Transcript Using Transportation Distances for Measuring Melodic Similarity Pichaya Tappayuthpijarn

Using Transportation
Distances for Measuring
Melodic Similarity
Pichaya Tappayuthpijarn
Qiang Wang
Outline
Introduction
 Melodic Similarity Measuring
 The Earth Mover’s Distance (EMD)
 The Proportional Transportation Distance
(PTD)
 Results & Conclusion

Introduction
Weighted notes are well suited to
represent music.
 Measuring melodic similarity by comparing
weighted notes.
 Using EMD or PTD to measure the
similarity.

Melodic Similarity Measuring

Weighted Notes represented by (Time, Pitch,
Weight). The weights only reflect the note
durations.
Properties of a Metric
**For pseudo-metric, only properties i, iii and iv holds.
The Earth Mover’s Distance (EMD)

measures the minimum amount of work
needed to transform one into the other by
moving weight.
Minimize the overall cost
 d
iI jJ
with constraints
f
ij ij
W, U are the total weights of A, B
respectively,
Example : a weight flow with EMD
The Proportional Transportation
Distance (PTD)
EMD v.s. PTD
 PTD is a modified version of EMD.
 In the case of unequal total weight,
triangle inequality does not hold for the
EMD.

By PTD, triangle inequality holds, making
database search more efficient by using
indices.
The Proportional Transportation
Distance
for both point set, divide every point’s
weight by its point set’s total weight
 then calculate the EMD for the resulting
point sets.

Properties of PTD

A pseudo-metric.
Triangle inequality holds true
a+b>=c

Gives clear distinction of groups.
The fact that the EMD allows partial matching, while the
PTD matches all notes, leads to a clear distinction of
these groups by the PTD, but not the EMD.

Can recognize augmented versions of the
same melody as similar.
Result & Conclusion
PTD leads to the identification of about
3.9% of 100 randomly chosen search
( for r = 1).
 For r = 5, we need less than 1000
calculations instead of 476,000.


PTD Indexing reduces the query
running time.
Thank you!