1990????Cortes ? Vapnik ???

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

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

2
??

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

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

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

4
???????????

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

5
SVM????????????

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

6
????

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

7
??????

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

8
????????????

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

9
????????

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

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

• Marginalized ???????
• Morgan??????
• ?????
• ?????

11
???????

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

12
Marginalized ????

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

13
Marginalized ???????(1)

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

14
Marginalized ???????(2)
15
Marginalized ???????(3)
16
Marginalized ???????(4)
17
Marginalized ???????(5)
18
Marginalized ???????(6)
19
Marginalized ???????(7)

• Marginalized ??????????????

20
Marginalized ???????????

• ??(???)?????????????
• ????????????????????????
• ??????????(????)??????????????????
• ????????????????(??????)???????????????????????
• ? ????(Morgan Index)???????

21
Morgan??????

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

22
Morgan??????????

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

23
?????

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

24
???????? ????
Marginalized ???? ?????
???
25
???????? ????
26
??

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

?????

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

27
?????????????????

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

28
???????????

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

29
??????? (Fold Recognition)

• ???3???????????????(fold)???
• ?????1000?????????????????(Chotia, 1992)????

30
SCOP??????

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

31
Super Family ??

• ????? SCOP ????????????????????

32
????????????
33
???????????????????

• 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)

34
????????

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

35
??????????(1) (Smith-Waterman??????)

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

36
??????????(2)
????? ??
37
LA????

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

38
?????????(HMM)

• HMM???????????
• ??
• ??????S
• ????
• S1,2,n
• ????(k?l)
• akl
• ????
• ek(b)

39
HMM????????????

• Viterbi??????
• ?????????????
• Parsing(????)
• Baum-Welch??????
• (EM??????)
• ???????????????
• Learning(??)

40
??HMM

• ???HMM
• 1????1??????
• ?????
• ??HMM
• 1???????????
• ?????????

41
LA???????(1)

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

42
LA???????(2)

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

43
LA?????SW??????

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

??
44
LA?????SW???

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

45
SVM-pairwise vs. LA kernel
SVM-pairwise
LA kernel
x
y
????
x
SW???
y
?????????
Pair HMM
??????
(0.2, 0.3, 0.1, 0.01)
(0.9, 0.05, 0.3, 0.2)
??
0.253
?????
0.227
46
SVM-pairwise vs. LA-kernel
47
???????????

• 2???? x ? y ?????K(x,x) ? K(x,y)??????????
• ?????????????????????????????????????
• (????)???

48
????????

• LA kernel ???
• 1????O(n2)?????????????
• ?????????????????????
• 1CPU?????????
• ?????
• SGI ORIGIN 3800 (R14000(500MHz) 256CPU)
• PC???? HPC (2.8GHz Xeom 8CPU)
• ???
• LSF (Load Sharing Facility) ? script ??????
• ????????(????????????CPU???)
• ?????Kernel?????
• ???????????????

49
????????
50
ROC???????
??????????????
51
mRFP???????
??????????????
52
??

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

??

• ?????????(??????)????????????????

53
????

• 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 (to appear soon)
• 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, in press.