Convolution and Its Applications to Sequence Analysis

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Convolution and Its Applications to Sequence
Analysis

• Student Bo-Hung Wu
• Advisor Professor Herng-Yow Chen R. C. T. Lee
• Department of Computer Science Information
  Engineering
• National Chi Nan University

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The Definition of Convolution in the Continuous
Case
Example
Reference Lecture notes, Introduction to
communication, R. C. T. Lee et al.
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Exact String-Matching Problem Input. Text string
TT1T2Tn and pattern string PP1P2Pm
where Ti, Pi ?(alphabet) and mltn. Output.
All locations i in T where
TiTi1Ti2Tim-1P1P2Pm
It is obvious that string matching is related to
convolution.
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Convolution in the Discrete Case
Definition Let Xltx0, , xmgt, Ylty0, , yngt be
two given vectors, xi, yi D. Let and be
two given functions, where
Then the convolution of X and Y with respect to
and is
for k0 mn
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Consider the exact string-matching problem, how
can we use convolution to solve it?FP74 First
we reverse Y to be
Second we define the functions and to be
as follows
Note that the process of this convolution is
equal to the one of the sliding window approach.
FP74
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Applying Convolution to Sequence Analysis

• The common substring with k-mismatch allowed
  problem
• Common substrings with k-mismatches allowed among
  multiple sequences problem
• Determining the similarity of two DNA sequences
• Searching in a DNA sequences database
• Finding repeating groups in a DNA sequence
• An aid for detection in transposition
• An aid for detecting insertion/deletion
• An aid for detecting the overlapping of segments
  resulting from the shot-gun operations
• The corresponding pair-wise nucleotides in a DNA
  sequence
• An aid for looking for similar regions in a DNA
  sequence with a distance constraint

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The Corresponding Pair-wise Nucleotides in a DNA
Sequence
Substitution rule A ? T T ? A C ? G G ? C
Example Sacttgacgtgaac
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Experiments

• We apply convolution on DNA sequences and English
  compositions to find the similarity of them.
• In the following experiments, we used the
  following DNA sequences as the input data.
  (Clustering was known in advance for
  evaluating.)
• C1(0-25) Hepatitis B virus C2(26-162)
  Human mitochondrion C3(163-1041) Other
  viruses

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Experiment The Comparison of English
compositions.

• We applied convolution on two English
  compositions to detect whether they are similar
  or not.

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Conclusion and Future Work

• We have shown that several applications related
  to sequences analysis which we discovered can be
  solved by means of convolution.
• Convolution can be used as a negative answer
  filter.
• In practical parts, we did some experiments. The
  experimental results confirm that this approach
  is feasible.
• By arranging appropriate operations to be the
  functions in the convolution, we can solve more
  problems related to sequences analysis.
• For example, we hope that we may apply
  convolution to help solve protein structure
  comparison.

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Thank you.