decide

decide

EE-214/2011EE-214/2011

iii plog|xplog)x(g

No caso particular iii ,N~|xp

1122 p|xpp|xp

-1 0 1 2 3 4 5 6 7 8-1

0

1

2

3

4

5

6

7

x1x2

( 2, 2 )

( 1, 1 )

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iii plog|xplog)x(g

No caso particular iii ,N~|xp

xx

2

1exp

2

1)x(p 1T

2

1

2

d

1122 p|xpp|xp

,N~x;Rx d

i1T

i ploglog2

12log

2

dxx

2

1)x(g

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Caso I : iI2i

0 2 4 6 8 10 12 140

2

4

6

8

10

12

14

x1

x2

i1T

i ploglog2

12log

2

dxx

2

1)x(g

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Caso I : iI2i

i2

2

ii plog

2

x)x(g

i1T

i ploglog2

12log

2

dxx

2

1)x(g

iiTi

Ti

T2

plogx2xx2

1

Igual para todos os i

ii

Ti2

Ti2i plog

2

1x

1)x(g

ai

ijji2ji cx1

)x(g)x(g)x(g

EE-214/2011EE-214/2011

Caso I : iI2i

i1T

i ploglog2

12log

2

dxx

2

1)x(g

ijji2ji cx1

)x(g)x(g)x(g

0 2 4 6 8 10 12 140

2

4

6

8

10

12

14

x1

x2

g(x)

EE-214/2011EE-214/2011

i1T

i ploglog2

12log

2

dxx

2

1)x(g

0 1 2 3 4 5 6 7-2

0

2

4

6

8

10

Caso II : i

arbitrário mas igual para

g(x)

EE-214/2011EE-214/2011

Caso III : i arbitrários ( cada i )

i1T

i ploglog2

12log

2

dxx

2

1)x(g

0 2 4 6 8 10 12-1

0

1

2

3

4

5

6

7

8

9

1 2 3 4 5 6 7 8 91

2

3

4

5

6

7

8

9

x1

x2

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0 2 4 6 8 10 121

2

3

4

5

6

7

8

9

10

11

x1

x2

A ou B ?

A

B

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0 2 4 6 8 10 121

2

3

4

5

6

7

8

9

10

11

x1

x2

A ou B ?A

B

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Distância de Mahalanobis

0 2 4 6 8 10 121

2

3

4

5

6

7

8

9

10

11

x1

x2 A ou B ?A

B

)x()x(),x(d 1T2

EE-214/2011EE-214/2011

Distância

d: X X R+

Propriedades requeridas:

d(x,y) 0d(x,y) = 0 x=yd(x,y) = d(y,x)d(x,z) + d(z,y) d(x,y)

Distância de Minkowski:

k

1d

1i

k

ii ba)y,x(d

k=1 Manhattan

k=2 Euclidiana

EE-214/2011EE-214/2011

Agrupamento Hierárquico

1 2

2

1

x1

x2

1.0 1.01.0 0.71.2 0.71.2 1.20.8 1.00.7 0.72.0 2.01.8 1.81.8 2.12.3 2.02.3 1.72.0 2.4

Dados:

EE-214/2011EE-214/2011

1.0 1.01.0 0.71.2 0.71.2 1.20.8 1.00.7 0.72.0 2.01.8 1.81.8 2.12.3 2.02.3 1.72.0 2.4

Dados:

>> x =

1.0000 1.0000 1.0000 0.7000 1.2000 0.7000 1.2000 1.2000 0.8000 1.0000 0.7000 0.7000 2.0000 2.0000 1.8000 1.8000 1.8000 2.1000 2.3000 2.0000 2.3000 1.7000 2.0000 2.4000

>> y=pdist(x,'euclidean');

>> z=linkage(y,'average');

>> dendrogram(z)

EE-214/2011EE-214/2011

1 5 4 2 3 6 7 9 8 12 10 11

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.0 1.01.0 0.71.2 0.71.2 1.20.8 1.00.7 0.72.0 2.01.8 1.81.8 2.12.3 2.02.3 1.72.0 2.4

Dados:


EE-214/2011EE-214/2011

1 5 4 2 3 6 7 9 8 12 10 11

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1 1.0 1.02 1.0 0.73 1.2 0.74 1.2 1.25 0.8 1.06 0.7 0.77 2.0 2.08 1.8 1.89 1.8 2.110 2.3 2.011 2.3 1.712 2.0 2.4

Dados:

1 2

2

1

x1

x2


EE-214/2011EE-214/2011

1 5 4 2 3 6 7 9 8 12 10 11

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1 2

2

1

x1

x2

1 1.0 1.02 1.0 0.73 1.2 0.74 1.2 1.25 0.8 1.06 0.7 0.77 2.0 2.08 1.8 1.89 1.8 2.110 2.3 2.011 2.3 1.712 2.0 2.4

