BADCFEHGBIHJnKL?M/?SEHKLJnPkQLR%.CN;TKUEnEHJnWXA ...ssoares/artigos/tese.pdf · d jzaµcnj...
Transcript of BADCFEHGBIHJnKL?M/?SEHKLJnPkQLR%.CN;TKUEnEHJnWXA ...ssoares/artigos/tese.pdf · d jzaµcnj...
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ã�ZhX[U ��bdV�V�b¼Ò(äâ� Ó ]�g `�W)a.b�Ò�c�X Ó m o�bdo�U ã�Z�åÏæ�U���U n o)U n `�U�Vf�jUE ¡�� 9 ¡ : �s¡ �f�PLYHPL<@C>J ¡H� 9 ¡�� �H� �c�EHA>JHg=;=jLE � � 9 �O¡ � � 9m�gs¶bl�;=J �Hù 9 ��� 9 � ��HJZ<>ì ù�� �a� � � : ��HPLg=;=EHj � � 9i� � �O� ���?BjLjLJHj � ù 9 �a� ��� :M�EHA@;sE �s� 9O9 � � �M�EHA@;=jUE � ù 9 �O¡ : � 9´5?SjUEaCNE :s: 9 �Z� ¡ �
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100
120
140
160
180
200
220
20 40 60 80 100 120
Altu
ra (
cm)
Massa (kg)
AnaAugusto
Carolina
Flavio
Jose
Julian
Lennon
Maria
Marina
Renata
"Cluster 1""Cluster 2""Cluster 3""Cluster 4"
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d�?Bg=E�m�;TYZPLA>E��ewú�e�tqrPL?'JZ<êYZA@PLd�JZ<|EHYHJZANEu<NIHJ�C>A>�S<B�XEHdkA>?B<@?Bj CFEajLKLJVE/<@?BYZPL;Tj CN?hSJZjk�UYZPkANE�^GBIHJLzXYZA@PLd�J|fê�LhSJZR�d²JZ<DCNJ|d�JZA�f�PLYZPL<DCNJ3�Lf�jUE|?��HJZ<@ìOLYHA>PLd�J�¾��khSJZR�d²JZ<DCNJyd�JZAíM/EHA>;TjUEk��HPkg=;sEajï�Àc�EHA@JZg=;TjUE�?n��?BjLjkJZj¤$?�LjUEHg=R�?Bj C>?J�YZA>PLd�JVc���ºîJZA@R'EaKLJ*d�JZA�M�EHA@;sEk�tm�gs¶bl�;=J*?´µ?BjLEaCFEkw
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ç
AnaAugusto
CarolinaFlavio
JoseJulian
Lennon
Maria
Marina
Renata
"Cluster A’""Cluster B’""Cluster C’"
20 40
60 80
100 120
Massa (kg) 100 120
140 160
180 200
220
Altura (cm)
0
10
20
30
40
50
60
Idade
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ÁXj CNA@?SCFEajrC>JL�µdUEHA>E9qrPUEHgTq�Pk?BA%C>;=d�J9Kk?�KUEHKkJZ<B��jkJZA>R%EHg=R�?Bj C>?u?S<@C>?B<<>IHJ-;TjL;=hS;sEHgTR%?SjrC>?hSJZj lZ?SA@CN;TKLJZ<µdUEHA>EêlaEHg=JZA@?B<¿j�PkR%ìSA>;=hSJZ<µEHj CN?S<íKL?�<>?SA>?SRÒPL<NEaKLJZ<íd�JZA�PLRüEHg=YZJHA>;TC>R%Jkwp:�?B<@CNEºîJHA>R%Ek�ojL?B<DCN?�C>ANEHQLEHg=�LJk�olaEHR�JZ<µ?BjeºîJehBEHA�JH<�dLA@JZQLg=?SR'Ea<5Kk?êhBgTPL<@C>?BA@;=}bEaGbIHJ%hBJZRôKUEHKkJZ<�jrPe^R�ìBA@;=hSJZ<�JZPï�±jLJnhbEa<>JuKL?�KUEHKLJZ<�hBEaCN?SYZ\ZA>;ThBJZ<S��?B<DCN?B<�<>?SR%dkA>?�<>?SANIHJuhBJZj lH?BA@C>;=KLJH<�dUEaANE3KUE�^KkJZ<3jrPLR%ìSA>;ThBJZ<Sw ��?B<DCN?S<uhBEH<>JH<B��EOKL;=<@<>;=R�;=g=EHA>;TKUEHKL?3d�J�KL?*<>?SA3R%?SKL;=KLE9hBJHR%J E-Kk;=<@CNÿHje^hS;sE[?Bj C>A>?�KkJZ;=<yd�JZj CNJZ<Sw4�]JeKkJ-EHgTYZJZA@;TCNR�J�Kk?/hSg=PL<DCN?BA@;=}BEHGbIHJVJZd�?BA>EV<@JZQLA>?nPLRðhSJZj�ö@PLj C>JS = {x1, x2, . . . , xn}
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p #%$'&'( )+*,$.- /z }| {2
666666666666666666664
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. . .
