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Modern Geomatics Technologies and Applications

• In this method, only the values of the pixels that have been changed are examined. It makes sense that fixed samples
will change almost definitively, but samples that have changed will mostly affect their neighbor pixels, which only
happens in experimental modelling methods.

Fig 4. Variable space created by two hypothetical variables [20]

In this figure, the small triangles represent the variable pixels, the rhombuses represent the fixed pixels, and the black
square represents the pixels which their position will be assessed under the influence of the sub-potential and unknown potential.
The circle shown as a dotted line in the figure represents the range k, which is assumed to be 6 pixels within the circle for the
change state and 3 pixels for the steady state. Also, the lines shown are the linear distances of the pixels considered in the variable
space[8].
Like the k-nearest neighbor method, the learning process based on the similarity weight sample is influenced by
inappropriate variables. In this method, the independent variables have different significance in determining the transfer.
The importance of this difference is due to weighting, which means that variable values are multiplied by a distributive
or relative weight and the variable ability between different land use layers is determined for the intended transfer. In this method,
the weight of the variable significance is calculated from the ratio between the standard deviation of the variable pixels in the
area where the particular class changes or the specific transfer to the variable deviation of the variable pixels in relation to the
total changes in the region as follows[9].

ℎ = 1 − ( ) (2)

where P Indicates the standard deviation of the variable pixels in the change area, and Q is the standard deviation of the variable
pixels in relation to the total changes occurred in the region. If a variable has a stronger relationship with the change in the study
area, the standard deviation of the variable pixels in the change area will be smaller than the standard deviation from the total
change and in this case, the weight will have a higher relationship, which indicates the importance of the variable in the change
that occurred.

4.2. Cellular automaton

Modelling based on the automatic cell method is often appropriate for the spatial and temporal distribution of phenomena,
so the use of this model in the study of spatial and temporal changes such as distribution and spatial expansion of a user is
appropriate in urban studies[10][11] . An automatic cell is a model that generalizes local small-scale processes to large-scale
patterns. In this method, which further examines the patterns of spatial distribution dynamics, the desired space is divided into
networks and the relationship between network houses is expressed with specific rules, which are usually the same throughout
the network[12][13] .
In general, each automatic cell model includes a network consisting of a non-empty and finite set of modes, separate cells,
and a general update rule, which calculates the state of each cell at moment t + 1 based on the state of that cell and its neighbouring
cells at time t. Each cell in the network can have two or more modes, so an automatic cell model can be multi-continuous or
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