Package: umap-learn-modified
UMAPUniform 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 dataThe data is uniformly distributed on a Riemannian manifold;The Riemannian metric is locally constant (or can be approximated as such);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 inour paper on ArXiv:McInnes, L, Healy, J,UMAP: Uniform Manifold Approximation and Projection
for Dimension Reduction, ArXiv e-prints 1802.03426, 2018The 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 isavailable via ReadTheDocs.How to use UMAPThe umap package inherits from sklearn classes, and thus drops in neatly
next to other sklearn transformers with an identical calling API.importumapfromsklearn.datasetsimportload_digitsdigits=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:importumapfromsklearn.datasetsimportload_digitsdigits=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 seethe UMAP documentationBenefits of UMAPUMAP has a few signficant wins in its current incarnation.First of all UMAP isfast. 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 thehdbscanclustering 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 ascosine distanceandcorrelation
distance. You can finally embed word vectors properly using cosine distance!Fifth, UMAP supports adding new points to an existing embedding via
the standard sklearntransformmethod. 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 theyparameter in the fit method.Finally UMAP has solid theoretical foundations in manifold learning
(seeour 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 ExamplesUMAP 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 undercorrelationdistance in 2 minutes and 39 seconds (note the longer time
required for correlation distance computations):InstallingUMAP depends uponscikit-learn, and thusscikit-learn’s dependencies
such asnumpyandscipy. UMAP adds a requirement fornumbafor
performance reasons. The original version used Cython, but the improved code
clarity, simplicity and performance of Numba made the transition necessary.Requirements:numpyscipyscikit-learnnumbaInstall OptionsConda install, via the excellent work of the conda-forge team:condainstall-cconda-forgeumap-learnThe 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:pipinstallumap-learnIf pip is having difficulties pulling the dependencies then we’d suggest installing
the dependencies manually using anaconda followed by pulling umap from pip:condainstallnumpyscipycondainstallscikit-learncondainstallnumbapipinstallumap-learnFor a manual install get this package:wgethttps://github.com/lmcinnes/umap/archive/master.zipunzipmaster.ziprmmaster.zipcdumap-masterInstall the requirementssudopipinstall-rrequirements.txtorcondainstallscikit-learnnumbaInstall the packagepythonsetup.pyinstallHelp and SupportDocumentation is atReadTheDocs.
The documentationincludes a FAQthat
may answer your questions. If you still have questions then pleaseopen an issueand I will try to provide any help and guidance that I can.CitationIf 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:@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:@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,}LicenseThe 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 pleaseconsider contributing to NumFOCUS.ContributingContributions 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 allequally valuableso please don’t feel
you can’t contribute. To contribute pleasefork the projectmake 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.