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110 lines
2.7 KiB
Plaintext
110 lines
2.7 KiB
Plaintext
This is a quick description of the Viterbi aka dynamic programming
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algorithm.
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Its reason for existence is that Wikipedia has become very poor on
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describing algorithms in a way that makes it useable for understanding
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them or anything else actually. It tends now to describe the very same
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algorithm under 50 different names and pages with few understandable
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by even people who fully understand the algorithm and the theory behind.
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Problem description: (that is what it can solve)
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assume we have a 2d table, or you could call it a graph or matrix if you
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prefer
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O O O O O O O
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O O O O O O O
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O O O O O O O
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O O O O O O O
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That table has edges connecting points from each column to the next column
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and each edge has a score like: (only some edge and scores shown to keep it
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readable)
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O--5--O-----O-----O-----O-----O
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2 / 7 / \ / \ / \ /
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\ / \ / \ / \ / \ /
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O7-/--O--/--O--/--O--/--O--/--O
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\/ \/ 1/ \/ \/ \/ \/ \/ \/ \/
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/\ /\ 2\ /\ /\ /\ /\ /\ /\ /\
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O3-/--O--/--O--/--O--/--O--/--O
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/ \ / \ / \ / \ / \
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1 \ 9 \ / \ / \ / \
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O--2--O--1--O--5--O--3--O--8--O
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Our goal is to find a path from left to right through it which
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minimizes the sum of the score of all edges.
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(and of course left/right is just a convention here it could be top down too)
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Similarly the minimum could be the maximum by just flipping the sign,
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Example of a path with scores:
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O O O O O O O
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>---O. O O .O-2-O O O
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5. .7 .
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O O-1-O O O 8 O O
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.
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O O O O O O-1-O---> (sum here is 24)
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The Viterbi algorithm now solves this simply column by column
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For the previous column each point has a best path and a associated
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score:
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O-----5 O
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\
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\
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O \ 1 O
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\/
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/\
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O / 2 O
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/
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/
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O-----2 O
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To move one column forward we just need to find the best path and associated
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scores for the next column
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here are some edges we could choose from:
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O-----5--3--O
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\ \8
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\ \
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O \ 1--9--O
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\/ \3
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/\ \
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O / 2--1--O
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/ \2
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/ \
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O-----2--4--O
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Finding the new best paths and scores for each point of our new column is
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trivial given we know the previous column best paths and scores:
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O-----0-----8
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\
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\
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O \ 0----10
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\/
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/\
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O / 0-----3
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/ \
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/ \
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O 0 4
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the Viterbi algorithm continues exactly like this column for column until the
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end and then just picks the path with the best score (above that would be the
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one with score 3)
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Author: Michael Niedermayer
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Copyright LGPL
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