The technical solution used for the study consisted of two main components:
1. The k-means cluster algorithm and the improved entropy weight method to develop the flood risk map.
2. The Traditional cluster algorithm and TOPSIS method were compared to the improved entropy-cluster algorithm, in order to verify the proposed approach as applied to flood risk management.

Unsupervised Clustering:

Step 1: Selection of the indices: 

• Digital elevation model (DEM)
• Slope (SL)
• Distance to the river (DR)
• Length of drainage conduits (LDC)
• Building area (BA)
• Maximum Inundation Depth (MD) and Maximum Inundation Velocity (MVE).

Step 2: Quantification of the indices. The seven indices are transformed into grid layers by using the raster calculation in GIS. A PCSWMM software (software which is advanced modelling software for EPA SWMM 5 stormwater, wastewater and watershed systems) is used to obtain the MD and MVE value.

Step 3: Calculation of the weights for the indices. AHP and entropy weight method is presented to determine the index weights. The AHP method was applied to determine the weights comprehensively by considering the subject's attributes of the data. The index weight was calculated by improved entropy weight method that integrates the AHP and entropy weight method.

Step 4: Determining optimal cluster numbers.Using the silhouette function (Rosseeuw, 1987; Nakamura et al., 2008; Gaitani et al., 2010), the optimal number of clusters was determined in advance. Cluster analysis was sequentially performed beginning with two clusters and ending with eight clusters. Determining that the cluster number K=5, exhibits the maximum mean and the minimal number of negative values. Therefore, the optimal number of five clusters was used in the study.

Step 5: k-means cluster analysis. The number of flood risk level is defined based on the cluster numbers. The flood risk level of each cluster is determined by the average values of indices of each cluster.

• Randomly initialized the cluster centre c.
• The Euclidean Distance was calculated.
• Each point was moved to its nearest cluster centre.
• Update the centres of clusters
• Computed the objective function

Step6: Determining flood risk levels. The number of flood risk level is defined based on the cluster numbers. Also, the spatial distribution map of flood risk was generated.

Traditional cluster algorithm and TOPSIS method were compared to the improved entropy-cluster algorithm by using the deviation degree Dj.

• Dataset 1: Digital elevation model (DEM, m), from Institute of Geographic Sciences and Natural Resources Research, Chinese Academy of Sciences (http://www.resdc.cn/Default.aspx), no date.
• Dataset 2: River data and drainage data, from Haikou Municipal Water Authority, no date.
• Dataset 3: Rainfall data:, from China Meteorological Administration Meteorological Data Center (http://data.cma.cn/data/cdcdetail/dataCode/A.0012.0001.html), no date.
• Dataset 4: Observations of historical storm events, field investigation during “Rammasun” typhoon, July 2014.
• Dataset 5: Slope (SL, °), from DEM by Geographic Information System (GIS).
• Dataset 6: Distance to the river (DR, m), Euclidean distance in the Geographic Information System (GIS).
• Dataset 7: Length of drainage conduits (LDC, m), from drainage data by Geographic Information System (GIS).
• Dataset 8: Building area (BA, m2): from satellite remote sensing image by Haikou Municipal Water Authority.
• Dataset 9: Maximum inundation depth (MD, m) and maximum inundation velocity (MVE, m/s), from the stormwater management model (PCSWMM).

• The flood risk map generated shows that the high-risk areas cover 13.7% of the total area and generally exhibit higher inundation depth and lower elevations.
• The lowest risk and lower risk areas show higher elevation, lower inundation depth, and a large distance from rivers.
• The study provided a new method for flood risk assessment based on urban flood inundation model, improved entropy weight method and k-means cluster algorithm.
• The research provided a new method for flood control and disaster reduction planning in Haidian Province and beyond.
• The traditional cluster algorithm and TOPSIS method were compared with the improved entropy-cluster algorithm. The results indicated that the proposed approach is feasible and exhibits the most reasonable classification result.

• The accuracy in classifying the flood risk was limited by the availability of data and a more comprehensive index system should be developed in a future study.
• Socio-economic factors such as population density and gross domestic product density were not considered due to data constraints. More reasonable results can be obtained when more indices are adopted and additional studies should be performed further once the solid information is available.