Dados:


EE-214/2011EE-214/2011

1 5 4 2 3 6 7 9 8 12 10 11

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1 2

2

1

x2

x1

1 1.0 1.02 1.0 0.73 1.2 0.74 1.2 1.25 0.8 1.06 0.7 0.77 2.0 2.08 1.8 1.89 1.8 2.110 2.3 2.011 2.3 1.712 2.0 2.4

Dados:


EE-214/2011EE-214/2011

K-means

1 2

2

1

x1

x2

1.0 1.01.0 0.71.2 0.71.2 1.20.8 1.00.7 0.72.0 2.01.8 1.81.8 2.12.3 2.02.3 1.72.0 2.4

Dados:

EE-214/2011EE-214/2011

1.0 1.01.0 0.71.2 0.71.2 1.20.8 1.00.7 0.72.0 2.01.8 1.81.8 2.12.3 2.02.3 1.72.0 2.4

Dados:

>> x =

1.0000 1.0000 1.0000 0.7000 1.2000 0.7000 1.2000 1.2000 0.8000 1.0000 0.7000 0.7000 2.0000 2.0000 1.8000 1.8000 1.8000 2.1000 2.3000 2.0000 2.3000 1.7000 2.0000 2.4000

>> [idx,c]=kmeans(x,2)

idx =

2 2 2 2 2 2 1 1 1 1 1 1

c =

2.0333 2.0000 0.9833 0.8833

EE-214/2011EE-214/2011

K-means

1 2

2

1

x1

x2

1.0 1.01.0 0.71.2 0.71.2 1.20.8 1.00.7 0.72.0 2.01.8 1.81.8 2.12.3 2.02.3 1.72.0 2.4

Dados:c = 2.0333 2.0000

0.9833 0.8833

EE-214/2011EE-214/2011

K-means

1 2

2

1

x1

x2

EE-214/2011EE-214/2011


EE-214/2011EE-214/2011

251,5 12,2 0,0 19,51.000,7 2,5 351,0 16,0 0,0 30,7 298,4 14,0

0 200 400 600 800 1000 12000

5

10

15

20

25

30

35

40

rotaçao [rpm]

corr

ente

[A

]

Centróides

EE-214/2011EE-214/2011

0 200 400 600 800 1000 12000

5

10

15

20

25

30

35

40

rotaçao [rpm]

corr

ente

[A

]

1

2

3

4

5

6

2 5 1 6 4 30

100

200

300

400

500

600

700

800

EE-214/2011EE-214/2011

Aprendizado Competitivo

Entrada

RNA

Padrão 1 Padrão 3Padrão 2

EE-214/2011EE-214/2011

A regra competitiva de atualização dos pesos é:

O tamanho do passo (0 < < 1) controla o tamanho da atualização em cada passo.

nnnn iii *** 1 wxww

2arg min ii

wxvencedor 2arg min ii

wxvencedor

wi* wiwi

x

EE-214/2011EE-214/2011

>> P=x';

>> net=newc([0 10 ; 0 20],3);

>> net=train(net,P);

>> xsim = sim(net,P);

>> Yc = vec2ind(xsim);

x =

2.8912 4.6925 2.6977 4.1531 3.0674 4.6355 3.3912 5.3341 3.0143 2.7596 3.6210 4.2673 2.8230 2.7786 3.8884 3.7128 2.2805 4.1053 3.0817 2.5987 2.0551 2.6898 2.4385 4.2339 2.3248 4.0878 3.3256 4.9084 2.7722 2.1358 2.4511 4.5631 3.0654 4.4797 2.9662 5.4541 2.7239 3.9596 2.1473 4.1791 6.0088 0.6796 5.3473 1.1695 6.3248 1.9968 4.9683 1.6344 5.3939 2.2423 6.0501 2.6200 6.4412 2.3042 6.4970 1.3510 6.1491 2.6364 7.3517 3.8455

7.0299 2.6696 5.4482 1.8907 6.9373 3.1359 6.3841 2.7066 7.3473 3.1661 6.4294 3.3694 6.0328 0.7340 6.3068 3.6512 7.4664 3.3202 6.0249 2.4205 4.2419 11.8915 4.1505 11.0143 4.2313 11.6063 3.4451 10.9294 3.7475 11.7190 3.7444 12.5351 3.6118 9.6320 3.9555 9.5597 4.2682 9.6711 4.4645 12.2583 4.3494 11.9162 4.0312 10.1017 3.5433 11.4301 3.9182 9.4428 4.1586 10.8102 4.0116 13.5573 4.0372 10.7638 3.6609 11.7846 3.3139 11.4386 3.9235 10.7200

EE-214/2011EE-214/2011

NEWC Create a competitive layer.

net = newc(PR,S,KLR,CLR)

TRAIN Train a neural network.

