1990????Cortes ? Vapnik ???

1
??????????????????????

• ?????
• ???? ?????
• ????????????????

2
???????????

• ???????????????????????
• 1990????Cortes ? Vapnik ???
• ???????????????????????????????????????
• ???????????????????????????????????????????
• ????
• ???????????????????
• ??????????
• ???????????
• ????????
• c.f. Kernel Methods in Computational Biology, MIT
  Press, 2004

3
???????????

• ????????????????(???????)???????????
• ?????????????????????????????

4
SVM????????????

• ?????????????(SVM)
• ???????????????????????(??)???
• ????????????????????????????????????????

5
????

• ??????????????????????
• F(x) (??????)??????????????
• ???? K(x,y)f(x)f(y)
• x ? y ??????? ? K(x,y)??

6
??????

• ?????? K(x,y) xy
• ??????? K(x,y) (xy c)d
• RBF???? K(x,y) exp (-x - y2 /2s2 )
• ?????????(????????????)
• K(x,y) tanh (?xy - d)

7
????????????

• ??????? K(x,y)f(x)f(y)
• Mercer?????? ? ????
• ??????
• ?????? ( x1,x2,,xn ??????)

8
????????

• ???????????(feature vector)????????????
• ?????????
• ?????? ?????
• ???????? x ????
• F(x) (???, ??, ???, logP,)
• ???????? x,y ?????????
• F(x) ? F(y) ??????

9
?????????????????

1. SCOP????????????
2. ??????
3. ??????(???????HMM)
4. ?????
5. ???????
6. ?????

10
???????????

• ???????????????????(3????)????????????
• ???????????
• ???????????????????45?????

11
??????? (Fold Recognition)

• ???3???????????????(fold)???
• ????????????????????????(Chotia, 1992)????

12
SCOP??????

• ?????????????????????
• ???????????????

SCOP Root
Class.1
Class.2
?????
Fold.1
Fold.2
?????
Super Family.1
Super Family.2
?????
Family.1
Family.2
Family.3
mkkrltitlsesvlenlekmaremglsksamisvalenykkgq
ispqarafleevfrrkqslnskekeevakkcgitplqvrvwfinkrmrs
13
Super Family ??

• ????? SCOP ????????????????????

Super Family.1
???????
madqlteeqiaefkeafslfdkdgdgtittkelgtvmrslgqnpteaelq
dminevdadgngtidfpefltmmark
Super Family.2
Super Family.3

14
????????????
15
???????????????????

• HMM???????????
• Fisher ???? (Jaakkola et al., 2000)
• Marginalized ???? (Tsuda et al., 2002)
• ???????????????
• Spectrum ???? (Leslie et al., 2002)
• Mismatch ???? (Leslie et al., 2003)
• ?????????????????????
• SVM pairwise (Liao Noble, 2002)

16
????????

• ?????????????????????
• 2?????3???????????????
• ???????????????(?????)
• ???????????????????(????????)???

17
?????(????)

• ???(???????)?????????
• PAM250, BLOSUM45 ??

18
???????????

• ???2?????????????????????????
• ??????????????????(????????)??????????O(mn)???????
  (m,n???????)

19
????????????????(1)(Needleman-Wunsch??????)

• ????????????????
• ???????????????????????
• ????????????

20
????????????????(2)
DP (?????)??? ????(???)???
? O(mn)??
???????????? F(m,n)??max??????? F(i,j)???????????
(???????)
21
??????????(1) (Smith-Waterman??????)

• ???????????????????
• ???????????????
• ?????????????????
• ????HEAWGEH ? GAWED ????
• A W G E
• A W -E
• ????????????

22
??????????(2)
????? ??
23
LA????

• SW???????????????????
• ? MAX ??????????????
• ?????HMM?????????????
• ???
• SW?????????????HMM???
• SW?????? ???????
• LA????
• ??????????????(????)?
• ???????????O(mn)???LA?????????????

24
LA???????(1)

• ??(??)?????? Kaß (x,y)
• ???????? Kgß (x,y)

25
LA???????(2)

• ?????????(convolution)
• ??????????? n ?????????
• LA????

26
LA?????SW??????

• p(????)??????
• S(x,y,p) ??????p????
• ?????????????

??
27
LA?????SW???

• SW??? 1????????????????
• LA???? ????????????????

