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https://github.com/lmcinnes/umap

Uniform Manifold Approximation and Projection
https://github.com/lmcinnes/umap

dimensionality-reduction machine-learning topological-data-analysis umap visualization

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Uniform Manifold Approximation and Projection

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README 

        
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  :alt: UMAP logo

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====

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.



Documentation is `available via Read the Docs `_.



**New: this package now also provides support for densMAP.** The densMAP algorithm augments UMAP

to preserve local density information in addition to the topological structure of the data.

Details of this method are described in the following `paper `_:



Narayan, A, Berger, B, Cho, H, *Assessing Single-Cell Transcriptomic Variability

through Density-Preserving Data Visualization*, Nature Biotechnology, 2021



----------

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:



* Python 3.6 or greater

* numpy

* scipy

* scikit-learn

* numba

* tqdm

* `pynndescent `_



Recommended packages:



* For plotting

   * matplotlib

   * datashader

   * holoviews

* for Parametric UMAP

   * tensorflow > 2.0.0



**Install Options**



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



.. code:: bash



    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:



.. code:: bash



    pip install umap-learn



If you wish to use the plotting functionality you can use



.. code:: bash



    pip install umap-learn[plot]



to install all the plotting dependencies.



If you wish to use Parametric UMAP, you need to install Tensorflow, which can be

installed either using the instructions at https://www.tensorflow.org/install

(recommended) or using



.. code:: bash



    pip install umap-learn[parametric_umap]



for a CPU-only version of Tensorflow.



If you're on an x86 processor, you can also optionally install `tbb`, which will

provide additional CPU optimizations:



.. code:: bash



    pip install umap-learn[tbb]



If pip is having difficulties pulling the dependencies then we'd suggest installing

the dependencies manually using anaconda followed by pulling umap from pip:



.. code:: bash



    conda install numpy scipy

    conda install scikit-learn

    conda install numba

    pip install umap-learn



For a manual install get this package:



.. code:: bash



    wget https://github.com/lmcinnes/umap/archive/master.zip

    unzip master.zip

    rm master.zip

    cd umap-master



Optionally, install the requirements through Conda:



.. code:: bash



    conda install scikit-learn numba



Then install the package



.. code:: bash



    python -m pip install -e .



---------------

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.



.. code:: python



    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:



.. code:: python



    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. 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. This includes very high dimensional sparse datasets. UMAP

has successfully been used directly on data with over a million dimensions.



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 it partners well with the `hdbscan

`_ clustering library (for

more details please see `Using UMAP for Clustering

`_).



Third, UMAP often performs better at preserving some aspects of global structure

of the data than most implementations of 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.



Seventh, UMAP supports a variety of additional experimental features including: an

"inverse transform" that can approximate a high dimensional sample that would map to

a given position in the embedding space; the ability to embed into non-euclidean

spaces including hyperbolic embeddings, and embeddings with uncertainty; very

preliminary support for embedding dataframes also exists.



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.



------------------------

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.

For the best possible performance we recommend installing the nearest neighbor

computation library `pynndescent `_ .

UMAP will work without it, but if installed it will run faster, particularly on

multicore machines.



For a problem such as the 784-dimensional MNIST digits dataset with

70000 data samples, UMAP can complete the embedding in under a minute (as

compared with around 45 minutes for scikit-learn's t-SNE implementation).

Despite this runtime efficiency, UMAP still produces high quality embeddings.



The obligatory MNIST digits dataset, embedded in 42

seconds (with pynndescent installed and after numba jit warmup)

using a 3.1 GHz Intel Core i7 processor (n_neighbors=10, min_dist=0.001):



.. image:: images/umap_example_mnist1.png

    :alt: UMAP embedding of MNIST digits



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 49 seconds (n_neighbors=5, min_dist=0.1):



.. image:: images/umap_example_fashion_mnist1.png

    :alt: UMAP embedding of "Fashion MNIST"



The UCI shuttle dataset (43500 sample in 8 dimensions) embeds well under

*correlation* distance in 44 seconds (note the longer time

required for correlation distance computations):



.. image:: images/umap_example_shuttle.png

    :alt: UMAP embedding the UCI Shuttle dataset



The following is a densMAP visualization of the MNIST digits dataset with 784 features

based on the same parameters as above (n_neighbors=10, min_dist=0.001). densMAP reveals

that the cluster corresponding to digit 1 is noticeably denser, suggesting that

there are fewer degrees of freedom in the images of 1 compared to other digits.



.. image:: images/densmap_example_mnist.png

    :alt: densMAP embedding of the MNIST dataset



--------

Plotting

--------



UMAP includes a subpackage ``umap.plot`` for plotting the results of UMAP embeddings.

This package needs to be imported separately since it has extra requirements

(matplotlib, datashader and holoviews). It allows for fast and simple plotting and

attempts to make sensible decisions to avoid overplotting and other pitfalls. An

example of use:



.. code:: python



    import umap

    import umap.plot

    from sklearn.datasets import load_digits



    digits = load_digits()



    mapper = umap.UMAP().fit(digits.data)

    umap.plot.points(mapper, labels=digits.target)



The plotting package offers basic plots, as well as interactive plots with hover

tools and various diagnostic plotting options. See the documentation for more details.



