A New Auto-associative Memory Based on Lattice Algebra

This paper presents a novel, three-stage, auto-associative memory based on lattice algebra. The first two stages of this memory consist of correlation matrix memories within the lattice domain. The third and final stage is a two-layer feed-forward network based on dendritic computing. The output nodes of this feed-forward network yield the desired pattern vector association. The computations performed by each stage are all lattice based and, thus, provide for fast computation and avoidance of convergence problems. Additionally, the proposed model is extremely robust in the presence of noise. Bounds of allowable noise that guarantees perfect output are also discussed.

[1]  W. J. Nowack.  Methods in Neuronal Modeling , 1991, Neurology.

[2]  Alberto Sanfeliu,et al.  Progress in Pattern Recognition, Speech and Image Analysis , 2003, Lecture Notes in Computer Science.

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

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

[5]  Peter Sussner,et al.  Morphological associative memories , 1998, IEEE Trans. Neural Networks.

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

[7]  Joel L. Davis,et al.  Single neuron computation , 1992 .

[8]  Peter Sussner,et al.  Morphological bidirectional associative memories , 1999, Neural Networks.

[9]  Gerhard X. Ritter,et al.  Morphological perceptrons , 1999, IJCNN'99. International Joint Conference on Neural Networks. Proceedings (Cat. No.99CH36339).

[10]  Gerhard X. Ritter,et al.  Kernel Computation in Morphological Bidirectional Associative Memories , 2003, CIARP.

[11]  Bartlett W. Mel.  Synaptic integration in an excitable dendritic tree. , 1993, Journal of neurophysiology.

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

[13]  Gerhard X. Ritter,et al.  Neurons, Dendrites, and Pattern Classification , 2003, CIARP.

[14]  Michael A. Arbib,et al.  The handbook of brain theory and neural networks , 1995, A Bradford book.

[15]  Peter Sussner,et al.  Observations on morphological associative memories and the kernel method , 2000, Neurocomputing.

[16]  Gerhard X. Ritter,et al.  Reconstruction of Patterns from Noisy Inputs Using Morphological Associative Memories , 2003, Journal of Mathematical Imaging and Vision.