An R package implementing the UMAP dimensionality reduction method.
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An R implementation of the Uniform Manifold Approximation and Projection (UMAP) method for dimensionality reduction (McInnes et al. 2018), that also implements the supervised and metric (out-of-sample) learning extensions to the basic method. Translated from the Python implementation.
August 1 2020 New metric supported: Pearson correlation (with
metric = "correlation"). This should give similar results to the Python UMAP (and sklearn) implementation of the
March 16 2020 A new version (0.1.8) is on CRAN. This is a minor release in terms of features, but you can now export the UMAP graph (https://github.com/jlmelville/uwot/issues/47), and there are some bug fixes for: loading Annoy indexes (https://github.com/jlmelville/uwot/issues/31), reproducibility across platforms (https://github.com/jlmelville/uwot/issues/46) and we no longer use RcppParallel for the multi-threading support, which should lead to fewer installation problems.
March 4 2020 I had to cancel my submission of version 0.1.7 to CRAN because of a broken example in a library using uwot. In the mean time I have switched to using
std::threadrather than tinythread++.
March 1 2020 Version 0.1.6 was rejected from CRAN due to undefined behavior issues that originate from RcppAnnoy and RcppParallel. I am hopeful that the Annoy behavior is fixed and a suitable version of RcppAnnoy will be released onto CRAN eventually. The RcppParallel issues originate with the use of tbb and seems much harder to deal with. As there is no way to use RcppParallel without tbb yet, I am temporarily replacing the use of RcppParallel with just a subset of the code needed to run parallel for loops with the tinythread++ library.
December 4 2019 Version 0.1.5 released on CRAN. This fixes a couple of crash bugs, including one where the R API was being called from inside a thread. This may have been causing the issues seen by users of monocle and seurat.
September 23 2019 Version 0.1.4 released on CRAN. This ensures compatibility with RcppAnnoy 0.0.13 when using
April 6 2019. uwot is now on CRAN. Also, some minor-to-horrible bugs in the
lvishperplexity routine have been fixed.
March 27 2019. Default behavior of the stochastic gradient descent optimization has changed again: the random number generator is now from the PCG family, linked via the dqrng package. This replaces the old routine, based on my translation of the Python UMAP implementation of the Tausworthe "taus88" PRNG into C++. If you have any concern about the quality of the random numbers used to optimize UMAP, stick with this new default PRNG. However it is slower, so to get the old behavior back set
pcg_rand = FALSE.
For visualization purposes, it seems reasonable to use the old PRNG (
pcg_rand = FALSE), along with multiple threads during SGD (
n_sgd_threads = "auto"), and the UMAP gradient approximation (
approx_pow = TRUE), which combined will show a very noticeable speed up during optimization. I have added a new parameter,
fast_sgd, which if set to
TRUE, sets these options for you.
uwotmakes use of C++ code which must be compiled. You may have to carry out a few extra steps before being able to build this package:
Windows: install Rtools and ensure
C:\Rtools\binis on your path.
Mac OS X: using a custom
~/.R/Makevarsmay cause linking errors. This sort of thing is a potential problem on all platforms but seems to bite Mac owners more. The R for Mac OS X FAQ may be helpful here to work out what you can get away with. To be on the safe side, I would advise building
uwotwithout a custom
See function man page for help
Non-numeric columns are ignored, so in a lot of cases you can pass a data
frame directly to umap
iris_umap 100-1000 columns) using PCA to reduce
dimensionality is highly recommended to avoid the nearest neighbor search
taking a long time. Keeping only 50 dimensions can speed up calculations
without affecting the visualization much
Apart from the man pages in R: you may be interested in:
uwotoutput to the Python UMAP implementation.