---------------

Parametric UMAP

---------------



Parametric UMAP provides support for training a neural network to learn a UMAP based

transformation of data. This can be used to support faster inference of new unseen

data, more robust inverse transforms, autoencoder versions of UMAP and

semi-supervised classification (particularly for data well separated by UMAP and very

limited amounts of labelled data). See the

`documentation of Parametric UMAP `_

or the

`example notebooks `_

for more.



-------

densMAP

-------



The densMAP algorithm augments UMAP to additionally preserve local density information

in addition to the topological structure captured by UMAP. One can easily run densMAP

using the umap package by setting the ``densmap`` input flag:



.. code:: python



    embedding = umap.UMAP(densmap=True).fit_transform(data)



This functionality is built upon the densMAP `implementation `_ provided by the developers

of densMAP, who also contributed to integrating densMAP into the umap package.



densMAP inherits all of the parameters of UMAP. The following is a list of additional

parameters that can be set for densMAP:



 - ``dens_frac``: This determines the fraction of epochs (a value between 0 and 1) that will include the density-preservation term in the optimization objective. This parameter is set to 0.3 by default. Note that densMAP switches density optimization on after an initial phase of optimizing the embedding using UMAP.



 - ``dens_lambda``: This determines the weight of the density-preservation objective. Higher values prioritize density preservation, and lower values (closer to zero) prioritize the UMAP objective. Setting this parameter to zero reduces the algorithm to UMAP. Default value is 2.0.



 - ``dens_var_shift``: Regularization term added to the variance of local densities in the embedding for numerical stability. We recommend setting this parameter to 0.1, which consistently works well in many settings.



 - ``output_dens``: When this flag is True, the call to ``fit_transform`` returns, in addition to the embedding, the local radii (inverse measure of local density defined in the `densMAP paper `_) for the original dataset and for the embedding. The output is a tuple ``(embedding, radii_original, radii_embedding)``. Note that the radii are log-transformed. If False, only the embedding is returned. This flag can also be used with UMAP to explore the local densities of UMAP embeddings. By default this flag is False.



For densMAP we recommend larger values of ``n_neighbors`` (e.g. 30) for reliable estimation of local density.



An example of making use of these options (based on a subsample of the mnist_784 dataset):



.. code:: python



    import umap

    from sklearn.datasets import fetch_openml

    from sklearn.utils import resample



    digits = fetch_openml(name='mnist_784')

    subsample, subsample_labels = resample(digits.data, digits.target, n_samples=7000,

                                           stratify=digits.target, random_state=1)



    embedding, r_orig, r_emb = umap.UMAP(densmap=True, dens_lambda=2.0, n_neighbors=30,

                                         output_dens=True).fit_transform(subsample)



See `the documentation `_ for more details.



----------------

Help and Support

----------------



Documentation is at `Read the Docs `_.

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 make use of this software for your work we would appreciate it if you

would cite the paper from the Journal of Open Source Software:



.. code:: bibtex



    @article{mcinnes2018umap-software,

      title={UMAP: Uniform Manifold Approximation and Projection},

      author={McInnes, Leland and Healy, John and Saul, Nathaniel and Grossberger, Lukas},

      journal={The Journal of Open Source Software},

      volume={3},

      number={29},

      pages={861},

      year={2018}

    }



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

current reference:



.. code:: bibtex



   @article{2018arXivUMAP,

        author = {{McInnes}, L. and {Healy}, J. and {Melville}, 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,

   }



Additionally, if you use the densMAP algorithm in your work please cite the following reference:



.. code:: bibtex



    @article {NBC2020,

        author = {Narayan, Ashwin and Berger, Bonnie and Cho, Hyunghoon},

        title = {Assessing Single-Cell Transcriptomic Variability through Density-Preserving Data Visualization},

        journal = {Nature Biotechnology},

        year = {2021},

        doi = {10.1038/s41587-020-00801-7},

        publisher = {Springer Nature},

        URL = {https://doi.org/10.1038/s41587-020-00801-7},

        eprint = {https://www.biorxiv.org/content/early/2020/05/14/2020.05.12.077776.full.pdf},

    }



If you use the Parametric UMAP algorithm in your work please cite the following reference:



.. code:: bibtex



    @article {SMG2020,

        author = {Sainburg, Tim and McInnes, Leland and Gentner, Timothy Q.},

        title = {Parametric UMAP: learning embeddings with deep neural networks for representation and semi-supervised learning},

        journal = {ArXiv e-prints},

        archivePrefix = "arXiv",

        eprint = {2009.12981},

        primaryClass = "stat.ML",

        keywords = {Statistics - Machine Learning,

                    Computer Science - Computational Geometry,

                    Computer Science - Learning},

        year = 2020,

        }



-------

License

-------



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.