Cluster analysis of Chinese city-level data

We need to create a natural clustering of cities in China based on their geographic location (their distance from one another) and an importance factor we assign to each city. This will help us group cities with largest importance and nearest to each other as a larger geographical cluster. We do not wish to do the clustering based on what prefecture or province the cities belong to, as this will not allow us to create an efficient segmentation, as we may have cities within the borders of several prefectures that form a more important cluster when grouped together than if we simply group them into their respective prefectures. We will provide the following data in excel format: -> City name (Approximately 2.6k cities) -> Province name (of the city) -> Latitude (to determine geographical location) -> Longitude (to determine geographical location) -> Importance factor (nominal value to determine importance factor of a city) Deliverables 1. Core Analysis: The deliverable will require the natural clustering of cities as well as a descriptive methodology (algorithm) that was used to cluster the cities. A. We may require doing several iterations of the clustering, as we may adjust the values for the importance factors B. We would like to see several options for the number of natural geographical clusters depending on the output of the analysis; the main focus being: i. Mega-clusters, identifying 5-10 major clusters for highest importance areas (i.e. Beijing and Shanghai centered mega-clusters) C. Clusters mapped in Tableau 2. Excel spreadsheet: All the data we sent plus a new column indicating which clustering group the city belongs to. 3. Heat Map: Create a heat map of China with the natural clusters (darkness of color based on importance factor of natural cluster (the natural cluster is the sum of the importance factor of each individual city). A. We prefer that the mapping be done in Tableau so we can make adjustments ourselves, if this is not possible, we will need you to perform the adjustments as we move along. 1. The map must have a good quality to include it in a power point presentation 2. We may need to modify the color scheme of the heat map 3. We will need to label the location of certain key cities in China (a few key cities) 4. We should be able to see the geographical limits (borders) between the natural cluster