uwotrelies on the underlying compiler and C++ standard library on your machine and this can result in differences in output even with the same input data, arguments, packages and R version. If you require reproducibility between machines, it is strongly suggested that you stick with the same OS and compiler version on all of them (e.g. a fixed LTS of a Linux distro and gcc version). Otherwise, the following can help:
tumapmethod instead of
umap. This avoid the use of
std::powin gradient calculations. This also has the advantage of being faster to optimize. However, this gives larger clusters in the output, and you don't have the ability to control that with
umap, it's better to provide
bdirectly with a fixed precision rather than allowing them to be calculated via the
min_distparameters. For default UMAP, use
a = 1.8956, b = 0.8006.
approx_pow = TRUE, which avoids the use of the
init = "spca"rather than
init = "spectral"(although the latter is the default and preferred method for UMAP initialization).
In summary, your chances of reproducibility are increased by using:
For small (N < 4096) and Euclidean distance, exact nearest neighbors are found using the FNN package. Otherwise, approximate nearest neighbors are found using RcppAnnoy. The supported distance metrics (set by themetricparameter) are:
Exactly what constitutes the cosine distance can differ between packages.
uwottries to follow how the Python version of UMAP defines it, which is 1 minus the cosine similarity. This differs slightly from how Annoy defines its angular distance, so be aware that
uwotinternally converts the Annoy version of the distance. Also be aware that the Pearson correlation distance is the cosine distance applied to row-centered vectors.
If you need other metrics, and can generate the nearest neighbor info externally, you can pass the data directly to
nn_methodparameter. See the Nearest Neighbor Data Format section for more details. Please note that the Hamming support is a lot slower than the other metrics. I do not recommend using it if you have more than a few hundred features, and even then expect it to take several minutes during the index building phase in situations where the Euclidean metric would take only a few seconds.
Coordinate initialization uses RSpectra to do the eigendecomposition of the normalized Laplacian.
The optional PCA initialization and initial dimensionality reduction uses irlba.
The smooth k-nearest neighbor distance and stochastic gradient descent optimization routines are written in C++ (using Rcpp, aping the Python code as closely as possible. It is my first time using Rcpp, so let's assume I did a horrible job.
For the datasets I've tried it with, the results look at least reminiscent of those obtained using the official Python implementation. Below are results for the 70,000 MNIST digits (downloaded using the snedata package). On the left is the result of using the official Python UMAP implementation (via the reticulate package). The right hand image is the result of using
| | | |-----------------------------------|---------------------------------| | | |
The project documentation contains some more examples.
December 31 2018 Updated timings, keeping better track of versions numbers.
To get a feel for the performance of
uwot, here are some timings for processing the MNIST dataset, compared with some other methods. I wouldn't take them very seriously, but they show that
uwotis competitive with other methods.
partial_pca = TRUE|14m 13s| |openTSNE (Python)|0.3.0-py37h830ac7b1000|`njobs=4
| 6m 4s| |[openTSNE (Python)](https://github.com/pavlin-policar/openTSNE)|0.3.0-py37h830ac7b_1000|njobs=4, negativegradientmethod="bh"
| 17m 56s| |[FIt-SNE (C++)](https://github.com/KlugerLab/FIt-SNE)|[1.0.0](https://github.com/KlugerLab/FIt-SNE/releases/download/v1.0.0/FItSNE-Windows-1.0.0.zip)|nthreads = 4
|2m 43s| |[FIt-SNE (C++)](https://github.com/KlugerLab/FIt-SNE)|[1.0.0](https://github.com/KlugerLab/FIt-SNE/releases/download/v1.0.0/FItSNE-Windows-1.0.0.zip)|nthreads = 4
+ PCA to 50D|1m 11s| |[LargeVis (C++)](https://github.com/lferry007/LargeVis)|[feb8121](https://github.com/lferry007/LargeVis/commit/feb8121e8eb9652477f7f564903d189ee663796f)|-threads 4
