Split quaternion-valued twin-multistate Hopfield neural networks. (English) Zbl 1439.82035
Complex-valued Hopfield neural networks with a multistate activation function can be designed to process multi-level data for different kind of applications. In the present article the author concentrates on a special architecture, the so-called split quaternion-valued Hopfield neural networks with a T-multistate activation function which is understood as a pair of complex-valued multistate activation functions. The goal is to evaluate the performance of the network by means of simulations. There is a discussion on the obtained results.
Reviewer: Claudia Simionescu-Badea (Wien)
MSC:
| 82C32 | Neural nets applied to problems in time-dependent statistical mechanics |
| 68T05 | Learning and adaptive systems in artificial intelligence |
Keywords:
quaternion-valued Hopfield neural network; split quaternion; commutative quaternion; multistate neuronSoftware:
CIFARReferences:
| [1] | Antonuccio, F., Split-quaternions and the Dirac equation, Adv. Appl. Clifford Algebras, 25, 1, 13-29 (2015) · Zbl 1325.35184 · doi:10.1007/s00006-014-0475-z |
| [2] | Arena, P.; Fortuna, L.; Muscato, G.; Xibilia, MG, Multilayer perceptrons to approximate quaternion valued functions, Neural Netw., 10, 2, 335-342 (1997) · doi:10.1016/S0893-6080(96)00048-2 |
| [3] | Catoni, F.; Cannata, R.; Catoni, V.; Zampetti, P., N-dimensional geometries generated by hypercomplex numbers, Adv. Appl. Clifford Algebras, 15, 1, 1-25 (2005) · Zbl 1114.53003 · doi:10.1007/s00006-005-0001-4 |
| [4] | Ghadami, F.; Rahebi, J.; Yayli, Y., Spline split quaternion interpolation in Minkowski space, Adv. Appl. Clifford Algebras, 23, 4, 849-862 (2013) · Zbl 1287.53015 · doi:10.1007/s00006-013-0410-8 |
| [5] | Hitzer, E.; Nitta, T.; Kuroe, Y., Applications of Clifford’s geometric algebra, Adv. Appl. Clifford Algebras, 23, 2, 377-404 (2013) · Zbl 1269.15022 · doi:10.1007/s00006-013-0378-4 |
| [6] | Isokawa, T., Nishimura, H., Matsui, N.: Commutative quaternion and multistate Hopfield neural networks. Proceedings of IEEE World Congress on Computational Intelligence 1281-1286 (2010). 10.1109/IJCNN.2010.5596736 |
| [7] | Isokawa, T., Nishimura, H., Saitoh, A., Kamiura, N., Matsui, N.: On the scheme of quaternionic multistate Hopfield neural network. Proceedings of Joint 4th International Conference on Soft Computing and Intelligent Systems and 9th International Symposium on advanced Intelligent Systems 5, 809-813 (2008). 10.14864/softscis.2008.0.809.0 |
| [8] | Isokawa, T.; Nishimura, H.; Kamiura, N.; Matsui, N., Associative memory in quaternionic Hopfield neural network, Int. J. Neural Syst., 18, 2, 135-145 (2008) · doi:10.1142/S0129065708001440 |
| [9] | Kim, H.; Hirose, A., Unsupervised fine land classification using quaternion autoencoder-based polarization feature extraction and self-organizing mapping, IEEE Trans. Geosci. Remote Sens., 56, 3, 1839-1851 (2017) · doi:10.1109/TGRS.2017.2768619 |
| [10] | Kobayashi, M., Symmetric quaternionic Hopfield neural networks, Neurocomputing, 240, 110-114 (2017) · doi:10.1016/j.neucom.2017.02.044 |
| [11] | Kobayashi, M., Three-dimensional quaternionic Hopfield neural networks, IEICE Trans. Fundam. Electron. Commun. Comput. Sci., E100-A, 7, 1575-1577 (2017) · doi:10.1587/transfun.E100.A.1575 |
| [12] | Kobayashi, M., Quaternionic Hopfield neural networks with twin-multistate activation function, Neurocomputing, 267, 304-310 (2017) · doi:10.1016/j.neucom.2017.06.013 |
| [13] | Kobayashi, M., Twin-multistate commutative quaternion Hopfield neural networks, Neurocomputing, 320, 150-156 (2018) · doi:10.1016/j.neucom.2018.09.023 |
| [14] | Kobayashi, M., Hyperbolic Hopfield neural networks with directional multistate activation function, Neurocomputing, 275, 2217-2226 (2018) · doi:10.1016/j.neucom.2017.10.053 |
| [15] | Kobayashi, M., Noise robust projection rule for hyperbolic Hopfield neural networks, IEEE Trans. Neural Netw. Learn. Syst., 31, 1, 352-356 (2020) · doi:10.1109/TNNLS.2019.2899914 |
| [16] | Krizhevsky, A.: Learning multiple layers of features from tiny images. Technical report. University of Toronto (2009) |
| [17] | Minemoto, T., Isokawa, T., Kobayashi, M., Nishimura, H., Matsui, N.: Pattern retrieval by quaternionic associative memory with dual connections. International Conference on Neural Information Processing 317-325 (2016). 10.1007/978-3-319-46675-0_35 |
| [18] | Minemoto, T.; Isokawa, T.; Nishimura, H.; Matsui, N., Quaternionic multistate Hopfield neural network with extended projection rule, Artif. Life Robot., 21, 1, 106-111 (2016) · doi:10.1007/s10015-015-0247-4 |
| [19] | Muezzinoglu, MK; Guzelis, C.; Zurada, JM, A new design method for the complex-valued multistate Hopfield associative memory, IEEE Trans. Neural Netw., 14, 4, 891-899 (2003) · doi:10.1109/TNN.2003.813844 |
| [20] | Parcollet, T., Morchid, M., Linares, G.: Deep quaternion neural networks for spoken language understanding. IEEE Automatic Speech Recognition and Understanding Workshop. 504-511 (2017). 10.1109/ASRU.2017.8268978 |
| [21] | Valle, M.E.: A novel continuous-valued quaternionic Hopfield neural network. Proceedings of Brazilian Conference on Intelligent Systems 97-102 (2014). 10.1109/BRACIS.2014.28 |
| [22] | Zhu, X., Xu, Y., Xu, H., Chen, C.: Quaternion convolutional neural networks. Proceedings of the European Conference on Computer Vision. 631-647 (2018). 10.1007/978-3-030-01237-3_39 |
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