langevitour(dataset, labels)

Use directly from R.
R Markdown → static HTML.

Interaction, calculations, and drawing done in Javascript.

Seek a “good” projection. (Cook et al., 1995)

Spin randomly. (Asimov, 1985)

Touring data

GGobi in action

Animate linear, orthonormal projections of data.

Previous software does this by choosing distinct projections then interpolating.

langevitour’s novel feature is using Langevin Dynamics to produce a smooth random path of projections.

  • Grand Tour introduced by Daniel Asimov in 1985.

  • XGobi, GGobi - interactive desktop applications.

  • tourr - R package for tour calculation and animation.

  • Ongoing interdisciplinary research by Di Cook and collaborators, e.g. slice tours.

Langevin Dynamics

“Stochastic Differential Equation”

Constrained Langevin Dynamics

The “position” should always represent an orthonormal projection.

langevitour uses “Position Based Dynamics”, a simple and stable way to maintain constraints in a physics engine.

Each timestep:

  1. Update velocity \(\mathbf{v} \leftarrow \mathbf{v} - \mathrm{damping} + \mathrm{noise} + \mathrm{forces}\)
  2. Propose new position \(\mathbf{x} \leftarrow \mathbf{x} + \Delta t\ \mathbf{v}\)
  3. Fix the proposed \(\mathbf{x}\) by finding the nearest valid orthonormal projection. (SVD and set singular values to 1)
  4. Fix \(\mathbf{v}\) to be consistent with the actual step taken by \(\mathbf{x}\).


Guided Tour

langevitour can sample projections near an optimum defined by a potential energy function.