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REMOVING THE VARIANCE TERM: REAL-VALUED CODES

If with a specific application we want to make use of the representational capacity of real-valued codes and if we are satisfied with decorrelated (instead of independent) representational units, then we might remove the $V$-Term from (4) by setting $\alpha = 0$. In this case, we want to minimize

\begin{displaymath}\beta I + \gamma H .\end{displaymath}

Note that with real-valued units the invertibility criterion theoretically can be achieved with a single unit. In that case, the independence criterion would force all other units to take on constant values in response to all input patterns. In noisy environments, however, it may turn out to be advantageous to code the input into more than one representational unit. This has already been noted by Linsker (1988) in the context of his Infomax principle.



Juergen Schmidhuber 2003-02-13


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