[net,tr,Y,E,Pf,Af] = train(NET,P,T,Pi,Ai,VV,TV)

VEC2IND Transform vectors to indices.

vec =

1 0 0 0 0 0 1 0 0 1 0 1

ind =

1 3 2 3

>> P=x';

>> net=newc([0 10 ; 0 20],3);

>> net=train(net,P);

>> xsim = sim(net,P);

>> Yc = vec2ind(xsim);

EE-214/2011EE-214/2011

0 1 2 3 4 5 6 7 8 92

4

6

8

10

12

14

16

x1

x2

x =

2.8912 4.6925 2.6977 4.1531 3.0674 4.6355 3.3912 5.3341 3.0143 2.7596 3.6210 4.2673 2.8230 2.7786 3.8884 3.7128 2.2805 4.1053 3.0817 2.5987 2.0551 2.6898 2.4385 4.2339 2.3248 4.0878 3.3256 4.9084 2.7722 2.1358 2.4511 4.5631 3.0654 4.4797 2.9662 5.4541 2.7239 3.9596 2.1473 4.1791 6.0088 0.6796 5.3473 1.1695 6.3248 1.9968 4.9683 1.6344 5.3939 2.2423 6.0501 2.6200 6.4412 2.3042 6.4970 1.3510 6.1491 2.6364 7.3517 3.8455

7.0299 2.6696 5.4482 1.8907 6.9373 3.1359 6.3841 2.7066 7.3473 3.1661 6.4294 3.3694 6.0328 0.7340 6.3068 3.6512 7.4664 3.3202 6.0249 2.4205 4.2419 11.8915 4.1505 11.0143 4.2313 11.6063 3.4451 10.9294 3.7475 11.7190 3.7444 12.5351 3.6118 9.6320 3.9555 9.5597 4.2682 9.6711 4.4645 12.2583 4.3494 11.9162 4.0312 10.1017 3.5433 11.4301 3.9182 9.4428 4.1586 10.8102 4.0116 13.5573 4.0372 10.7638 3.6609 11.7846 3.3139 11.4386 3.9235 10.7200

EE-214/2011EE-214/2011

Entrada

0 1 2 3 4 5 6 7 8 92

4

6

8

10

12

14

16

x1

x2

Padrão 1

Padrão 3

Padrão 2

RNA

Padrão 1 Padrão 3Padrão 2

EE-214/2011EE-214/2011

RNA

x1 = 2 x2 = 4

Padrão 1

Padrão 3

Padrão 2

0 1 2 3 4 5 6 7 8 92

4

6

8

10

12

14

16

x1

x2

Padrão 1

Padrão 3

Padrão 2

EE-214/2011EE-214/2011

x1 = 6 x2 = 5

RNA

Padrão 1

Padrão 3

Padrão 2

0 1 2 3 4 5 6 7 8 92

4

6

8

10

12

14

16

x1

x2

Padrão 1

Padrão 3

Padrão 2

EE-214/2011EE-214/2011

Redes de Kohonen

• RNA de 1 camada simples composta de uma camada de entrada e outra de saída

• Aprendizado não-supervisionado

Unidades de Entrada

Unidades concorrentes de Saída

EE-214/2011

Unidades de Entrada


Redes de Kohonen

EE-214/2011

1. Camada de entrada é apresentada

Unidades de Entrada


EE-214/2011

2. A distância do padrão de entrada para os pesos para cada unidade de saída é calculada através da fórmula euclidiana:

Onde j é a unidade de saída e é a distância resultante.

2|||| jj wxy

jy

Unidades de Entrada


EE-214/2011

• Cada vez que um vetor de entrada é apresentado para a rede, a distância em relação a ele para cada unidade na camada de saída é calculada

• A unidade de saída com a menor distância em relação ao vetor de entrada é a vencedora

Unidades de Entrada


unidadevencedora

EE-214/2011

• Os pesos são ajustados de acordo com o vencedor• Os vizinhos se aproximam de acordo com o treinamento e a estrutura

se auto-organiza

Unidades de Entrada


unidadevencedora

EE-214/2011EE-214/2011

nnnnn iiiii wxww *,1

n

dn ii

ii 2

2*,

*, 2exp

2arg min ii

wxvencedor 2arg min ii

wxvencedor

x

wi* wiwi

di,i*

EE-214/2011

Pessoas de Sexo e Idades Variados

Sexo Idade

EE-214/2011

EE-214/2011EE-214/2011

P=x';net = newsom([0 10; 0 20],[1 3],... 'gridtop','dist',0.9,200,0.01,0);net.trainParam.epochs = 100;net = train(net,P);

x =

1.6972 4.2944 0.8341 2.6638 2.0877 4.7143 2.2014 5.6236 1.1975 3.3082 2.8336 4.8580 2.8324 5.2540 1.9737 2.4063 2.2291 2.5590 2.1222 4.5711 1.8693 3.6001 2.5081 4.6900 1.5882 4.8156 3.5282 4.7119 1.9045 5.2902 2.0798 4.6686 2.7467 5.1908 2.0415 2.7975 1.9330 3.9802 1.4174 3.8433 5.8771 5.0000 7.1801 4.6821 6.2605 6.0950 7.9906 3.1260 6.4364 5.4282 7.3701 5.8956 7.1535 5.7310 6.3547 5.5779

