Itakura–Saito distance

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The Itakura–Saito distance is a measure of the perceptual difference between an original spectrum P(\omega) and an approximation \hat{P}(\omega) of that spectrum. It was proposed by Fumitada Itakura and Shuzo Saito in the 1970s while they were with NTT.

The distance is defined as:[1]

D_{IS}(P(\omega),\hat{P}(\omega))=\frac{1}{2\pi}\int_{-\pi}^{\pi} \left[ \frac{P(\omega)}{\hat{P}(\omega)}-\log \frac{P(\omega)}{\hat{P}(\omega)} - 1 \right] \, d\omega

The Itakura–Saito distance is a Bregman divergence, but is not a true metric since it is not symmetric[2] and it does not fulfil triangle inequality.

See also[edit]


  1. ^ Alan H. S. Chan, Sio-Iong Ao (2008). Advances in industrial engineering and operations research. Springer. p. 51. ISBN 978-0-387-74903-7. 
  2. ^ A. Banerjee et al. (2004). "Clustering with Bregman Divergences". In Michael W. Berry, Umeshwar Dayal, Chandrika Kamath, and David Skillicorn. Proceedings of the Fourth SIAM International Conference on Data Mining. SIAM. pp. 234–245. ISBN 978-0-89871-568-2.