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I am studying the AdaBoost algorithm. The update rule for a weak hypothesis is:

$Dt+1(i) = Dt(i)exp(−αtyiht(xi))/zt $

where $zt$ is a normalization factor chosen so that $Dt+1$ is a distribution.

What does the 'normalization factor' mean? Could I have an explanation with an example, please?

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The normalization factor is used to reduce any probability function to a probability density function with total probability of one. See Wikipedia.

Say your unnormalized value is [0.1, 0.2, 0.3, 0.2]. You normalize it by dividing it by $z_t=0.1+0.2+0.3+0.2=0.8$, therefore get the normalized value [0.125, 0.25, 0.375, 0.25] which sums up to 1..

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