Tutorial: Mean Center, Median Center and Central Feature(Plug-in Method)

Q: Find the Median Center and Central Feature of Starbucks Stores in Gangnam, Seoul.

Before you begin this tutorial, do the following first:

• Install the Spatial Analyzer Plugin
• Start Spatial Analyzer
• Add Starbucks Layer
• Add a Basemap

Finding the Median Center and Central Feature

[1] At the top of the screen, click the Processing menu, then click Toolbox. The Processing Toolbox panel will appear on the right side of the window.

[2] In the Processing Toolbox, expand SpatialAnalyzer at the bottom. Under Spatial Central Tendency, double-click Centers (Mean Center, Median Center, Central Feature)

[3] In the Spatial Central Tendency window, ensure Median Center and Central Feature are checked, then click Run. (By default, Mean Center, Median Center, and Central Feature are selected.)

Weight Field lets you compute weighted centers using an attribute instead of pure distance. Examples include seating capacity, sales revenue, or number of employees. If you choose “sales revenue,” the resulting mean or median center will shift toward higher-revenue areas.

Group Field computes centers separately for each category when your data is classified. For example, if there is an administrative-district attribute, selecting that field will calculate centers per district. This method is discussed further in cluster analysis.

Result

Three point layers representing the Mean Center, Median Center, and Central Feature are created.

Theory: Central Feature

The Central Feature in spatial analysis refers to the single object among all points that has the shortest total distance to all other points. In other words, it identifies the actual point considered the most central among the dataset. For example, suppose Starbucks branch managers in Seoul need to gather at one store for a meeting. The store that minimizes the total travel distance for all managers becomes the central feature.

The central feature is similar to the median center, but while the median center selects an arbitrary point in the analysis space, the central feature selects one of the actual data points. Therefore, identifying the central feature is generally easier than calculating a median center.

The central feature is defined as the actual point \( P_j \) that satisfies the following condition:

$$ P_j = \arg\min_{P_k \in \{P_1, P_2, \ldots, P_n\}} \sum_{i=1}^{n} d(P_k, P_i) $$

• \( d(P_k, P_i) \) : the distance from point \( P_k \) to each other point \( P_i \)
• \( P_j \): the point with the shortest total distance to all other points, i.e., the central feature

Unlike the mean center or median center, which are calculated center points, the central feature is an actual data point within the dataset. Typically, the Euclidean distance is used, but it can also be extended to network distance or weighted distance depending on the analysis context.

Application Examples

• Identifying the most representative location among crime incidents (the core scene)
• Finding the actual store located closest to the customer distribution center
• Determining the accident site that is, on average, the nearest to all other traffic accident locations
• Extracting the most centrally located public institution within a city