Colloquium Speaker

Prof. Anna Lubiw, School of Computer Science, University of Waterloo
A Geometric Approach to Music Pattern Matching
Date: Thursday, February 10, 2005
Time: 11:00AM
Place: Gould-Simpson, Room 701
Refreshments will be served in the 7th floor lobby of Gould-Simpson at 10:45 AM


The music pattern matching problem is to find occurrences of a small fragment of music called the "pattern" in a larger body of music called the "score". String matching approaches have been most thoroughly investigated, but they cannot cope with polyphonic music (where multiple notes are played simultaneously). A geometric interpretation converts the problem to that of translating a set of horizontal line segments in the plane to find the best match in a larger set of horizontal line segments. Our contribution is that we use fairly general weight functions to measure the quality of a match, thus enabling approximate pattern matching. We give an algorithm with running time $O(nm \log m)$, where $n$ is the size of the score and $m$ is the size of the pattern. We show that the problem, in this geometric formulation, is unlikely to have a significantly faster algorithm because it is at least as hard as a basic problem called 3-SUM that is conjectured to have no subquadratic algorithm. We present some examples to show the potential of this method for finding minor variations of a theme, and for finding polyphonic musical patterns in a polyphonic score.

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