|12m 43s| |[largeVis (R package)](https://github.com/elbamos/largevis)|[e51871e](https://github.com/elbamos/largeVis/commit/e51871e689642177c184527efab668d248717fa9)|saveneighbors = FALSE, saveedges = FALSE, threads = 4
|33m 58s| |uwot::lvish
|[0.0.0.9009](https://github.com/jlmelville/uwot/releases/tag/v0.0.0.9009)|nthreads = 4, nsgdthreads = 4
| 5m 52s| |[UMAP (Python)](https://github.com/lmcinnes/umap)|0.3.7-py37_1000||1m 25s| |[umap (R package)](https://cran.r-project.org/package=umap)|[09f6020](https://github.com/tkonopka/umap/commit/09f60205c572fc1fbfa3e985b48572098fc9b17d)|method = "naive"
| 9m 14s| |uwot|[0.0.0.9009](https://github.com/jlmelville/uwot/releases/tag/v0.0.0.9009)|nthreads = 0
| 3m 11s| |uwot|[0.0.0.9009](https://github.com/jlmelville/uwot/releases/tag/v0.0.0.9009)|nthreads = 4
| 2m 0s| |uwot|[0.0.0.9009](https://github.com/jlmelville/uwot/releases/tag/v0.0.0.9009)|nthreads = 4, approxpow = TRUE
| 1m 24s| |uwot|[0.0.0.9009](https://github.com/jlmelville/uwot/releases/tag/v0.0.0.9009)|nthreads = 4, approxpow = TRUE, nsgdthreads = 4
| 1m 16s| |uwot|[0.0.0.9009](https://github.com/jlmelville/uwot/releases/tag/v0.0.0.9009)|nthreads = 4, approxpow = TRUE, pca = 50`| 48s|
Some notes on how these numbers were generated: I ran this on a Windows machine, using R 3.5.2 and Python 3.7.0. The official LargeVis implementation was built with Visual Studio 2017 Community Edition and may not be properly optimized (the VS solution is available in my fork).
For R packages, the MNIST data was downloaded via the snedata package. For Python packages, the
sklearn.datasets.fetch_mldata('MNIST original')was used. The LargeVis source code contains a MNIST example with the data already present.
For FIt-SNE, I used the provided Windows binary via the R wrapper (and hence used the MNIST data from the
snedatapackage). The reported time for second FIt-SNE entry in the table and includes the 13 seconds it takes to reduce the dimensionality to 50 via PCA, using irlba (this is the same package and dimension reduction used by Rtsne and the last reported time for uwot).
The default openTSNE uses the same FFT approach that FIt-SNE does, so I don't know why it's much slower, apart from the use of the numpy version of FFT rather than the FFTW library, but my understanding was that it shouldn't make much difference with a dataset the size of MNIST. Perhaps this is a Windows thing.
uwot, the bottleneck with typical settings is the nearest neighbor search, which is currently provided by Annoy, whereas the Python implementation uses pynndescent, a nearest neighbor descent approach.
On the optimization side of things,
uwotdefaults are conservative. Using
approx_pow = TRUEuses the
fastPrecisePowapproximation to the
powfunction suggested by Martin Ankerl. For what I think seem like typical values of
0.9) and the squared distance (
1000), I found the maximum relative error was about
0.06. However, I haven't done much testing, beyond looking to see that results from the examples page are not obviously worsened. Results in the table above with
approx_pow = TRUEdo show a worthwhile improvement.
n_sgd_threadswith more than 1 thread will not give reproducible results, but should not behave any worse than LargeVis in that regard, so for many visualization needs, this is also worth trying.
By the deeply unscientific method of me looking at how much memory the R session was taking up according to the Task Manager, processing MNIST with four threads saw the memory usage increase by nearly 1 GB at some points. There are some manual calls to
gc()after some stages to avoid holding onto unused memory for longer than usual. The larger the value of
n_neighbors, the more memory you can expect to take up (see, for example, the discussion of the
You can (and should) adjust the number of threads via the
n_threads, which controls the nearest neighbor and smooth knn calibration, and the
n_sgd_threadsparameter, which controls the number of threads used during optimization. For the
n_threads, the default is half of whatever RcppParallel thinks should be the default. For
n_sgd_threadsthe default is
0, which ensures reproducibility of results with a fixed seed.
