Particle Trajectories in a Data Potential
This sonification model allows to get an auditory presentation of high-dimensional
data using an deterministic dynamic process. Given an arbitrary high-dimensional
function V(x), test particles are injected in the domain of V. Regarding
V as an potential function and using Newtons laws of motion, these test
particles move along a well defined path or trajectory through data space.
Given a data set {x_i}, i=1..N, V can be constructed by a superposition
of 1-point potentials phi(x-x_i) which are shifted to data point x_i. Using
negative Gaussians with bandwidth sigma, a smooth function V is the result.
The test particles are moving in data space according to Newtons law
of motion. They are considered as point masses with a given constant mass
m and initial Energy E_0. However, we added a friction term to the equations
of motion so that the particles converge to local minima of V. These potential
troughs correspond to clusters in the data.
No, consider, we throw 50 test particles into data space at random position,
compute their trajectories and use the kinetic energy as a function of
time as the sound pressure. What do we expect to get ? The particles will
move around the domain of V until their energy loss forces them to move
into throughs of V. The deeper they get into the trough, the more harmonic
is the shape of V. We know that particles in an harmonic potential will
perform quasiperiodic motions. Thus, the kinetic energy of the particles
will also vary periodically. This will be heard as pitched tones.
Literature
For further details on this model, take a look to Listen
to your Data: Model-Based Sonification of Data Analysis
Contact
Thomas Hermann: thermann@techfak.uni-bielefeld.de
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Last modified: 2001-05-22