Real-estate price prediction with deep neural network and principal component analysis

Mostofi, Fatemeh; Toğan, Vedat; Başağa, Hasan Basri

doi:10.2478/otmcj-2022-0016

Figures & Tables

The methodology followed in this study. DNN, deep neural networks; PCA, principal component analysis; SRA, stepwise regression analysis.

Frequency of (a) No. of stories, (b) No. of floors and (c) neighbourhood.

Outline of DNN procedure. DNN, deep neural networks.

PCA-DNN model. DNN, deep neural networks; PCA-DNN, principal component analysis-deep neural networks; PCA, principal component analysis.

Structure of (a) DNN and (b) SRA-DNN models. DNN, deep neural networks; SRA-DNN, stepwise regression analysis-deep neural networks.

Training and validation of MSE for the different number of neurons, in supervised learning scenarios of DNN, SRA-DNN and PCA-DNN models. DNN, deep neural networks; MSE, mean square error; PCA-DNN, principal component analysis-deep neural networks; SRA-DNN, stepwise regression analysis-deep neural networks.

Training and validation of MSE for the different number of layers, in supervised learning scenarios of DNN, SRA-DNN and PCA-DNN models. DNN, deep neural networks; MSE, mean square error; PCA-DNN, principal component analysis-deep neural networks; SRA-DNN, stepwise regression analysis-deep neural networks.

Unsupervised (a) and supervised (b) training and validation of MSE values for best performing DNN, SRA-DNN and PCA-DNN models. DNN, deep neural networks; MSE, mean square error; PCA-DNN, principal component analysis-deep neural networks; SRA-DNN, stepwise regression analysis-deep neural networks.

Contribution of number of principal components in error obtained in PCA-DNN model. MSE, mean square error; PCA-DNN, principal component analysis-deep neural networks.

Learning pattern for unsupervised learning and supervised learning (a) and training and validation accuracy (b) for DNN, SRA-DNN and PCA-DNN models. DNN, deep neural networks; PCA-DNN, principal component analysis-deep neural networks; SRA-DNN, stepwise regression analysis-deep neural networks.

Total variance preserved by principal components (a). MSE values were obtained for selected principal components (b). Detailed influence of first three principal components (c). Influence of all principal components (d). MSE, mean square error; PCs, project characteristics.

Feature correlation with price (a). Feature influence on price unit (b). PC, project characteristic.

The optimum network architecture of the three selected models_

Factors	DNN Model	SRA-DNN Model	PCA-DNN Model
Number of neurons	30	20	30
Number of neurons (output layer)	20	20	20
Number of layers	5	5	5
Total trainable parameters	2,061	1,921	2,041
Activation function (output layer)	Linear	Linear	Linear
Activation function	relu	relu	relu
Optimisation function	Adam	Adam	Adam
Loss function	mse	mse	mse
Number of features	17	10	15

Performance of selected optimum DNN, SRA-DNN and PCA-DNN models_

Model	Wall times	CPU time	Epoch	MAE	MAPE	MSE
DNN	3.02 s	3.32 s	20	0.43	27%	0.42
SRA-DNN	6.06 s	7.05 s	30	0.42	22%	0.39
PCA-DNN	6.27 s	7.27 s	160	0.23	14%	0.10

PC attributes – numerical and categorical labels and frequencies_

Identifier	Feature name	Mean	Standard deviation	Feature type	Feature attributes	Frequency of attribute
PC1	Area	313.88	105.94	Numerical	(89, 286]	497
					(286, 482]	664
					(482, 678]	74
					(678, 874]	7
					(874, 1070]	2
PC2	Room	3.08	0.86	Numerical	1 bedroom	45
					2 bedrooms	168
					3 bedrooms	776
					4 bedrooms	166
					5 bedrooms	79
					6 bedrooms	9
					7 bedrooms	1
PC3	Saloon	1.04	0.20	Numerical	0 saloon	3
					1 saloon	1,191
					2 saloons	50
PC4	Building age	11.14	11.95	Numerical	0–4 years	595
					5–10 years	218
					11–15 years	163
					16–20 years	135
					21–25 years	71
					26–30 years	38
					≥31 years	24
PC5	No. of stories	7.27	2.66	Numerical	1–15 stories	Illustrated in Figure 2a.
PC6	Floor No.	3.90	3.05	Numerical	–1 to 15 floor	Illustrated in Figure 2b.
PC7	No. of bathrooms	1.61	0.59	Numerical	1 bathroom	549
					2 bathrooms	635
					3 bathrooms	54
					4 bathrooms	6
PC8	Balconies	0.05	0.22	1	With balcony	1,182
PC8	Balconies	0.05	0.22	2	Without balcony	62
PC9	Furniture	0.97	0.18	1	Furnished	42
PC9	Furniture	0.97	0.18	2	Not furnished	1,202
PC10	Amenities	0.68	0.46	1	Amenities included	394
PC10	Amenities	0.68	0.46	2	Amenities not included	850
PC11	Credit availability	0.10	0.30	1	Available	1,118
PC11	Credit availability	0.10	0.30	2	Unavailable	126
PC12	Video call	0.53	0.50	1	Available	589
PC12	Video call	0.53	0.50	2	Unavailable	655
PC13	Swap option	0.84	0.37	2	Ready for swap	200
PC13	Swap option	0.84	0.37		No swap	1,044
PC14	Heating system	0.78	1.66	1	Natural gas	1,006
				2	Central	173
				3	gas stove	6
				4	Air conditioning	6
				5	Stove	29
				6	Underfloor heating	17
				7	Fireplace	7
PC15	Occupancy condition	0.54	0.80	1	Unoccupied	812
				2	Occupied by owner	243
				3	Under rent	189
PC16	Selling agency	0.18	0.46	1	Real-estate agent	1,052
				2	Construction company	36
				3	Private owners	156
PC17	Neighbourhood			42	1–42 districts	Illustrated in Figure 2c.

Real-estate price prediction with deep neural network and principal component analysis

Figures & Tables

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The optimum network architecture of the three selected models_

Performance of selected optimum DNN, SRA-DNN and PCA-DNN models_

PC attributes – numerical and categorical labels and frequencies_

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