|
Asymmetric von Mises Scaling |
|
This website introduces asymmetric von Mises scaling (AMISESCAL). AMISESCAL is
a kind of asymmetric multidimensional scaling (AMDS) using a technique
deriving from directional statistics. This method is a statistical model
analyzing an asymmetric matrix to visualize the structure underlying the
matrix. Quick Introduction PPT |
|
Directional Statistics |
|
Directional statistics is a branch of
statistics that deals with angles, courses, and directions as data. This
branch of statistics is used in magnetic field analysis, animal migration,
disease transmission route, etc. For example, as shown in the figure below,
we obtain the directions to which migratory birds flew away as data. And, our
concern is which angle the birds prefers to migrate. Then, in the histogram
of the directional statistics, frequencies are summarized on the circle.
|
|
von Mises Distribution |
|
The
normal distribution is the most important distribution in statistics. The von
Mises distribution can be considered to be the normal distribution of
directional statistics. The functional form of this distribution is as
follows:
μ:
Mean Direction Parameter κ: Concentration Parameter The
domain of the definition of θ is
[0, 2π]. The von Mises distribution has two parameters: mean direction (μ) and concentration (κ). Mean direction is the
parameter regulating the highest density direction of the distribution, and
concentration is the parameter for adjusting the depth around the mean
direction. |
|
The left graph in the figure below shows
four von Mises distributions with varying parameters. On the other hand, the
right graph shows the four distributions on the unit circle. It is often easy
to understand the angle of the mean direction (μ) and the size of the concentration (κ) of a von Mises distribution by showing
it on a circle.
|
