Flameplot - Comparison of (high) dimensional embeddings.

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Medium Blog

Also checkout The Similarity between t-SNE, UMAP, PCA, and Other Mappings to get a structured overview and usage of flameplot.

Method

To compare the embedding of samples in two different maps, we propose a scale dependent similarity measure. For a pair of maps X and Y, we compare the sets of the, respectively, kx and ky nearest neighbours of each sample. We first define the variable rxij as the rank of the distance of sample j among all samples with respect to sample i, in map X. The nearest neighbor of sample i will have rank 1, the second nearest neighbor rank 2, etc. Analogously, ryij is the rank of sample j with respect to sample i in map Y. Now we define a score on the interval [0, 1], as (eq. 1)

Schematic overview

Schematic overview to systematically compare local and global differences between two sample projections. For illustration we compare two input maps (x and y) in which each map contains n samples (step 1). The second step is the ranking of samples based on Euclidean distance. The ranks of map x are subsequently compared to the ranks of map y for kx and ky nearest neighbours (step 3). The overlap between ranks (step 4), is subsequently summarized in Score: Sx,y(kx,ky).

Functions in flameplot

scores = flameplot.compare(map1, map2)
fig    = flameplot.plot(scores)
X,y    = flameplot.import_example()
fig    = flameplot.scatter(Xcoord,Ycoord)

Install flameplot from PyPI

pip install flameplot

Import flameplot package

import flameplot as flameplot

Documentation pages

On the documentation pages you can find detailed information about the working of the flameplot with examples.

Examples

Example: Comparison between two maps follow the quantification of local similarity approach.

Example: Comparison 2D embeddings: PCA vs tSNE

Example: Comparison Random data vs. t-SNE

Example: Scatterplots

Support

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* Star this repo at the github page.
* Other contributions can be in the form of feature requests, idea discussions, reporting bugs, opening pull requests.
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Cheers Mate.