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## 2.4 Dot Graph

The Dot Graph represents the comparison of each car to all other cars. The comparison is graphically laid out in a dot graph, where the close proximity of points denotes a similarity in values. The comparison utilizes some or all of the following variables: Miles Per Gallon, Acceleration, Horse Power, Cylinders, Cubic Inches, and Weight. The user may set which values to include, as well as what order to include the variables in. The priority of variables is then logarithmically translated into a simple equation:

var_priority_1 * 32 + var_priority_2 * 16 + var_priority_3 * 8 + etc.

 Figure 1.18: Dot Graph Settings Click image to enlarge, or click here to open
The comparison of all cars is represented by a square matrix, in which each car is represented once in each row and column. The resulting matrix is thus NUM_CARS x NUM_CARS large. Dot Graph makes use of Multidimensional Scaling, which in turn uses Singular Value Decomposition, in order to project the NUM_CARS degree comparison onto 2 dimensions. It should be noted that the SVD algorithm was adopted from the FORTRAN LINPACK, and is, unfortunately, very slow. On a Sparc III, 750 MHz, the algorithm can take up to 15 seconds to complete; on a Sparc II, 400MHz, up to 90 seconds.

In a graph that compares all values, we will notice a dominant scattering of red dots on the right (American automobiles), and a dominant scattering of white and blue dots on the left (Japanese and European automobiles). This would suggest the difference between American and non-American automobiles, which is most notably due to the values of cubic inches, weight, and miles per gallon fuel usage.

 Figure 1.19: All Parameters included in graph Click image to enlarge, or click here to open
In a graph that compares acceleration and weight, we not only notice the same behavior as in the previous graph (American vs. non-American automobiles), but we can also quite visibly make out the inverse proportionality between acceleration and weight by the diagonal band of dots. We deduce, correctly and rather obviously, that the heavier a car, the slower its acceleration.

 Figure 1.20: Graph with Parameters for Acceleration and Weight Click image to enlarge, or click here to open
When moving the mouse over the dot graph, the dot closest to the mouse pointer is highlighted, and the corresponding car is displayed in an iconified version. Furthermore, a line connects the highlighted dot with the icon of the car. Should more than one car be represented by the same dot, then moving the mouse pointer horizontally toggles between all the different cars that are matched by this dot.

 Figure 1.21: Moving the mouse over the graph Click image to enlarge, or click here to open
Clicking the mouse button when a car is highlighted, selects the car in all visualization frames. Selections work as toggles: clicking on an unselected car selects it; clicking on a selected car unselects it. All selected cars are marked green.

 Figure 1.22: Selected cars Click image to enlarge, or click here to open
The functionality of the graph when zooming up to 1000% remains the same as for the original graph: moving the mouse over the graph highlights the closest matching car.

 Figure 1.23: Zoomed in at 400% Click image to enlarge, or click here to open
When zooming in more than 1000%, the graph now displays iconified cars for every dot on the screen.

 Figure 1.24: Zoomed in at 1180% Click image to enlarge, or click here to open