I have also exposed the
grain_sizeparameter. If a thread would process less than
grain_sizenumber of items, then no multithreading is carried out.
I've not experienced any problems with using multiple threads for a little while, but if you have any problems with crashing sessions, please file an issue.
distobject. For larger distance matrices, you can pass in a
sparseMatrix(from the Matrix package). Neither approach is supremely efficient at the moment. Proper sparse matrix support is limited by the nearest neighbor search routine: Annoy is intended for dense vectors. Adding a library for sparse nearest neighbor search would be a good extension.
n_sgd_threadsis set larger than
1, then even if you use
set.seed, results of the embeddings are not repeatable, This is because there is no locking carried out on the underlying coordinate matrix, and work is partitioned by edge not vertex and a given vertex may be processed by different threads. The order in which reads and writes occur is of course at the whim of the thread scheduler. This is the same behavior as largeVis.
uwoton anything much larger than MNIST and Fashion MNIST (so at least around 100,000 rows with 500-1,000 columns works fine). Bear in mind that Annoy itself says it works best with dimensions < 100, but still works "surprisingly well" up to 1000.
pcaoption to reduce the dimensionality, e.g
pca = 100.
umap(and the Laplacian Eigenmap initialization,
init = "laplacian") can sometimes run into problems. If it fails to converge it will fall back to random initialization, but on occasion I've seen it take an extremely long time (a couple of hours) to converge. Recent changes have hopefully reduced the chance of this happening, but if initialization is taking more than a few minutes, I suggest stopping the calculation and using the scaled PCA (
init = "spca") instead.
R CMD checkcurrently reports the following note:
GNU make is a SystemRequirements., which is expected and due to using RcppParallel. On Linux, it sometimes notes that the
libssub-directory is over 1 MB. I am unsure if this is anything to worry about.
Some other dimensionality reduction methods are also available in
If you choose the UMAP curve parameters to be
a = 1and
b = 1, you get back the Cauchy distribution used in t-Distributed Stochastic Neighbor Embedding and LargeVis. This also happens to significantly simplify the gradient leading to a noticeable speed-up: for MNIST, I saw the optimization time drop from 66 seconds to 18 seconds. The trade off is that you will see larger, more spread-out clusters than with the typical UMAP settings (they're still more compact than you see in t-SNE, however). To try t-UMAP, use the
Note that usingumap(a = 1, b = 1)doesn't use the simplified gradient, so you won't see any speed-up that way.
lvish: a LargeVis-ish method
As UMAP's implementation is similar to LargeVis in some respects, this package also offers a LargeVis-like method,lvish:# perplexity, init and n_epoch values shown are the defaults # use perplexity instead of n_neighbors to control local neighborhood size mnist_lv
Althoughlvishis like the real LargeVis in terms of the input weights, output weight function and gradient, and so should give results that resemble the real thing, note that:
umap, where no scaling is carried out. Scaling can be controlled by the
search_kparameter is twice as large than Annoy's default to compensate.
n_trees, is not dynamically chosen based on data set size. In LargeVis, it ranges between 10 (for N < 100,000) and 100 (for N > 5,000,000). The
lvishdefault of 50 would cover datasets up to N = 5,000,000, and combined with the default
search_k, seems suitable for the datasets I've looked at.
umap. You may be able to get away with fewer epochs, and using the UMAP initialization of
init = "spectral", rather than the default Gaussian random initialization (
init = "lvrand") can help.
