Cellular automata (CA) with given evolution rules have been widely investigated, but the inverse problem of extracting CA rules from observed data is less studied. Current CA rule extraction approaches are both time consuming and inefficient when selecting neighborhoods. We give a novel approach to identifying CA rules from observed data and selecting CA neighborhoods based on the identified CA model. Our identification algorithm uses a model linear in its parameters and gives a unified framework for representing the identification problem for both deterministic and probabilistic CA. Parameters are estimated based on a minimum variance criterion. An incremental procedure is applied during CA identification to select an initial coarse neighborhood. Redundant cells in the neighborhood are then removed based on parameter estimates, and the neighborhood size is determined using the Bayesian information criterion. Experimental results show the effectiveness of our algorithm and that it outperforms other leading CA identification algorithms.
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"Most of the developed algorithms for neighborhood detection of CA adopt the coarse-to-fine approach, which detects an initial neighborhood first and then refines it by choosing significant neighbors  or removing redundant neighbors  from the initial neighborhood . Sun et al.  developed an approach to determine the initial neighborhood, which calculates the variance estimation by varying the neighborhood size, until the variance is smaller than criterion σ "
[Show abstract][Hide abstract] ABSTRACT: An important step in the identification of cellular automata (CA) is to detect the correct neighborhood before parameter estimation. Many authors have suggested procedures based on the removal of redundant neighbors from a very large initial neighborhood one by one to find the real model, but this often induces ill conditioning and overfitting. This is true particularly for a large initial neighborhood where there are few significant terms, and this will be demonstrated by an example in this paper. By introducing a new criteria and three new techniques, this paper proposes a new adaptive fast CA orthogonal-least-square (Adaptive-FCA-OLS) algorithm, which cannot only adaptively search for the correct neighborhood without any preset tolerance but can also considerably reduce the computational complexity and memory usage. Several numerical examples demonstrate that the Adaptive-FCA-OLS algorithm has better robustness to noise and to the size of the initial neighborhood than other recently developed neighborhood detection methods in the identification of binary CA.
IEEE transactions on systems, man, and cybernetics. Part B, Cybernetics: a publication of the IEEE Systems, Man, and Cybernetics Society 06/2012; 42(4). DOI:10.1109/TSMCB.2012.2185790 · 6.22 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: According to the maximum likelihood principle, a maximum likelihood least squares identification method is presented for input nonlinear finite impulse response moving average (IN-FIR-MA) systems (e.g., Hammerstein FIR-MA systems). The simulation results indicate that the proposed algorithm is effective.
[Show abstract][Hide abstract] ABSTRACT: When farmland is abandoned pasture is rapidly taken over by woody vegetation. As tree dispersal depends on the presence of a seed source nearby and other local conditions, and can be measured in discrete annual time steps, a Cellular Automata model (CA) is a natural fit for modelling this phenomenon. The model presented here is a stochastic CA, with a relaxed definition of neighbourhood. The aim is to explore sources of uncertainty in the model, and techniques for handling and visualising uncertainty. The results show that it is possible to realistically model vegetation change using CA, acknowledging and incorporating uncertainty.
Proceedings of the SIRCNZ conference, Dunedin, New Zealand; 08/2013