BM 20160609

Fri Jun 10 17:45:54 CDT 2016 f34d9e93c2743fad676cc7f796cdd56b2a9e51f4

Direct Brownian Motion + Optional Calculation of Covariance

Bifurcating structure simulation

Pure birth process, 8 tips and 7 internal nodes

Data points and Brownian samples

As previously have been implemented, directly simulating from \(X \sim N_R(0,\Sigma)\) is more principled and keeps the ground truth, but is less flexible for potential tweaks (when we move away from Brownian motion). After discussion with Kushal we decide to simulate directly along the tree structure while being able to calculate the covariance matrix as the ground truth for future references. Simulation procedure is implemented in DSC2.

Methods for Manifold learning

6 methods (or 9 considering variants on LLE) are implemented in the current version.

  • Global distances:
    • PCA (covariance)
    • MDS (dissimilarities)
  • Local distances:
    • t-SNE (t-distributed Stochastic Neighbor Embedding)
    • Spectral embedding
    • Locally linear embedding including standard, LTSA, Hessian and modified LLE
    • LTSA: Local Tangent Space Alignment

Run

Only executes part of the DSC (avoid calculating covariance matrix for now)

dsc exec vcv-bm.dsc -j8 -s "(SimTree * PlotTree) * SimBM * (ManifoldDR * PlotDR)"

Results