Examples#

After reading the documentation, the best way to learn more is by playing with code examples.

Our Python notebooks show how to use PyMDE on real (and synthetic) datasets. You can read these notebooks, or better yet, execute them and experiment by modifying the cells’ contents and seeing what happens.

You can run the notebooks by either downloading them locally and starting a Jupyter server, or by opening them in Google Colab.

MNIST#

We recommend starting with our MNIST notebook, which highlights many of the things you can do in PyMDE, using the MNIST dataset as a case study.

In this notebook, you’ll see how to use the pymde.preserve_neighbors function to embed vector data, how to create MDE problems for preserving neighbors from scratch, how to sanity-check an embedding, and how to use an embedding to look for outliers in the original data.

Fashion MNIST#

The Fashion MNIST notebook is analogous to the MNIST notebook, except it uses the Fashion MNIST dataset.

Single-Cell Genomics#

This notebook is similar to the MNIST notebook (but with less explanatory text). The dataset embedded here contains single-cell mRNA transcriptomes of cells taken from human patients with severe COVID-19 infections (and also from healthy controls). We’ll see that similar cells are placed near each other in the embedding, and cells from healthy and sick are also somewhat separated.

Google Scholar#

The Google Scholar notebook uses pymde.preserve_distances to embed an academic coauthorship network, which we collected from Google Scholar. (This network contains most authors on Google Scholar whose h-index is at least 50.)

This example embeds a graph with roughly 40,000 nodes and (after preprocessing) 80 million edges. If you have a GPU, computing the embedding shouldn’t take much longer than a minute, but it will take longer to compute on a CPU.

Word Embedding#

This notebook shows how to make basic word embeddings. The words being embedded are the 5000 most popular academic interests on Google Scholar.

Population Genetics#

The population genetics notebook embeds genomic data of individuals thought to be of European ancestry, and recovers what appears to be a map of Europe.

US Counties#

The US counties notebook embeds 3,220 US counties, described by demographic data, into two dimensions. The resulting embedding is colored by the fraction of voters who voted for Democratic candidates in the 2016 presidential election (voting data was not used in computing the embedding). Moreover, the resulting embedding vaguely resembles a map of the US (though no geographic data was used in computing the embedding).

Anchor Constraints#

With an anchor constraint, you can pin some embedding vectors to values that you specify ahead of time. This is useful when you have prior knowledge of where some of the items should end up (e.g., you might be doing semi-supervised learning, or you might be laying out a graph with some nodes pinned in place).

This notebook gives an example of how to use an anchor constraint, using graph drawing as an example.

Updating Embeddings#

With PyMDE, you can easily add new points to an existing embedding using an anchor constraint (to pin the existing embedding in place).

This notebook gives an example of how to do this, using MNIST as an example. We first embed half the images in the MNIST dataset. Then we augment the embedding with vectors for the remaining images.

Drawing Graphs#

PyMDE can be used to layout graphs in the Cartesian plane in an aesthetically pleasing way. Compared to many other graph layout libraries, PyMDE can scale to much larger datasets. PyMDE also lets you design custom layouts, by choosing your own distortion functions and constraints.

This notebook shows various ways of drawing graphs with PyMDE. It also introduces the pymde.Graph class.

Dissimilar Edges and Negative Weights#

When creating an embedding for preserving neighbors, an important hyper-parameter is the number of dissimilar edges to include, and the size of the negative weights. Using as many dissimilar edges as there are similar edges, and choosing the negative weights to all be -1, usually works just fine. But different choices do lead to different embeddings.

This notebook explores the effect these hyper-parameters have on the embedding.