Orthonormal Basis Lattice Neural Networks

Lattice based neural networks are capable of resolving some difficult non-linear problems and have been successfully employed to solve real-world problems. In this paper a novel model of a lattice neural network (LNN) is presented. This new model generalizes the standard basis lattice neural network (SB-LNN) based on dendritic computing. In particular, we show how each neural dendrite can work on a different orthonormal basis than the other dendrites. We present experimental results that demonstrate superior learning performance of the new Orthonormal Basis Lattice Neural Network (OB-LNN) over SB-LNNs.

[1]  Gerhard X. Ritter,et al.  Learning In Lattice Neural Networks that Employ Dendritic Computing , 2006, FUZZ-IEEE.

[2]  Athanasios Kehagias,et al.  Text classification using the /spl sigma/-FLNMAP neural network , 2001, IJCNN'01. International Joint Conference on Neural Networks. Proceedings (Cat. No.01CH37222).

[3]  L. Iancu,et al.  A morphological auto-associative memory based on dendritic computing , 2004, 2004 IEEE International Joint Conference on Neural Networks (IEEE Cat. No.04CH37541).

[4]  Peter Sussner,et al.  Morphological perceptron learning , 1998, Proceedings of the 1998 IEEE International Symposium on Intelligent Control (ISIC) held jointly with IEEE International Symposium on Computational Intelligence in Robotics and Automation (CIRA) Intell.

[5]  H. Longuet-Higgins Understanding the Brain , 1968, Nature.

[6]  William H. Press,et al.  Numerical Recipes Example Book , 1989 .

[7]  M. Grana,et al.  Some applications of morphological neural networks , 2001, IJCNN'01. International Joint Conference on Neural Networks. Proceedings (Cat. No.01CH37222).

[8]  Charles R. Johnson,et al.  Topics in Matrix Analysis , 1991 .

[9]  Peter Sussner,et al.  Binary autoassociative morphological memories derived from the kernel method and the dual kernel method , 2003, Proceedings of the International Joint Conference on Neural Networks, 2003..

[10]  Peter Sussner,et al.  A fuzzy autoassociative morphological memory , 2003, Proceedings of the International Joint Conference on Neural Networks, 2003..

[11]  Zhang Yun,et al.  Using multi-layer morphological neural network for color images retrieval , 2004, Fifth World Congress on Intelligent Control and Automation (IEEE Cat. No.04EX788).

[12]  Idan Segev,et al.  Dendritic processing , 1998 .

[13]  Peter Sussner,et al.  An introduction to morphological neural networks , 1996, Proceedings of 13th International Conference on Pattern Recognition.

[14]  G. Brindley,et al.  THE UNDERSTANDING OF THE BRAIN , 1973 .

[15]  Vassilios Petridis,et al.  Fuzzy Lattice Neurocomputing (FLN) models , 2000, Neural Networks.

[16]  Gerhard X. Ritter,et al.  Morphological perceptrons with dendritic structure , 2003, The 12th IEEE International Conference on Fuzzy Systems, 2003. FUZZ '03..

[17]  Yun Zhang,et al.  Color images restoration with multi-layer morphological(MLM) neural network , 2003, Proceedings of the 2003 International Conference on Machine Learning and Cybernetics (IEEE Cat. No.03EX693).

[18]  Vassilios Petridis,et al.  Fuzzy lattice neural network (FLNN): a hybrid model for learning , 1998, IEEE Trans. Neural Networks.

[19]  Bogdan Raducanu,et al.  Morphological neural networks for vision based self-localization , 2001, Proceedings 2001 ICRA. IEEE International Conference on Robotics and Automation (Cat. No.01CH37164).

[20]  Gerhard X. Ritter,et al.  Lattice algebra approach to single-neuron computation , 2003, IEEE Trans. Neural Networks.

[21]  W. Press,et al.  Numerical Recipes Example Book (C). , 1989 .

[22]  Vassilios Petridis,et al.  Clustering and Classification in Structured Data Domains Using Fuzzy Lattice Neurocomputing (FLN) , 2001, IEEE Trans. Knowl. Data Eng..

[23]  J. Gallier,et al.  COMPUTING EXPONENTIALS OF SKEW-SYMMETRIC MATRICES AND LOGARITHMS OF ORTHOGONAL MATRICES , 2002 .