28
SVM?????????????? (1)

• ?????????????SVM???
• ???????????SVM?????????????

Super Family.1
SVM.1
???????
madqlteeqiaefkeafslfdkdgdgtittkelgtvmrslgqnpteaelq
dminevdadgngtidfpefltmmark
Super Family.2
SVM.2
Super Family.3
SVM.3
29
SVM?????????????? (2)

• ????
• ????????????????????????(??)
• ??
• ?????????????????????????(??)
• ???
• ?????????????????????????????????(??????)

30
??????????

• LA???????
• 1????O(mn)??(xm, yn)
• ????????? N ?????????? n
• ? ??? O(N2n2) ?? ? ??????

???
31
????????

• LA???????
• 1????O(mn)????????????
• ?????????????????????
• 1CPU?????????
• ?????
• SGI ORIGIN 3800 (R14000(500MHz) 256CPU)
• PC???? HPC (2.8GHz Xeom 8CPU)
• ???
• LSF (Load Sharing Facility) ? script ??????
• ????????(????????????CPU???)
• ??????????????
• ????????????????

32
????????
33
ROC???????
??????????????
34
mRFP???????
??????????????
35
??

• ???????????????????????
• Smith-Waterman?????????HMM??????
• ??????????????????????
• ????????????

??

• ?????????(??????)????????????????

36
??????????????????
37
???????

• ??? G(V,E)
• ????????????????????????
• ??????????(?????????)
• V ????? E ????
• ??????????????????????
• ???????????????????????
• ???????
• ?????? G1(V1,E1) ?G2(V2,E2) ????????

38
Marginalized ????

• Tsuda??2002????
• ??
• h,h ??????K????
• ?????RNA?????????

39
Marginalized ???????(1)

• Kashima??2003????
• h ??? G1 ??????
• h ??? G2 ??????
• l(h) ?? h ????(???)??
• K(x,y) ????????????
• (? K(x,y)1 if xy, otherwise 0 )

40
Marginalized ???????(2)
41
Marginalized ???????(3)
42
Marginalized ???????(4)
43
Marginalized ???????(5)

• ??????????
• h ??? G1 ??????
• h ??? G2 ??????
• ??????????????????????????????????????????????????
  ?
• (V1V2V1V2??????????)

44
Marginalized ???????(6)
45
Marginalized ???????(7)
46
Marginalized ???????(8)

• Marginalized ??????????????

47
Marginalized ???????????

• ??(???)?????????????
• ????????????????????????
• ??????????(???x???????y????)2)??????????????????
• ????????????????(??????)???????????????????????
• ? ????(Morgan Index)???????
• ?????????????

48
Morgan??????

• ??????????????????????1960?????
• CAS(Chemical Abstract Service)???
• ??????????(???)??????????????????????
• ????????????????
• ???????????????????(?????)
• ? Marginalized ?????????????????????????????????
• ???????????????????????????????
• ? ????????????????????????

49
Morgan??????????

• ?????????1??????
• ?????? x ?????????
• x ?????????????????x ??????

50
?????

• MUTAG ??????
• ???????????????
• ?????????????????????
• 125?????63???????
• ??1????????????????????????????????
• ??????
• SVM???????GIST (http//microarray.cpmc.columbia.ed
  u/gist)
• ???
• ?? C ???

51
???????? ????
Marginalized ???? ?????
???
52
???????? ????
53
??

• ?????????????????????
• Marginalized???????????
• ????????

?????

• ????????????????
• ???????
• ?????????(??????)
• ???????

54
????

• SVM?????????
• N. Cristianini J. Shawe-Taylor An
  Introduction to Support Vector Machines and Other
  Kernel-based Learning Methods, Cambridge Univ.
  Press, 2000.
• ????????????????????
• Kernel Methods in Computational Biology, MIT
  Press, 2004.
• Marginalized Kernel Morgan Index
• P. Mahe, N. Ueda, T. Akutsu, J-L. Perret, J-P.
  Vert Extensions of marginalized graph kernels,
  Proc. 21st Int. Conf. Machine Learning, 552-559,
  2004.
• LA????
• H. Saigo, J-P Vert, N. Ueda, T. Akutsu Protein
  homology detection using string alignment
  kernels, Bioinformatics, 201682-1689, 2004.