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Understand algorithm for AudioLocalMeasurements, & ModifiedKullbackLeibler?

Posted 6 months ago
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I recently was doing some experiments with AudioLocalMeasurements for some music analysis tasks, and in the process of trying to explain what I did to someone I realized that I didn't know what the ModifiedKullbackLeibler measurement is computing. Specifically, what is modified versus regular KL divergence, and what is done to the frequency spectra of the windows being compared? Without understanding what the algorithm is actually reporting, it's hard to make any interpretation of the results that it computes.

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I haven't heard from anyone in the know, but have run across one instance of someone referring to a modified KL measure. Specifically "Music Structure Analysis from Acoustic Signals" by Roger B. Dannenberg and Masataka Goto. Is the algorithm in Mathematica at all related to what they describe?

Not to sound too cranky, but I really like Mathematica yet find it very awkward when communicating results with others if my tool of choice has apparently useful methods that can't be explained to them. It's really, really difficult to perform any kind of defensible science if my answer to someone about an algorithm I applied was "I ran it through an ill-defined black box".

The implementation is from Brossier, P. M. (2006). Automatic annotation of musical audio for interactive applications (Doctoral dissertation), which itself is a variation of the one presented in Hainsworth, S. W., & Macleod, M. D. (2003, September). Onset Detection in Musical Audio Signals. In ICMC.

The formula is: d[k] = Log[1 + X[k]/(X[k - 1] + epsilon)] where X[k] is the kth frame of the magnitude spectrogram. The result is then standardized (using Standardize[res,Mean,Max]).

Excellent! Thank you!

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