The urban sprawl dynamics: does a neural network understand the spatial logic better than a cellular automata?

The used NN are listed in table 1.

_______________________Set 1_______________________			_____________________Set 2_____________________
Topology	Order	Learning Law	Topology	Order	Learning Law
FF		Bm	FF		Bm
FF		Bp	FF		Bp
FF		_____Sn_____
Self	DA	Bp	Self ~	DA	Bp
			Self	DA	Bm
			Self	SA	Bm
			Self	SA	Bp
Tasm	DA	Bm	Tasm	DA	Bm
Tasm	DA	Bp	Tasm	DA	Bp
Tasm	SA	Bm	Tasm	SA	Bm
Tasm	SA	Bp	Tasm	SA	Bp
Tasm	SA	Cm
Tasm	SA	_____Sn_____
Learning Law: Bp = Back Propagation (standard) Sn = Sine Net (Semeion) Bm = Bi-Modal Network (Semeion) Cm = Contractive Map (Semeion) Topology: FF = Feed Forward (standard) Self = Self Recurrent Network (Semeion) Tasm = Temporal Associative Subjective Memory (Semeion) Order: DA = Dynamic and Adaptive Recurrency (Semeion) _____________________________SA = Static and Adaptive Recurrency (Semeion____________________

Table 1 - The different architectures of SANN

7. Learning and validation of the SANNs

The Statistical functions used to evaluate the results are presented in Annexe 2. Each
function measures, separately, the error of each output vector component of SANNs
related to the correspondent Target value given in Input.

The first evaluation of the results is given by the statistical functions in table 2.

	Residential	Industrial	Commercial	Average
RMSE	0.06756	0.05543	0.03290	0.09338
Real Error	-0.00262	-0.00938	-0.00550	-0.00583
Relative Error	0.05983	0.04911	0.01867	0.04254
Error Variance	0.11412	0.09735	0.05214	0.08787
NMSE	0.15737	0.22162	0.38873	0.25591
Squared R	0.84310	0.78374	0.62216	0.74967
Linear Corr.	0.91820	0.88529	0.78877	0.86409

Table 2 - Statistical measures of validation

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