TY - JOUR
T1 - Stable patterns realized by a class of one-dimensional two-layer CNNs
AU - Takahashi, Norikazu
AU - Nagayoshi, Makoto
AU - Kawabata, Susumu
AU - Nishi, Tetsuo
N1 - Funding Information:
Manuscript received December 10, 2007; revised March 11, 2008. First published May 20, 2008; current version published December 12, 2008. This work was supported in part by Grant-in-Aid for Scientific Research (b) 19310099 from the Ministry of Education, Culture, Sports, Science and Technology. This paper was recommended by Associate Editor M. Di Marco.
PY - 2008
Y1 - 2008
N2 - Stable patterns that can be realized by a class of 1-D two-layer cellular neural networks (CNNs) are studied in this paper. We first introduce the notions of potentially stable pattern, potentially stable local pattern, and local pattern set. We then show that all of 256 possible sets can be realized as the local pattern set of the two-layer CNN, while only 59 sets can be realized as the local pattern set of the single-layer CNN. We also propose a simple way to optimize the template values of the CNN, which is formulated as a set of linear programming problems, and present the obtained values for all of 256 sets.
AB - Stable patterns that can be realized by a class of 1-D two-layer cellular neural networks (CNNs) are studied in this paper. We first introduce the notions of potentially stable pattern, potentially stable local pattern, and local pattern set. We then show that all of 256 possible sets can be realized as the local pattern set of the two-layer CNN, while only 59 sets can be realized as the local pattern set of the single-layer CNN. We also propose a simple way to optimize the template values of the CNN, which is formulated as a set of linear programming problems, and present the obtained values for all of 256 sets.
KW - Cellular neural networks (CNNs)
KW - Hidden layer
KW - Stable patterns
KW - Template optimization
KW - Two layers
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U2 - 10.1109/TCSI.2008.925828
DO - 10.1109/TCSI.2008.925828
M3 - Article
AN - SCOPUS:58049209271
SN - 1057-7122
VL - 55
SP - 3607
EP - 3620
JO - IEEE Transactions on Circuits and Systems I: Regular Papers
JF - IEEE Transactions on Circuits and Systems I: Regular Papers
IS - 11
ER -