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Uniform Manifold Approximation and Projection
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Project description
UMAP
Uniform Manifold Approximation and Projection (UMAP) is a dimension reductiontechnique that can be used for visualisation similarly to t-SNE, but also forgeneral non-linear dimension reduction. The algorithm is founded on threeassumptions about the data:
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- The 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 fuzzytopological structure. The embedding is found by searching for a low dimensionalprojection of the data that has the closest possible equivalent fuzzytopological structure.
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The details for the underlying mathematics can be found inour paper on ArXiv:
McInnes, L, Healy, J, UMAP: Uniform Manifold Approximation and Projectionfor Dimension Reduction, ArXiv e-prints 1802.03426, 2018
The important thing is that you don’t need to worry about that—you can useUMAP right now for dimension reduction and visualisation as easily as a dropin replacement for scikit-learn’s t-SNE.
Documentation is available via Read the Docs.
Installing
UMAP depends upon scikit-learn, and thus scikit-learn’s dependenciessuch as numpy and scipy. UMAP adds a requirement for numba forperformance reasons. The original version used Cython, but the improved codeclarity, simplicity and performance of Numba made the transition necessary.
Requirements:
- Python 3.6 or greater
- numpy
- scipy
- scikit-learn
- numba
Recommended packages:
- For plotting
- matplotlib
- datashader
- holoviews
Installing pynndescent can significantly increase performance, and in later versionsit will become a hard dependency.
Install Options
Conda install, via the excellent work of the conda-forge team:
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:
If you wish to use the plotting functionality you can use
to install all the plotting dependencies.
If pip is having difficulties pulling the dependencies then we’d suggest installingthe dependencies manually using anaconda followed by pulling umap from pip:
For a manual install get this package:
Install the requirements
or
Install the package
How to use UMAP
The umap package inherits from sklearn classes, and thus drops in neatlynext to other sklearn transformers with an identical calling API.
There are a number of parameters that can be set for the UMAP class; themajor ones are as follows:
- n_neighbors: This determines the number of neighboring points used inlocal approximations of manifold structure. Larger values will result inmore global structure being preserved at the loss of detailed localstructure. In general this parameter should often be in the range 5 to50, with a choice of 10 to 15 being a sensible default.
- min_dist: This controls how tightly the embedding is allowed compresspoints together. Larger values ensure embedded points are more evenlydistributed, while smaller values allow the algorithm to optimise moreaccurately with regard to local structure. Sensible values are in therange 0.001 to 0.5, with 0.1 being a reasonable default.
- metric: This determines the choice of metric used to measure distancein the input space. A wide variety of metrics are already coded, and a userdefined function can be passed as long as it has been JITd by numba.
An example of making use of these options:
UMAP also supports fitting to sparse matrix data. For more detailsplease 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 highdimensional data without too much difficulty, scaling beyond what most t-SNEpackages can manage. This includes very high dimensional sparse datasets. UMAPhas successfully been used directly on data with over a million dimensions.
Second, UMAP scales well in embedding dimension—it isn’t just forvisualisation! You can use UMAP as a general purpose dimension reductiontechnique as a preliminary step to other machine learning tasks. With alittle care it partners well with the hdbscan clustering library (formore details please see Using UMAP for Clustering).
Third, UMAP often performs better at preserving some aspects of global structureof the data than most implementations of t-SNE. This means that it can oftenprovide a better “big picture” view of your data as well as preserving local neighborrelations.
Fourth, UMAP supports a wide variety of distance functions, includingnon-metric distance functions such as cosine distance and correlationdistance. You can finally embed word vectors properly using cosine distance!
Fifth, UMAP supports adding new points to an existing embedding viathe standard sklearn transform method. This means that UMAP can beused 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 asextra information for dimension reduction (even if it is just partiallabelling) you can do that—as simply as providing it as the yparameter 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 toa given position in the embedding space; the ability to embed into non-euclideanspaces including hyperbolic embeddings, and embeddings with uncertainty; verypreliminary 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 furtherextensions that will soon be added to the library.
Performance and Examples
UMAP is very efficient at embedding large high dimensional datasets. Inparticular it scales well with both input dimension and embedding dimension.For the best possible performance we recommend installing the nearest neighborcomputation library pynndescent .UMAP will work without it, but if installed it will run faster, particularly onmulticore machines.
For a problem such as the 784-dimensional MNIST digits dataset with70000 data samples, UMAP can complete the embedding in under a minute (ascompared 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 42seconds (with pynndescent installed and after numba jit warmup)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 isthe more recent “Fashion MNIST” dataset of images of fashion items (again70000 data sample in 784 dimensions). UMAPproduced this embedding in 49 seconds (n_neighbors=5, min_dist=0.1):
The UCI shuttle dataset (43500 sample in 8 dimensions) embeds well undercorrelation distance in 44 seconds (note the longer timerequired for correlation distance computations):
Plotting
Adobe cs3 download for pc. 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 andattempts to make sensible decisions to avoid overplotting and other pitfalls. Anexample of use:
The plotting package offers basic plots, as well as interactive plots with hovertools and various diagnostic plotting options. See the documentation for more details.
Help and Support
Documentation is at Read the Docs.The documentation includes a FAQ thatmay answer your questions. If you still have questions then pleaseopen an issueand 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 youwould cite the paper from the Journal of Open Source Software:
If you would like to cite this algorithm in your work the ArXiv paper is thecurrent reference:
License
The umap package is 3-clause BSD licensed.
We would like to note that the umap package makes heavy use ofNumFOCUS sponsored projects, and would not be possible withouttheir support of those projects, so please consider contributing to NumFOCUS.
Contributing
Contributions are more than welcome! There are lots of opportunitiesfor potential projects, so please get in touch if you would like tohelp out. Everything from code to notebooks toexamples and documentation are all equally valuable so please don’t feelyou can’t contribute. To contribute pleasefork the projectmake your changes andsubmit a pull request. We will do our best to work through any issues withyou and get your code merged into the main branch.
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