Uniform Manifold Approximation and Projection

## UMAP

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

1. The data is uniformly distributed on a Riemannian manifold;
2. The Riemannian metric is locally constant (or can be approximated as such);
3. The manifold is locally connected.

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 details for the underlying mathematics can be found in our paper on ArXiv:

McInnes, L, Healy, J, UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction, ArXiv e-prints 1802.03426, 2018

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

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

embedding = umap.UMAP(n_neighbors=5,
min_dist=0.3,
metric='correlation').fit_transform(digits.data)
```

UMAP also supports fitting to sparse matrix data. For more details please see the UMAP documentation

### 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!

Fifth, UMAP supports adding new points to an existing embedding via the standard sklearn transform method. This means that UMAP can be used as a preprocessing transformer in sklearn pipelines.

Sixth, UMAP supports supervised and semi-supervised dimension reduction. This means that if you have label information that you wish to use as extra information for dimension reduction (even if it is just partial labelling) you can do that – as simply as providing it as the y parameter in the fit method.

Finally UMAP has solid theoretical foundations in manifold learning (see our paper on ArXiv). This both justifies the approach and allows for further extensions that will soon be added to the library (embedding dataframes 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):

### Installing

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.

Requirements:

• numpy
• scipy
• scikit-learn
• numba

Install Options

Conda install, via the excellent work of the conda-forge team:

```conda install -c conda-forge umap-learn
```

The conda-forge packages are available for linux, OS X, and Windows 64 bit.

PyPI install, presuming you have numba 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
```

or

```conda install scikit-learn numba
```

Install the package

```python setup.py install
```

### Help and Support

Documentation is at ReadTheDocs. The documentation includes a FAQ that may answer your questions. If you still have questions then please open an issue and I will try to provide any help and guidance that I can.

### Citation

If you would like to cite this algorithm in your work the ArXiv paper is the current reference:

```@article{2018arXivUMAP,
author = {{McInnes}, L. and {Healy}, J.},
title = "{UMAP: Uniform Manifold Approximation
and Projection for Dimension Reduction}",
journal = {ArXiv e-prints},
archivePrefix = "arXiv",
eprint = {1802.03426},
primaryClass = "stat.ML",
keywords = {Statistics - Machine Learning,
Computer Science - Computational Geometry,
Computer Science - Learning},
year = 2018,
month = feb,
}
```

The umap package is 3-clause BSD licensed.

We would like to note that the umap package makes heavy use of NumFOCUS sponsored projects, and would not be possible without their support of those projects, so please consider contributing to NumFOCUS.

### Contributing

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.