xi1 . . . xij . . . xip
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xn1 . . . xnj . . . xnp
3
777777777777777777775
JZjkKL?nJ�laEHgTJZAxij
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PEHdLA@?B<>?Sj CFEHKUE-E
<@?BYZPk;=AB��JHjLKL?�J3j��LR%?SA>Jn = 10
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021
2
666666666666666666666664
95 193 49 7
94 197 52 5
67 159 26 1
28 145 12 0
33 144 9 0
48 159 34 1
27 110 6 0
68 154 24 3
65 165 25 2
87 202 23 2
3
777777777777777777777775
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06571
2
666666666666666666666664
95000 193 49 7
94000 197 52 5
67000 159 26 1
28000 145 12 0
33000 144 9 0
48000 159 34 1
27000 110 6 0
68000 154 24 3
65000 165 25 2
87000 202 23 2
3
777777777777777777777775
J�qrPL?�jLJH<5gT?SlaEHA@;sEyEyPLR%E�JHPkCNA>E�dkg=JHCNEHYZ?BR KLJZ<íKUEaKLJZ<B�oEadLA>?S<>?Bj CNEHKUE%jLE%m�;TYZPLA>Ey�ew : w
100
120
140
160
180
200
220
20000 40000 60000 80000 100000 120000
Altu
ra (
cm)
Massa (g)
AnaAugusto
Carolina
Flavio
Jose
Julian
Lennon
Maria
Marina
Renata
"Cluster A""Cluster B""Cluster C"
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c$JZR�J|d�JeKk?BR�JZ<¿lH?BAB�kJZ<�hBgTPL<@C>?BA@<íEHdLA@?B<>?Sj CFEHKLJH<íjUIHJ|<>IHJ|JZ<�R�?B<@R%JH<$JZQkC>;=KLJH<$qrPUEHjLKkJE�PLjL;TKUEHKL?nKL?nR%EH<><>EVPeCN;=gT;=}BEHKUE�?SANE�J9Âr;=gTJZYZA>EHR'EewO~�<@C>J9J�hBJZA@A>?nd�JZA>qrPL?a�$jL?S<@CN?/hbEH<@JL�$J?S;¹øeJVA>?Sºî?SA>?SjrC>?*÷�hBJ�JZA>Kk?BjUEHKLE9EHg¹CNPLA>E[dUEH<><>E-E[CN?SA�<@?BPL<�laEHg=JZA@?B<�EHQk<>JZgTPkCNJZ<�hSJZRðR%?SjLJZA
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sf
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mf
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wf�<><>PkR%;TjLKLJ
sf
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zif =xif − mf
sf
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?xj = (xj1, xj2, . . . , xjp)
�
d(i, j) =√
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xi
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:;1
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666666666666666666666664
0.00 30.77 7.35 61.66 12.81 33.33 30.89 17.15 11.45 28.98
30.77 0.00 28.62 38.79 42.25 63.21 60.95 40.16 38.60 30.12
7.35 28.62 0.00 60.89 14.90 35.71 34.23 15.10 10.44 23.87
61.66 38.79 60.89 0.00 70.36 94.35 91.32 67.26 68.52 52.74
12.81 42.25 14.90 70.36 0.00 25.00 23.45 11.22 6.40 31.69
33.33 63.21 35.71 94.35 25.00 0.00 5.92 32.88 27.96 54.32
30.89 60.95 34.23 91.32 23.45 5.92 0.00 32.80 27.22 54.17
17.15 40.16 15.10 67.26 11.22 32.88 32.80 0.00 8.19 22.32
11.45 38.60 10.44 68.52 6.40 27.96 27.22 8.19 0.00 27.04
28.98 30.12 23.87 52.74 31.69 54.32 54.17 22.32 27.04 0.00
3
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d(i, j) = (|xi1 − xj1| + |xi2 − xj2| + · · · + |xip − xjp|)¼��ew��Z½
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a
b
c
Distancia de Manhattan = a + b
Distancia Euclidiana = c
x
x j
i
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W 9 zd(i, j) ≥ 0
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d(i, i) = 0
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d(i, j) = q
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hSJZRq ≥ 1
?q ∈ R
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cluster nao-convexo
cluster com baixa densidade
cluster esferico
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Altu
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Idade
Relacao Idade X Altura (cm)
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idade com ruido
altura com ruido
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I2 I1
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