EE3J2 Data Mining Lecture 12: Sequence Analysis (2) Martin Russell

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EE3J2 Data MiningLecture 12 Sequence Analysis
(2)Martin Russell
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Objectives

• Revise dynamic programming
• Examples

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Alignment path
A C X C C
D
A B C D
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Accumulated Distance

• The accumulated distance along the path p is the
  sum of distances along its length
• Large accumulative distance poor matches
  between symbols poor path
• Small accumulative distance good matches
  between symbols good path
• The path with the smallest accumulated distance
  is called the optimal path
• Computed using Dynamic Programming

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Dynamic Programming
Accumulated distance to this point
A C X C C
D
A B C D
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Formally
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Example application sequence retrieval
Corpus of sequential data
query sequence Q
AAGDTDTDTDD AABBCBDAAAAAAA BABABABBCCDF GGGGDDG
DGDGDGDTDTD DGDGDGDGD AABCDTAABCDTAABCDTAAB CDCDCD
TGGG GGAACDTGGGGGAAA . .
BBCCDDDGDGDGDCDTCDTTDCCC
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Example Edit Distance
Accumulated distance matrix A B C C D A 0 1 2 3
4 A 0 1 2 3 4 B 1 0 1 2 3 C 2 1 0 0 1 D 2 1 1 1
0 Forward path matrix A B C C D A \ _ _ _ _ A
_ _ _ _ B \ _ _ _ C \ _ _ D \
S1 AABCD KDEL0 S2 ABCCD KINS 0
A B C C D A \ _ _ _ _ A _ _ _ _ B \ _ _ _ C
\ _ _ D \ AABCCD AABCCD
Distance matrix A B C C D A 0 1 1 1 1 A 0 1 1 1
1 B 1 0 1 1 1 C 1 1 0 0 1 D 1 1 1 1 0
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Example 2 Edit Distance
Accumulated distance matrix A B C C D A 0
3 6 9 12 A 2 1 4 7 10 B 5 2 2 5 8 C 8
5 2 2 5 D 11 8 5 3 2 Forward path matrix
A B C C D A \ _ _ _ _ A \ _ _ _ B \ \ _ _ C
\ \ _ D \ \
S1 AABCD KDEL2 S2 ABCCD KINS 2
A B C C D A \ _ _ _ _ A \ _ _ _ B \ \ _ _ C
\ \ _ D \ ABCCD ABCCD
Distance matrix A B C C D A 0 1 1 1 1 A 0 1 1 1
1 B 1 0 1 1 1 C 1 1 0 0 1 D 1 1 1 1 0
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edit-dist.c

• New C program on course website
• Computes the edit distance between two sequences
• Prints out
• Distance matrix
• Forward accumulated distance matrix
• Forward path matrix
• Optimal path
• Optimal alignment

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edit-dist.c

• Format
• edit-dist seq1 seq2 ltKdelgt ltKinsgt
• Seq1 and seq2 are the sequences
• ltKdelgt and ltKinsgt optional, default 0

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Matching partial sequences

• In some applications the interest is in whether
  one sequence matches a subsequence of another
  sequence
• Example Bioinformatics
• Look for examples of a simple DNA sequence within
  a more complex sequence
• Infer evolutionary relationship between two
  organisms

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Partial alignment

• Simple intuitive solution is to allow Dynamic
  Programming to
• Start at any point in the first row
• End at any point in the final row
• Then proceed as before
• Unfortunately this has limitations

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Finding matching sub-sequences
Start DP from here
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Backwards Pass DP
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Backwards Pass DP

• Starts in bottom row, works right-to-left and
  bottom-to-top
• Otherwise, backwards accumulated distance matrix
  and backwards path matrix calculations analogous
  with forward-pass DP

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Forward-backward DP

• Suppose that we have done a complete forward DP
  and a complete backward DP
• We will have two path matrices
• Forward path matrix
• Backward path matrix
• For any point in bottom row can trace-back
  through forward path matrix and recover path
  ending in top row
• For any point in top row can trace-back through
  backward path matrix and recover path ending in
  bottom row

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Matching sub-sequences
Are paths the same? If so, then we have a
matching subsequence
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Matching subsequences

• If a path occurs as a consequence of tracing-back
  through the forward path matrix and tracing-back
  through the backward path matrix, then the
  corresponding section of the horizontal sequence
  is called a matching subsequence
• The matching subsequences are those which achieve
  a good match with the vertical pattern

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Matching subsequences
matching subsequence
X Z A B C
C Y Z
A B B C
We say that this subsequence most closely
resembles the original sequence ABBC
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Summary

• Revision of Dynamic Programming
• Examples Edit distance
• Motivation for interest in optimal subsequences
• Forward and backward dynamic programming
• Matching subsequences, subsequences which most
  closely resemble a given sequence