BM 20160607
Fri Jun 10 07:44:42 CDT 2016 a25c30dba323c9a63342500c051888f4373bfbed
Simulation via Covariance Matrix
Data points and Brownian samples
Sample directly from \(X \sim N_R(0,\Sigma)\) along the lines of this post. \(\Sigma_{ij} = COV(X_i, X_j)\) is well defined by the tree structure, i.e. distance to root from the MRCA of \(X_i\) and \(X_j\).
Here I allow observation on any position on the tree: on leaves, internal nodes and in-between notes. Tree structure simulation is implemented in BiTree.R, covariance calculation in VcvTree.R and data points sampling is implemented in VcvBM.R.
Simulation procedure is implemented in DSC2. Check vcv-bm.dsc for scenarios and parameter settings.
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
dsc exec vcv-bm.dsc -j8