The left-hand image below is the result of running the official LargeVis implementation on MNIST. The image on the right is that from running
lvishwith its default settings (apart from setting
n_threads = 8). Given they were both initialized from different random configurations, there's no reason to believe they would be identical, but they look pretty similar:
| | | |-----------------------------------------------|-----------------------------------------| | | |
Because the default number of neighbors is 3 times the
perplexity, and the default
perplexity = 50, the nearest neighbor search needs to find 150 nearest neighbors per data point, an order of magnitude larger than the UMAP defaults. This leads to a less sparse input graph and hence more edges to sample. Combined with the increased number of epochs, expect
lvishto be slower than
umap: with default single-threaded settings, it took about 20 minutes to embed the MNIST data under the same circumstances as described in the "Performance" section. With
n_threads = 4, it took 7 minutes. In addition, storing those extra edges requires a lot more memory than the
umapdefaults: my R session increased by around 3.2 GB, versus 1 GB for
As an alternative to the usual Gaussian input weight function, you can use the k-nearest neighbor graph itself, by setting
kernel = "knn". This will give each edge between neighbors a uniform weight equal to 1/
perplexity, which leads to each row's probability distribution having the target
perplexity. This matrix will then be symmetrized in the usual way. The advantage of this is that the number of neighbors is reduced to the same as the perplexity (indeed, the
n_neighborsparameter is ignored with this setting), and leads to less memory usage and a faster runtime. You can also get away with setting the perplexity to a much lower value than usual with this kernel (e.g.
perplexity = 15) and get closer to UMAP's performance. If you use the default LargeVis random initialization, you will still need more epochs than UMAP, but you can still expect to see a big improvement. Something like the following works for MNIST:
See the lvish examples page for more results.
Mixed Data Types
The default approach of UMAP is that all your data is numeric and will be treated as one block using the Euclidean distance metric. To use a different metric, set themetricparameter, e.g.metric = "cosine".
Treating the data as one block may not always be appropriate.uwotnow supports a highly experimental approach to mixed data types. It is not based on any deep understanding of topology and sets, so consider it subject to change, breakage or completely disappearing.
To use different metrics for different parts of a data frame, pass a list to themetricparameter. The name of each item is the metric to use and the value is a vector containing the names of the columns (or their integer id, but I strongly recommend names) to apply that metric to, e.g.:metric = list("euclidean" = c("A1", "A2"), "cosine" = c("B1", "B2", "B3"))
this will treat columnsA1andA2as one block of data, and generate neighbor data using the Euclidean distance, while a different set of neighbors will be generated with columnsB1,B2andB3, using the cosine distance. This will create two different simplicial sets. The final set used for optimization is the intersection of these two sets. This is exactly the same process that is used when carrying out supervised UMAP (except the contribution is always equal between the two sets and can't be controlled by the user).
You can repeat the same metric multiple times. For example, to treat the petal and sepal data separately in theirisdataset, but to use Euclidean distances for both, use:metric = list("euclidean" = c("Petal.Width", "Petal.Length"), "euclidean" = c("Sepal.Width", "Sepal.Length"))
As theirisexample shows, using column names can be very verbose. Integer indexing is supported, so the equivalent of the above using integer indexing into the columns ofirisis:metric = list("euclidean" = 3:4, "euclidean" = 1:2)
but internally,uwotstrips out the non-numeric columns from the data, and if you use Z-scaling (i.e. specifyscale = "Z"), zero variance columns will also be removed. This is very likely to change the index of the columns. If you really want to use numeric column indexes, I strongly advise not using thescaleargument and re-arranging your data frame if necessary so that all non-numeric columns come after the numeric columns.
supervised UMAP allows for a factor column to be used. You may now also specify factor columns in theXdata. Use the specialmetricname"categorical". For example, to use theSpeciesfactor in standard UMAP foririsalong with the usual four numeric columns, use:metric = list("euclidean" = 1:4, "categorical" = "Species")
Factor columns are treated differently from numeric columns:
cat2, and you would like them included in UMAP, you should write:
metric = list("categorical" = "cat1", "categorical" = "cat2", ...)
