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The earliest reference to a similar formula appears to be Armstrong (1985, p. 348), where it is called "adjusted MAPE" and is defined without the absolute values in the denominator. It was later discussed, modified, and re-proposed by Flores (1986).
MAPE puts a heavier penalty on negative errors, < than on positive errors. [9] As a consequence, when MAPE is used to compare the accuracy of prediction methods it is biased in that it will systematically select a method whose forecasts are too low.
In control theory, the RMSE is used as a quality measure to evaluate the performance of a state observer. [ 10 ] In fluid dynamics , normalized root mean square deviation (NRMSD), coefficient of variation (CV), and percent RMS are used to quantify the uniformity of flow behavior such as velocity profile, temperature distribution, or gas species ...
This is in contrast to RMSE which involves squaring the differences, so that a few large differences will increase the RMSE to a greater degree than the MAE. [ 4 ] Optimality property
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This page was last edited on 25 December 2021, at 09:39 (UTC).; Text is available under the Creative Commons Attribution-ShareAlike 4.0 License; additional terms may apply.
The MSE either assesses the quality of a predictor (i.e., a function mapping arbitrary inputs to a sample of values of some random variable), or of an estimator (i.e., a mathematical function mapping a sample of data to an estimate of a parameter of the population from which the data is sampled).
The predecessor of SSIM was called Universal Quality Index (UQI), or Wang–Bovik Index, which was developed by Zhou Wang and Alan Bovik in 2001. This evolved, through their collaboration with Hamid Sheikh and Eero Simoncelli, into the current version of SSIM, which was published in April 2004 in the IEEE Transactions on Image Processing. [1]