Neurocomputing in Space - High Dimensional Neurocomputing: Growth, Appraisal and Applications - page 127

Table 6.2 Comparison of testing error of second face set (Fig. 6.4 )
Test face

6.4 a 6.4 b 6.4 c 6.4 d 6.4 e

Test error (MSE) 3.11e-04 6.10e-03 4.90e-03 6.21e-04 7.32e-04

6.5 Inferences and Discussion

High-dimensional neural networks have been developed independently of their sim-
ilarity or unsimilarity to biological neural network. Nevertheless, many of their
applications are oriented to solution of the problems, which are natural for human
intelligence. The 3D vector-valued neural network and the corresponding 3D vector
version of the back-propagation algorithm (3DV-BP) are natural extensions of the
neural network of single and two dimensions. The 3DV-BP can be applied to mul-
tilayered neural networks whose threshold values, input, and output signals are all
3D real valued vectors, and whose weights are all 3D orthogonal matrices. It has
been well established in this chapter through variety of computational experiments
that 3DV-BP has ability to learn 3D motion. It is hence clear that phase information
of each point can effectively be maintained along with the decrease in the num-
ber of input parameters when solving the problem at hand—function mapping or
classification.

References

1. Tripathi, B.K., Kalra, P.K.: The novel aggregation function based neuron models in complex
domain. Soft Comput. 14 (10), 1069-1081. Springer, (2010)
2. Tripathi, B.K., Kalra, P.K.: On the learning machine for three dimensional mapping. Neural
Comput. Appl. 20 (01), 105-111. Springer, (2011)
3. Oh, B.J.: Face recognition by using neural network classifiers based on PCA and LDA. In:
Proceedings of the IEEE International Conference on Systems, Man and Cybernetics, pp.
1699-1703, 10-12 Oct 2005
4. Zhou, X., Bhanu, B.: Integrating face and gait for human recognition at a distance video. IEEE
Trans. Syst. Man Cybern. 37 (5), 1119-1137 (2007)
5. Pantic, M., Patras, I.: Dynamics of facial expression: recognition of facial actions and their
temporal segments from face profile image sequences. IEEE Trans. Syst. Man Cybern. 36 (2),
433-449 (2007)
6. Hietmeyer, R.: Biometric identification promises fast and secure processing of airline passen-
gers. Int. Civil Aviat. Organ. J. 55 (9), 10-11 (2000)
7. O'Tolle, A.J., Abdi, H., Jiang, F., Phillips, P.J.: Fusing face-verification algorithms and humans.
IEEE Trans. Syst. Man Cybern. 37 (5), 1149-1155 (2007)
8. Blanz, V., Vetter, T.: Face recognition based on fitting a 3D morphable model. IEEE Trans.
PAMI 25 (9), 1063-1074 (2003)
9. Abate, A.F., Nappi, M., Riccio, D., Sabatino, G.: Letters 2D and 3D face recognition: a survey.
Pattern Recognit. 28 , 1885-1906 (2007)
10. Tripathi, B.K., Kalra, P.K.: On efficient learning machine with root power mean neuron in
complex domain. IEEE Trans. Neural Network 22 (05), 727-738 (2011). ISSN: 1045-9227