# Cities around the world

(download Grapheur sample file)

### Data:

Each row contains the data of an important city, with the following columns:**Name:**Name of the city.**Poulation:**the number of inhabitans**Extension (km^2):**the extension in square kilometers**Latitude, Longitude:**geographical coordinates of each city.**X coordinate, Y coordinate, Z coordinate (1000 km):**cartesian coordinates of each city in a 3D Cartesian representation of the world.**Dissimilarity:**the matrix of distances between the cities.

### Objectives of data mining and visualization:

- Visualizing geographical data on the globe surface (3D).
- Adding more information by using color and size of the blobs (by using Grapheur 7D plot)
- Testing the capability of the Similarity Map to preserve distances among records. After starting from a matrix of distancies between the various cities one maps them to a two- or three-dimensional space while aiming at preserving the mutual distances as much as possible. Let's note that coordinates are assumed to be unknown in this experiment: one starts only from relationships (mutual distances).

### Grapheur sample visualization: Similarity Map

In the figure, a 3D plot of the network given by the 31 cities.The color code represents the population of the metropolitan area.

The size of the bubble is proportional to the extension of each city.

The gray level of the connection is higher for closer cities.

### Grapheur sample visualization: 7D plot

Let us compare the previous visualization with the plot of the cities obtained by using their Cartesian coordinates.The color code represents the population of the metropolitan area.

The size of the bubble is proportional to the extension of each city.

As expected, the two visualizations are similar (apart from a possible rotation in space): the Similarity Map is doing a good job of preserving distances (let's note that the Similarity Map starts only from distances and

**derives**the 3D coordinates).

**Download the Grapheur-ready data file: geography.rbi**

**References:**The distance matrix has been produced by John Burkardt, http://people.sc.fsu.edu/~jburkardt/ . The images of the cities are derived from the corresponding Wikipedia pages, www.wikipedia.org