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Itakura–Saito distance
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Itakura–Saito distance : ウィキペディア英語版
Itakura–Saito distance
The Itakura–Saito distance (or Itakura–Saito divergence) is a measure of the difference between an original spectrum P(\omega) and an approximation \hat(\omega) of that spectrum. Although it is not a perceptual measure it is intended to reflect perceptual (dis)similarity. It was proposed by Fumitada Itakura and Shuzo Saito in the 1960s while they were with NTT.〔Itakura, F., & Saito, S. (1968). Analysis synthesis telephony based on the maximum likelihood method. In Proc. 6th of the International Congress on Acoustics (pp. C–17–C–20). Los Alamitos, CA: IEEE.〕
The distance is defined as:〔

: D_(P(\omega),\hat(\omega))=\frac\int_^ \left(\frac-\log \frac - 1 \right ) \, d\omega
The Itakura–Saito distance is a Bregman divergence, but is not a true metric since it is not symmetric〔
〕 and it does not fulfil triangle inequality.
In Non-negative matrix factorization the Itakura-Saito divergence can be used as a measure of the quality of the factorization: this implies a meaningful statistical model of the components and can be solved through an iterative method.
== See also ==

* Log-spectral distance

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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