Fusion of Neural Networks, Fuzzy Systems and Genetic Algorithms: Industrial Applications Fusion of Neural Networks, Fuzzy Systems and Genetic Algorithms: Industrial Applications
by Lakhmi C. Jain; N.M. Martin
CRC Press, CRC Press LLC
ISBN: 0849398045   Pub Date: 11/01/98
  

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The TDNN has been trained on the first 2 sections of the corpus (vowels and V/C/V transitions) for a total of 1000 and 2000 iterations “by epoch,” respectively. In order to compare the system based on one single 5-output TDNN with the system based on a bank of 5 single-output TDNNs, parameters have been suitably configured to maintain a constant computational overhead.

The two most performant 5-output configurations NetA and NetB have been chosen for comparing the results. The former has 15 neurons with 3-order memory in the first hidden layer, 10 neurons with 6-order memory in the second, and 9-order memory neurons in the output layer. The latter has 25 neurons with 2-order memory in the first hidden layer, 10 neurons with 4-order memory in the second, and 6-order memory neurons in the output layer. The optimal single-output configuration is indicated as NetO. nU indicates the number of neurons contained in each layer; nD, the memory size (delay) of each layer; Nop1, the number of operations required to initialize the network; and NopS, the number of operations executed by the TDNN for each input vector, with obtained data reported in Table 1 have been obtained. It can be noticed that the number of operations executed by Net0 has been multiplied by 5 to take into consideration the presence of 5 TDNNs in parallel.

Table 1 Comparison of the various TDNN configurations with respect to the computational overhead they require. NetA and NetB are the two most performant 5-output configurations while Net0 indicates the optimal single-output configuration (in this case, the multiplication by 5 takes this parallelism into account to make the evaluation homogeneous with the other two (1051-8215/97$10.00 © 1997 IEEE).
  nU nD Nop1 NopS
Net0×5 12-8-3-1 2-4-6 22025 2375
NetA 12-15-10-5 3-6-9 24230 2450
NetB 12-25-10-5 2-4-6 20210 2660

Networks NetA and NetB have been trained according to two different procedures defined as T1 and T2, respectively.

T1 First learning on a corpus of vowels (DB1) with 1000 iterations, followed by a second learning on a corpus of V/C/V transitions (DB2) with 2000 iterations. A corpus of isolated words (DB3) has been used as a testing set.
T2 Learning on an extended corpus (DB1+DB2+DB3) with 1000+2000+2000 iterations. DB3 was also used as a testing set.

The performances of these three TDNN configurations have been evaluated in terms of MSE, MAX, and r for each of the 5 mouth articulatory parameters (LM, H, W, Lup, dw). The experimental results obtained by applying the two different training procedures T1 and T2 are reported in Tables 2 and 3, respectively.


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