BM 20160408B
Data On Nodes Thu May 12 22:41:17 CDT 2016 2659296c74bcec23c5dec54ac227ebf4d09dd60a
Bifurcating structure simulation
Pure birth process, 8 tips and 7 internal nodes, edge length \(t=50\)
Brownian data points on nodes
- Starting from root \(\{Y_1 = 0, Y_2 = 0, \ldots, Y_K = 0\}_{K}\)
- \(K\) data point (or “loci”) on each node
- Simulate instances of Brownian motion \[Y_k^{(t)} := N(\mu t, \sigma^2 t)\] where \(t\) is edge length; data on node \(T\) \[Y_k^{(T)} = \sum_{t=1}^T Y_k^{(t)}\]
- Repeat \(N\) times such that each node will have \(N\) “draws”
Simulation default setup: \(N = 100, K=100, \sigma = 0.1\)
Methods for Manifold learning
6 methods (or 9 considering variants on LLE)
- 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
./tree-dmr.sos -c tree-dmr.yml --date 20160416 \
--simulators bm_simulate bmf_simulate \
--analysts manifold_analyze