Study of the dependence of manifold learning algorithms on parameters
Next meeting: no meeting week of august 8
Plan for Weeks of August 2-15 (Priority lowest = LP < nothing < HP=highest )
- Generate rectangles with a fixed set of aspect ratios, uniformly sampled (code and 1 data set of each) -- pretty much done by Yujia
- same as above, with holes -- done by Yujia
- Generate swissroll, torus from rectangles: in fact, take points sampled from rectangles, with coordinates
$x_1,x_2$ and map them to points on swiss roll and torus, with coordinates (x,y,z) -- done Yujia, Hangliang - Generate rectangles with a fixed set of aspect ratios, non-uniformly sampled (code and 1 data set of each) -- done by Murray
- for all the above, let's unify the code and data [LP]
- Effect of aspect ratio on output of LLE embedding - done Yujia
- Effect of aspect ratio on output of Isomap embedding -- to use the same data and plotting style as LLE - done Hangliang
- Effect of aspect ratio on output of Spectral embedding -- to use the same data and plotting style as LLE. Note that for Spectral Embedding, one must use the radius_neighbors method. Ask me if not sure what this means. A radius must be selected. [HP]
- Effect of aspect ratio on output of t-SNE -- to use the same data and plotting style as LLE. [HP]
- UMAP -- first set of tasks-- for increasing m, can we recover the embedding for m=3 among the dimensions
$v_0, v_1, ... v_{m-1}$ ? Qirui - Effect of aspect ratio on output of UMAP (m=3 or 2 by case) to use the same data and plotting style as LLE [LP] done Qirui
- Effect of aspect ratio on output of t-SNE (m=3 or 2 by case) to use the same data and plotting style as LLE [HP]
- Write first draft of white paper, describing effects of aspect ratio on embeddings -- MMP
- t-SNE for data sampled uniformly on disk
Plan for week 2
- share with others what you have learned/done
- learn basics of manifold learning -- short tutorial by MMP
- plan and run first set of experiments
Plan for week 1
- learn scikit-learn manifold learning functions, specifically isomap, spectral_embedding, lle, [t-sne], [ltsa if available]
- learn megaman package by MMP
- learn t-sne (this is part of scikit-learn)
- learn UMAP
- write code that generates synthetic examples