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

Fatemeh Mostofi
Fatemeh Mostofi
, 
Vedat Toğan
Vedat Toğan
 und 
Hasan Basri Başağa
Hasan Basri Başağa
   | 31. Dez. 2022
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Article Category: Research Paper
Online veröffentlicht: 31. Dez. 2022
Seitenbereich: 2741 - 2759
Eingereicht: 18. Apr. 2022
Akzeptiert: 10. Nov. 2022
DOI: https://doi.org/10.2478/otmcj-2022-0016
Schlüsselwörter
© 2022 Fatemeh Mostofi et al., published by Sciendo
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Fig. 1

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

Fig. 2

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

Fig. 3

Data pre-processing stage.
Data pre-processing stage.

Fig. 4

Outline of DNN procedure. DNN, deep neural networks.
Outline of DNN procedure. DNN, deep neural networks.

Fig. 5

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

Fig. 6

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

Fig. 7

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 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.

Fig. 8

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.
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.

Fig. 9

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.
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.

Fig. 10

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.
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.

Fig. 11

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.
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.

Fig. 12

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.
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.

Fig. 13

Feature correlation with price (a). Feature influence on price unit (b). PC, project characteristic.
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
2 Without balcony 62
PC9 Furniture 0.97 0.18 1 Furnished 42
2 Not furnished 1,202
PC10 Amenities 0.68 0.46 1 Amenities included 394
2 Amenities not included 850
PC11 Credit availability 0.10 0.30 1 Available 1,118
2 Unavailable 126
PC12 Video call 0.53 0.50 1 Available 589
2 Unavailable 655
PC13 Swap option 0.84 0.37 2 Ready for swap 200
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.
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