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A.3 Iterative mean
The mean value of a distribution {x_{i}} can also be computed iteratively if the values x_{i} are drawn onebyone. Let
x be the average over the first t data points. We observe that
x 
= 
x_{i} 


= 
x_{i} + x_{t} 


= 
x_{i} + x_{t} 


= 
x + x_{t} . 
(A.13) 
Thus, the update rule for the temporary mean
c(t + 1) = x upon presentation of a value x is
c(t + 1) = c(t) + x  c(t) . 
(A.14) 
This rule is the same as for the center update in vector quantization with a learning rate that decays as 1/t.
Next: B. Algorithms
Up: A. Statistical tools
Previous: A.2 Maximum likelihood
Heiko Hoffmann
20050322