Combinatorial machine learning approaches for high-rise building cost prediction and their interpretability analysis

Figures & data

Table 1. High-rise building engineering cost data description.

Number	Feature	Definition	Measurement
x1	Estimated project duration	Time expected to complete the construction project from start to finish.	day
x2	Building Form	The external shape and structure of a building	/
x3	Above-ground floor area	Total area of all floors above the ground level	m^2
x4	Below-ground floor area	Total area of all floors below the ground level	m^2
x5	Structural type	Classification based on the building’s structural system and materials	/
x6	Above-ground floors	Number of floors located above the ground level	layer
x7	Below-ground floors	Number of floors located below the ground level	layer
x8	Average above-ground floor height	Average height from floor to ceiling of floors above ground	m
x9	Average below-ground floor height	Average height from floor to ceiling of floors below ground	m
x10	Civil defense	Features designed to protect occupants in emergencies or disasters	/
x11	Foundation type	The type of foundation the building is constructed on	/
x12	Exterior facade decoration	Decorative elements and materials on the building’s outer surfaces.	/
x13	Interior decoration	Design and furnishing of the building’s interior spaces	/
y	Unit construction cost	Cost of constructing a unit area of the building	¥/m^2

Table 2. Correlation matrix.

	x1	x2	x3	x4	x5	x6	x7	x8	x9	x10	x11	x12	x13
x1	1.00	0.08	0.21	0.06	0.07	0.30	0.11	0.01	0.11	0.06	0.06	0.18	0.02
x2	0.08	1.00	0.08	0.18	0.20	0.09	0.16	0.10	0.06	0.04	0.15	0.19	0.14
x3	0.21	0.08	1.00	0.38	0.03	0.54	0.11	0.00	0.17	0.14	0.05	0.06	0.02
x4	0.06	0.18	0.38	1.00	0.01	0.03	0.34	0.02	0.02	0.22	0.10	0.07	0.07
x5	0.07	0.20	0.03	0.01	1.00	0.02	0.11	0.18	0.17	0.01	0.04	0.02	0.03
x6	0.30	0.09	0.54	0.03	0.02	1.00	0.01	0.20	0.09	0.05	0.08	0.07	0.05
x7	0.11	0.16	0.11	0.34	0.11	0.01	1.00	0.10	0.16	0.06	0.06	0.09	0.09
x8	0.01	0.10	0.00	0.02	0.18	0.20	0.10	1.00	0.09	0.01	0.32	0.16	0.06
x9	0.11	0.06	0.17	0.02	0.17	0.09	0.16	0.09	1.00	0.05	0.06	0.02	0.04
x10	0.06	0.04	0.14	0.22	0.01	0.05	0.06	0.01	0.05	1.00	0.03	0.12	0.12
x11	0.06	0.15	0.05	0.10	0.04	0.08	0.06	0.32	0.06	0.03	1.00	0.01	0.08
x12	0.18	0.19	0.06	0.07	0.02	0.07	0.09	0.16	0.02	0.12	0.01	1.00	0.17
x13	0.02	0.14	0.02	0.07	0.03	0.05	0.09	0.06	0.04	0.12	0.08	0.17	1.00

Table 3. Explains the total variance.

Component	Initial Eigenvalues			The sum of Squared Loadings
	Total	Percentage of Variance	Cumulative %	Total	Percentage of Variance	Cumulative %
1	1.869	14.375	14.375	1.869	14.375	14.375
2	1.739	13.376	27.751	1.739	13.376	27.751
3	1.563	12.020	39.771	1.563	12.020	39.771
4	1.335	10.271	50.042	1.335	10.271	50.042
5	1.146	8.816	58.858	1.146	8.816	58.858
6	0.983	7.565	66.423	0.983	7.565	66.423
7	0.925	7.118	73.541	0.925	7.118	73.541
8	0.844	6.493	80.034	0.844	6.493	80.034
9	0.645	4.961	85.995	0.645	4.961	84.995
10	0.610	4.695	89.690
11	0.584	4.495	94.185
12	0.543	4.174	98.359
13	0.213	1.641	100.000

Figure 1. Prediction results of a single algorithm.

Table 4. Prediction performance of a single algorithm.

Algorithm	Training set MAE	Training set MSE	Test set MAE	Test set MSE
DT	42.5918	64.3188	76.4946	115.7478
BP	56.1981	77.334	53.0219	73.3111
SVM	37.6691	53.5418	63.4495	92.3683

Figure 2. Combined algorithm prediction results.

Table 5. Prediction results of the combination algorithm.

Algorithm	Training set MAE	Training set MSE	Test set MAE	Test set MSE
BP-DT	22.8516	39.9622	18.9013	32.2187
BP-SVM	9.2607	16.3149	13.1789	23.7317

Figure 3. Performance comparison of different prediction models.

Figure 4. Sorting diagram of SHAP values.

Figure 5. PDP and ICE charts for all features.

Figure 6. Interactive influence diagram of features.

Data availability statement

Data will be made available on request.