= Distortion measure
{disambiguate=information theory}
{title2=$d:\mathcal X\times\widehat{\mathcal X}\to[0,\infty)$}
= Distortion measure
{synonym}
A <distortion measure> assigns a nonnegative cost to replacing a source symbol $x$ by a reconstruction $\hat x$. It need not be a <metric>: the two <alphabets> may differ, and neither symmetry nor the <triangle inequality> is required. Choosing the cost is part of the model. For numerical symbols, $d(x,\hat x)=(x-\hat x)^2$ gives <mean squared error> after averaging; for exact symbol agreement, use <Hamming distortion>.
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