While the Mean Center itself represents a meaningful value indicating the central location of spatial data, it is also highly useful for analyzing dynamic changes over time. The figure below shows the mean center of the U.S. population every 10 years from 1790 to 2010. The small map in the upper-left corner is enlarged. Through this, we can observe how the socio-economic center of the United States has gradually shifted westward since independence.
This type of analysis is known as the Cumulative Mean Center, which shows how the spatial center has shifted over time. That is, it calculates the cumulative mean center up to each time point to trace the spatio-temporal trends in the center’s movement. The cumulative mean center is derived by computing the mean center of all points that have occurred up to each time stage.
Characteristics of the Cumulative Mean Center
- The mean center is updated each time a new time point is added.
- By connecting these values in a time series, the trajectory of movement in the central location over time can be visualized.
- It allows for the analysis of spatial trends such as directional movement or patterns of dispersion and concentration.
Application Examples
- Crime analysis: Tracking how the center of crime incidents shifts over time
- Urban expansion analysis: Visualizing how the center of development or population moves due to new town development or migration
- Logistics and mobility analysis: Monitoring delivery or vehicle movement centers across time
The cumulative mean center is a tool used to analyze the movement of spatial centers by chronologically accumulating spatial data, serving as a foundation for time-series spatial analysis. The results are typically visualized in the form of a linear trajectory, allowing a comprehensive understanding of change trends, directionality, and speed of the center.