Uniform Manifold Approximation and Projection
Uniform Manifold Approximation and Projection (UMAP) is a dimension reduction technique that can be used for visualisation similarly to t-SNE, but also for general non-linear dimension reduction. The algorithm is founded on three assumptions about the data
- The data is uniformly distributed on Riemannian manifold;
- The Riemannian metric is locally constant (or can be approximated as such);
- The manifold is locally connected (not globally, but locally).
From these assumptions it is possible to model the manifold with a fuzzy topological structure. The embedding is found by searching for a low dimensional projection of the data that has the closest possible equivalent fuzzy topological structure.
The important thing is that you don’t need to worry about that – you can use UMAP right now for dimension reduction and visualisation as easily as a drop in replacement for scikit-learn’s t-SNE.
How to use UMAP
The umap package inherits from sklearn classes, and thus drops in neatly next to other sklearn transformers with an identical calling API.
import umap from sklearn.datasets import load_digits digits = load_digits() embedding = umap.UMAP().fit_transform(digits.data)
There are a number of parameters that can be set for the UMAP class; the major ones are as follows:
- n_neighbors: This determines the number of neighboring points used in local approximations of manifold structure. Larger values will result in more global structure being preserved at the loss of detailed local structure. In general this parameter should often be in the range 5 to 50, with a choice of 10 to 15 being a sensible default.
- min_dist: This controls how tightly the embedding is allowed compress points together. Larger values ensure embedded points are more evenly distributed, while smaller values allow the algorithm to optimise more accurately with regard to local structure. Sensible values are in the range 0.001 to 0.5, with 0.1 being a reasonable default.
- metric: This determines the choice of metric used to measure distance in the input space. A wide variety of metrics are already coded, and a user defined function can be passed as long as it has been JITd by numba.
An example of making use of these options:
import umap from sklearn.datasets import load_digits digits = load_digits() embedding = umap.UMAP(n_neighbors=5, min_dist=0.3, metric='correlation').fit_transform(digits.data)
UMAP also supports fitting to sparse matrix data. This is currently experimental and may be slower than the eventual final implementation.
Further details and tutorials are coming.
Benefits of UMAP
UMAP has a few signficant wins in its current incarnation.
First of all UMAP is fast. It can handle large datasets and high dimensional data without too much difficulty, scaling beyond what most t-SNE packages can manage.
Second, UMAP scales well in embedding dimension – it isn’t just for visualisation! You can use UMAP as a general purpose dimension reduction technique as a preliminary step to other machine learning tasks. With a little care (documentation on how to be careful is coming) it partners well with the hdbscan clustering library.
Third, UMAP often performs better at preserving aspects of global structure of the data than t-SNE. This means that it can often provide a better “big picture” view of your data as well as preserving local neighbor relations.
Fourth, UMAP supports a wide variety of distance functions, including non-metric distance functions such as cosine distance and correlation distance. You can finally embed word vectors properly using cosine distance!
Finally UMAP has solid theoretical foundations in manifold learning (paper forthcoming). This both justifies the approach and allows for further extensions that will soon be added to the library (embedding dataframes, semi-supervised dimension reduction, etc.).
Performance and Examples
UMAP is very efficient at embedding large high dimensional datasets. In particular it scales well with both input dimension and embedding dimension. Thus, for a problem such as the 784-dimensional MNIST digits dataset with 70000 data samples, UMAP can complete the embedding in around 2.5 minutes (as compared with around 45 minutes for most t-SNE implementations). Despite this runtime efficiency UMAP still produces high quality embeddings.
The obligatory MNIST digits dataset, embedded in 2 minutes and 22 seconds using a 3.1 GHz Intel Core i7 processor (n_neighbors=10, min_dist=0 .001):
The MNIST digits dataset is fairly straightforward however. A better test is the more recent “Fashion MNIST” dataset of images of fashion items (again 70000 data sample in 784 dimensions). UMAP produced this embedding in 2 minutes exactly (n_neighbors=5, min_dist=0.1):
The UCI shuttle dataset (43500 sample in 8 dimensions) embeds well under correlation distance in 2 minutes and 39 seconds (note the longer time required for correlation distance computations):
UMAP depends upon scikit-learn, and thus scikit-learn’s dependencies such as numpy and scipy. UMAP adds a requirement for numba for performance reasons. The original version used Cython, but the improved code clarity, simplicity and performance of Numba made the transition necessary.
PyPI install, presuming you have numab and sklearn and all its requirements (numpy and scipy) installed:
pip install umap-learn
If pip is having difficulties pulling the dependencies then we’d suggest installing the dependencies manually using anaconda followed by pulling umap from pip:
conda install numpy scipy conda install scikit-learn conda install numba pip install umap-learn
For a manual install get this package:
wget https://github.com/lmcinnes/umap/archive/master.zip unzip master.zip rm master.zip cd umap-master
Install the requirements
sudo pip install -r requirements.txt
conda install scikit-learn numba
Install the package
python setup.py install
Help and Support
This project is still very young. I am currently trying to get example notebooks and documentation prepared, but it may be a while before those are available. In the meantime please open an issue and I will try to provide any help and guidance that I can. Please also check the docstrings on the code, which provide some descriptions of the parameters.
The umap package is 3-clause BSD licensed. Enjoy.
Contributions are more than welcome! There are lots of opportunities for potential projects, so please get in touch if you would like to help out. Everything from code to notebooks to examples and documentation are all equally valuable so please don’t feel you can’t contribute. To contribute please fork the project make your changes and submit a pull request. We will do our best to work through any issues with you and get your code merged into the main branch.