By John G. Webster (Editor)

ISBN-10: 0792344987

ISBN-13: 9780792344988

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**Additional info for 58.Speech and Audio Processing**

**Example text**

1 and 11 for an introduction). , quasi-Newton, conjugate gradient, Levenberg–Marquardt). The first (and also second) derivative of the error function in feed-forward neural networks can be calculated efficiently with a procedure called back-propagation (1), which requires a forward pass (calculate yk(xn;w) ᭙ k) and a backward pass [calculate (Ѩ/Ѩw)E vector] through the network for each of the N training vector pairs. All training procedures can be (1) off-line or batch methods, for which the weights w are updated after all N training samples have been used to calculate the first derivative, or (2) on-line methods, for which only a part of the training samples is used to get an estimate of the first derivative which is then used to update the weights.

This section therefore focuses on routing algorithms for direct networks, and only a few basic algorithms are outlined here. Basic routing algorithms for indirect networks are covered in the subsection ‘‘Indirect Networks’’ of the section on ‘‘Network Topologies’’ above. Deterministic Routing The most common deterministic routing strategy used in direct networks is dimension-order routing in which a message traverses the network by successively traveling over an ordered set of dimensions of path.

In Fig. 9(b), the transfer of a message from source node 1 to destination node 6 (over intermediate nodes 0 and 2) is shown in a hypercube with N ϭ 8 using the e-cube algorithm. , over intermediate nodes 5 and 7). However, cyclic dependences cannot occur when the e-cube algorithm is used, so that deadlocks are avoided (for a detailed explanation, see Ref. 21). The e-cube algorithm, initially proposed for hypercube networks, can be generalized for k-ary n-cubes (21). The original e-cube algorithm cannot guarantee deadlock freedom in these networks because of inherent cycles due to the wrap-around edge connections (see the subsection ‘‘Direct Networks’’ under ‘‘Network Topologies’’ above).

### 58.Speech and Audio Processing by John G. Webster (Editor)

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