5.4805 5.0403 6.9586 5.6771

6.2926 5.5689 7.4301 4.7444 7.3554 4.6225 8.1847 4.7041 7.4139 3.5249 6.5495 4.7660 7.2662 5.1184 6.2936 5.3148 6.9863 6.4435 6.9662 4.6490 3.2493 9.5747 3.3196 8.3572 3.3764 12.1836 2.6032 10.3776 3.0848 11.3928 3.0952 11.2809 2.5969 11.0258 2.7032 9.7953 3.4329 9.8634 2.9474 10.5507 3.1560 9.5769 3.0352 9.7329 2.7458 12.7670 2.7762 11.0669 3.1775 9.5392 2.6200 10.9505 3.3125 9.6460 3.2276 9.3809 2.6713 10.6867

2.8938 12.1442

NEWSOM Create a self-organizing map. net = newsom(PR,[d1,d2,...],tfcn,dfcn,olr,osteps,tlr,tns) PR - Rx2 matrix of min and max values for R input elements.Di - Size of ith layer dimension, defaults = [5 8].TFCN - Topology function, default = 'hextop'.DFCN - Distance function, default = 'linkdist'.OLR - Ordering phase learning rate, default = 0.9.OSTEPS - Ordering phase steps, default = 1000.TLR - Tuning phase learning rate, default = 0.02;TNS - Tuning phase neighborhood distance, default = 1.

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net = newsom([0 10; 0 20],[1 3],'gridtop','dist',0.9,200,0.01,0);

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RNA

x1 = 2 x2 = 4

Padrão 1

Padrão 3

Padrão 2

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net = newsom([0 10; 0 20],[3 3],'hextop','dist',0.9,200,0.01,1);

0 0.5 1 1.5 2 2.5

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EM (Expectation-Maximization)

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Cluster A Cluster B

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>> [W,M,V,L] = EM_GM(X,3,[],[],1,[])

EM algorithm for k multidimensional Gaussian mixture estimation X(n,d) - input data n=number of observations d=dimension of variable k - maximum number of Gaussian components allowed ltol - percentage of log likelihood difference between 2 iterations maxiter - maximum number of iteration allowed ([] for none) pflag - 1 for plotting GM for 1D or 2D cases only, 0 otherwise Init - structure of initial W, M, V: Init.W, Init.M, Init.V W(1,k) - estimated weights of GM M(d,k) - estimated mean vectors of GM V(d,d,k) - estimated covariance matrices of GM L - log likelihood of estimates

Patrick P. C. Tsui,Dept of Electrical and Computer EngUniversity of Waterloo

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x =

2.8912 4.6925 2.6977 4.1531 3.0674 4.6355 3.3912 5.3341 3.0143 2.7596 3.6210 4.2673 2.8230 2.7786 3.8884 3.7128 2.2805 4.1053 3.0817 2.5987 2.0551 2.6898 2.4385 4.2339 2.3248 4.0878 3.3256 4.9084 2.7722 2.1358 2.4511 4.5631 3.0654 4.4797 2.9662 5.4541 2.7239 3.9596 2.1473 4.1791 6.0088 0.6796 5.3473 1.1695 6.3248 1.9968 4.9683 1.6344 5.3939 2.2423 6.0501 2.6200 6.4412 2.3042 6.4970 1.3510 6.1491 2.6364 7.3517 3.8455

7.0299 2.6696 5.4482 1.8907 6.9373 3.1359 6.3841 2.7066 7.3473 3.1661 6.4294 3.3694 6.0328 0.7340 6.3068 3.6512 7.4664 3.3202 6.0249 2.4205 4.2419 11.8915 4.1505 11.0143 4.2313 11.6063 3.4451 10.9294 3.7475 11.7190 3.7444 12.5351 3.6118 9.6320 3.9555 9.5597 4.2682 9.6711 4.4645 12.2583 4.3494 11.9162 4.0312 10.1017 3.5433 11.4301 3.9182 9.4428 4.1586 10.8102 4.0116 13.5573 4.0372 10.7638 3.6609 11.7846 3.3139 11.4386 3.9235 10.7200

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Muito Obrigado!

agrupamento e classificação de padrões

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