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Helicality: An Isomap-based Measure of Octave Equivalence in Audio Data

2020-10-01 20:30:05
Sripathi Sridhar, Vincent Lostanlen
arXiv_SD
             
Abstract

Octave equivalence serves as domain-knowledge in MIR systems, including chromagram, spiral convolutional networks, and harmonic CQT. Prior work has applied the Isomap manifold learning algorithm to unlabeled audio data to embed frequency sub-bands in 3-D space where the Euclidean distances are inversely proportional to the strength of their Pearson correlations. However, discovering octave equivalence via Isomap requires visual inspection and is not scalable. To address this problem, we define "helicality" as the goodness of fit of the 3-D Isomap embedding to a Shepherd-Risset helix. Our method is unsupervised and uses a custom Frank-Wolfe algorithm to minimize a least-squares objective inside a convex hull. Numerical experiments indicate that isolated musical notes have a higher helicality than speech, followed by drum hits.

Abstract (translated)

URL

https://arxiv.org/abs/2010.00673

PDF

https://arxiv.org/pdf/2010.00673.pdf

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