OCR

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?????? ?????? ???????? II 1015-1215 ??????????
??????? ????? 1015-1155 ????????? ?? ??
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??????
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• ?????
• ????????
• OCR

?????????
?????????? ????????? ??DB??? ??????? OLAP
?????? (??????? Data Warehouse)

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????????? (????????)
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Association Rules
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????? X ? Y ??????No ? ??????????Yes
???? Pr(X??Y) ? 5 ??? Pr(YX) ?
32 ????????????? interesting ????
Interesting Rules ??????
?? B ? C ? interesting Pr(BC) ????? Pr(B) ?
Pr(C) ?????
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???

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

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????????????????(???????)??? ?????????????? ????
???
????A,B,C ? ABC ??????
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ABCD
????????????????(???????)??? ?????????????? ????
??? ??? Pr(AB) lt ?? ? Pr(ABC) lt ?? ???
B ? C ???? Pr(CB)Pr(BC)/ Pr(B) ??????????
ABC
ABD
ACD
BCD
AB
AC
BC
AD
BD
CD
A
B
C
D
f
A Pr(A)??? AB Pr(AB)lt??
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??????????
?????????????
?????????????????????????
ACDE
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??????????
?????????????
?????????????????????????
ACDE
Hash table
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??????????
?????????????
?????????????????????????
ACDE
Hash table
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??????????
?????????????
?????????????????????????
ABDE
Hash table
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????????????
???????????????????
? ????????5???
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????????????
ABCD
ABC
ABD
ACD
BCD
AB
AC
BC
AD
BD
CD
A
B
C
D
f
???1? ????? ?????
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ABCD
ABC
ABD
ACD
BCD
AB
AC
BC
AD
BD
CD
???2 ???
???
A
B
C
D
f
???1? ????? ?????
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ABCD
ABC
ABD
ACD
BCD
???
???3 ???
AB
AC
BC
AD
BD
CD
???2 ???
A
B
C
D
f
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ABCD
???1? ?????? ??
???
ABC
ABD
ACD
BCD
???3 ???
AB
AC
BC
AD
BD
CD
???2 ???
A
B
C
D
f
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???1? ?????? ??
ABCD
? 1 ? ? ? ?
ABC
ABD
ACD
BCD
???3 ???
AB
AC
BC
AD
BD
CD
???2? ????
? ? ?
A
B
C
D
f
???1? ????? ?????? ???
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A priori ??? 20??4???????????????
ABCD
???1? ?????? ??
? 1 ? ? ? ?
ABC
ABD
ACD
BCD
???3? ????
? ? ?
AB
AC
BC
AD
BD
CD
???2? ????
A
B
C
D
f
???1? ????? ?????? ???
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?????R ? ????????Yes
????
Pr(?????R )?10??????
???????????
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?????R ? ????????Yes
????
Pr(?????R )?10??????
???????????
???80??? Pr(?????R )??
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?????R ? ????????Yes ?? Pr(?????R) ???
?? ??????????? R
???? X ? ( Pr(?????X) , Pr(?????X,????????
Yes)
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?????R ? ????????Yes ?? Pr(?????R) ???
?? ??????????? R
???? X ? ( Pr(?????X) , Pr(?????X,????????
Yes)
O(M log M) M number of records
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(No Transcript)
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Clockwise Search
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Counter Clockwise Search
Clockwise, Counter Clockwise ?????????1????? ??
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(??,????)?S ? ????????Yes
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(??,????)?S ? ????????Yes
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(??,????)?S ? ????????Yes
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(??,????)?S ? ????????Yes
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???
????
X????
?????
p( (??,????)?S ) ????S?????? ???????
????????????????????????S ????????
????????????????????????S
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(??,????)? S ? ????????Yes
???? M, ????? n
??????? ?????????????? O(n1.5) ?????
????
???X???????????? ?????????????? X???O(n
M)?????O(n 1.5 M) ?????? n ? log M
?????????????? P NP ?????????
??
???????
????????
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(??,????)? S ? ????????Yes
S
p( ??,????)?S, ????????Yes )
p((??,????)?S)
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(??,????)? S ? ????????Yes
S
p( ??,????)?S, ????????Yes )
p((??,????)?S)
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Hand Probing ???????
1?? hand probing ???? X???? O(n) ????? O(n1.5)

hand probing ????O(log M)
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y ?x a
?? a ????

• ????????????????
• ???????????????

