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Self-Organising Maps: The Hybrid SOM–NG Algorithm
Published in Qurban A. Memon, Distributed Networks, 2017
Mario J. Crespo, Iván Machón, Hilario López, Jose Luis Calvo
where u(v) is 0 if the two closest prototypes are neighbours and 1 otherwise. When using a rectangular lattice, the topographical error can vary depending on the definition of neighbour. The von Neumann neighbourhood defines neighbours as those units with unitary distance; for rectangular lattices, there are four units that fulfil this condition. The Moore neighbourhood defines neighbours as the units within unitary Chebyshev distance; in usual Euclidean distance, it means those with a distance lesser or equal to 2, so all the eight units around will be neighbours.
Reconfigurable Architecture for Image Encryption Using a Three-Layer Artificial Neural Network
Published in IETE Journal of Research, 2022
M. Devipriya, M. Sreenivasan, M. Brindha
Cellular Automata is an abstract system, dynamical and discrete in its state, space and time. It can be considered as a lattice based structure of cells with finite value of current states to define a new state using the current cells. An m-dimensional space of a cellular system is defined as Pm. The elements of the cellular system Pm are called cells. Similarly, let the set of finite states is T and the elements in the set are called states. Therefore, the m-dimensional CA with the set of states T is defined by a function α: Pm →T for every cell. The function of a set of states n is α(n) and the new states are updated in a synchronous manner using a local rule or function of neighborhood interaction [30]. The Von Neumann neighborhood is a square lattice in two dimensions and it has a center cell and four neighboring cells. Figure 1 shows the Von Neumann-based cell and its neighborhood. Equation (4) shows the new state value using the current state and its neighbors. when it is the corner cell or the cell at the edges, then the number of neighborhood cells is lesser than eight.
Comparative Evaluation of the Fast Marching Method and the Fast Evacuation Method for Heterogeneous Media
Published in Applied Artificial Intelligence, 2021
The main component of a CA (Galán 2020; Hassan and Tazaki 2010; Ioannidis, Sirakoulis, and Andreadis 2011; Toffoli and Margolus 1987; von Neumann 1966; Wolfram 2002) is a regular grid of cells, denoted as , where each cell adopts one of the set of states. Three characteristics of CA are that they consist of many identical simple processing cells, interactions between cells take place in a small neighborhood compared to the grid size, and discrete time is used. In a two-dimensional square grid, the von Neumann neighborhood is formed by a cell and its vertical and horizontal neighbors, whereas the Moore neighborhood incorporates the diagonal neighbors.
Modelling flooding due to runoff from spoil heaps during heavy rainfall
Published in Mining Technology, 2022
Michael D. Bedford, Patrick J. Foster, Michael J. Gibson, Albert S. Chen
The so-called von Neumann neighbourhood is used, which means that the four cells directly north, south, west and east of a cell are considered its neighbours. In Figure 1, the cell being considered is marked with an asterisk, while the four neighbouring cells are marked with N, S, W and E. The other cells are not considered neighbours, so they are greyed out.