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?????? - ????????????
????????????? ?????????????? ????????????????
10-fold Cross Validation
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Classification
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???
?????? ????????????????
?? ??? ???? ??? GPT GOT
????
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???
?????? ????????????????
?? lt 125
Yes
No
Yes
No
????
Yes
?????????? ???? ??????????? ?? ????????????????
No
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??? ??????????
?????
?????
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??? ??????????
Quinlan??????? ???
?????
?????
n
Ent1- (p log p q log q)
Ent2
n1
n2
p
q

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S
???????????? ???????????? ????????? Hand
Probing ??? ?????????? (????????? ????????????)
S????????
S??????
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Ent(???XYZ??????) ? min(Ent(X),Ent(Y),ENT(Z))
?? Ent(Z)? ???????????? ?????? Branch and Bound
Search
???????O(logM)?Hand Probing
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???????
UC Irvine, Repository of Machine Learning
databases http//www.ics.uci.edu/mlearn/MLReposit
ory.html
10-fold Cross Validation
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??? (Regression Tree)
BPS GDM YEN TB3M TB30Y
SP500 GOLD 1.443530 0.407460
0.004980 7.02 9.31 210.88
326.00 1.446120 0.408050 0.004950 7.04
9.28 205.96 339.45


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Yes
No
No
Yes
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?
D2
D1
???
µ1
µ2
??????????????
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A
µ
?
D2
D1
???
µ2
µ1
??????? ???

D1?D2
D1 ( µ -µ1 )2 D2 ( µ -µ2 )2
??????????
D1?D2
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S
???????????? ???????????? ????????? Hand
Probing ??? ?????????? Branch and Bound
Search ?????O(log M)
S???? ????? ????
S??????
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???????
http//www.cs.utoronto.ca/delve/data/datasets.htm
l
10-fold Cross Validation
??????(???????) ?????? ?????? ??? X?? ???
?? ??? add10 9792 10 0.141 0.123 0.156 0.185
abalone 4177 8 0.521 0.515 0.534 0.539 kin-8fh
8192 8 0.447 0.433 0.459 0.479 kin-8fm 8192
8 0.225 0.197 0.257 0.249 kin-8nh 8192
8 0.649 0.618 0.619 0.655 kin-8nm 8192
8 0.494 0.449 0.478 0.541 pumadyn-kin-8fh 8192
8 0.412 0.402 0.409 0.410 pumadyn-kin-8fh 8192
8 0.0604 0.0595 0.0653 0.0632 pumadyn-kin-8fh 8192
8 0.347 0.337 0.353 0.355 pumadyn-kin-8fh 8192
8 0.0530 0.0496 0.0550 0.0535
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??? ???, ??,
???? (3102?) ????????

?? 102 103 ?
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??? ???, ??, ??????, ????, ???, ...
???? (102107?) ??????, SNP, ...

?? 102 104 ?
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Clustering
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Expression Patterns of Genes in Various Tissues
Brain in embryo
Five brain tissues of adult mouse
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Clustering genes via expression patterns is
promising.

• A set of genes are expected to share common
  rolesin cellular processes.

• Genes in the same group would be observed in
  the same tissue at the same time.

• Their expression patterns would be similar.

• Clustering genes by expression patterns would
  providesubstantial insight on real groups of
  genes.

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Graphical Representation of Expression Patterns
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Cluster of genes coding ribosomal proteins
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Tightness of a cluster C of points
diameter max x y x and y are points
in C

• intra-class variance (1 / C ) S x in C x
  c(C) 2
• C number of points in C
• c(C) centroid (mean) of C, S x in C x

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Diameter Problem

• NP-hard if k is treated as a variable

• Approximation within a factor a of the optimal
  diameter is NP-hard for a lt 2.

• Approximation factor of 2 is achieved by
  furthest point heuristic in O(n k)-time.
• (n number of points)

• O(n log k)-time version

Diameter1 Diameter2
Intra-class variance1 gtgt Intra-class variance2
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Intra-class Variance Problem

• O(n (d2)k1 )-time algorithm (d number of
  dimensions)

• O(n(1/e)d )-time e-approximate 2-clustering
  algorithm

Problems of k-clustering

• It is hard to guess an appropriate value for k,
  beforehand.

• It is not easy to avoid generating a
  false-positive cluster of large intra-class
  variance that may contain genes of different
  functions.

Our Approach

• Perform hierarchical clustering by e-approximate
  2-clustering.

• Stop dividing a cluster if its intra-class
  variance is no more than a given threshold.

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Cluster of genes coding ribosomal
proteins intra-class variance 209
Clusters of genes coding myelin intra-class
variance 128
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?????
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• ??????????
• Apriori
• Dynamic Itemset Counting
• ????
• ????
• Correlation
• ???????
• 2?????
• ????? ?????
• ?????
• NP?? NP??
• ?????
• ????

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• ???? / ??? / ???
• C4.5
• CART
• ??????
• NP-hardness / Parallel Search
• Optimized Ranges / Regions
• Boosting / Bagging / Weighted Majority
• ???????
• NP??
• ?????
• ???

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• ??????
• ???????
• ???????? Google / Clever
• ?????????
• Clustering / Nearest Neighborhood
• k-means / k-clustering
• ???????
• ????????
• ?????????