As a convenience, you can also write:
metric = list("categorical" = c("cat1", "cat2"), ...)
but that doesn't combine
cat2into one block, just saves some typing.
metricthat specifies only
categoricalentries. You must specify at least one of the standard Annoy metrics for numeric data. For
iris, the following is an error:
# wrong and bad metric = list("categorical" = "Species")
Specifying some numeric columns is required:
# OK metric = list("categorical" = "Species", "euclidean" = 1:4)
metricare still removed as usual.
ret_model = TRUEand so does not affect the project of data used in
umap_transform. You can still use the UMAP model to project new data, but factor columns in the new data are ignored (effectively working like supervised UMAP).
Some global parameters can be overridden for a specific data block by providing a list as the value for the metric, containing the vector of columns as the only unnamed element, and then the over-riding keyword arguments. An example:
umap(X, pca = 40, pcacenter = TRUE, metric = list( euclidean = 1:200, euclidean = list(201:300, pca = NULL), manhattan = list(300:500, pcacenter = FALSE) ))
In this case, the first
euclideanblock with be reduced to 40 dimensions by PCA with centering applied. The second
euclideanblock will not have PCA applied to it. The
manhattanblock will have PCA applied to it, but no centering is carried out.
pca_centerare supported for overriding by this method, because this feature exists only to allow for the case where you have mixed real-valued and binary data, and you want to carry out PCA on both. It's typical to carry out centering on real-value data before PCA, but not to do so with binary data.
The handling of
ydata has been extended to allow for data frames, and
metric: multiple numeric blocks with different metrics can be specified, and categorical data can be specified with
categorical. However, unlike
X, the default behavior for
yis to include all factor columns. Any numeric data found will be treated as one block, so if you have multiple numeric columns that you want treated separately, you should specify each column separately:
target_metric = list("euclidean" = 1, "euclidean" = 2, ...)
I suspect that the vast majority of
ydata is one column, so the default behavior will be fine most of the time.
The Python implementation of UMAP supports lots of distance metrics;
uwotdoes not, because it depends on the distance metrics supported by
RcppAnnoy, which in turn depends on those supported by
Annoy. For more flexibility, at the cost of convenience, you can generate nearest neighbor data for
Xby some other means and pass that to
lvish) directly via the
The format expected by
listcontaining the following two entries:
idx: a matrix of dimension
n_vertices x n_neighbors, where each row contains the indexes (starting at
1) of the nearest neighbors of each item (vertex) in the dataset. Each item is always the nearest neighbor of itself, so the first element in row
ishould always be
i. If it isn't then either you are using a really weird non-metric distance or your approximate nearest neighbor method is returning way too approximate results. In either case, you should expect bad results.
dist: a matrix of dimension
n_vertices x n_neighbors, where each row contains the distances of the nearest neighbors of each item (vertex) in the dataset, in Each item is always the nearest neighbor of itself, so the first element in row
ishould always be
If you use pre-computed nearest neighbor data, be aware that:
Xto NULL, as long as you don't try and use an initialization method that makes use of
init = "pca"or
init = "spca").
ret_model = TRUEdoes not produce a valid model.
umap_transformwill not work with this setting.
If you set
ret_nn = TRUE, the return value of
umapwill be a list, and the
nnitem contains the nearest neighbor data in a format that can be used with
nn_method. This is handy if you are going to be running UMAP multiple times with the same data and
scalesettings, because the nearest neighbor calculation can be the most time-consuming part of the calculation.
Normally the contents of
nnis itself a list, the value of which is the nearest neighbor data. The name is the type of metric that generated the data. As an example, here's what the first few items of the
iris5-NN data should look like:
lapply(umap(iris, ret_nn = TRUE, n_neighbors = 5)$nn$euclidean, head)
idx[,1] [,2] [,3] [,4] [,5] [1,] 1 18 5 40 29 [2,] 2 35 46 13 10 [3,] 3 48 4 7 13 [4,] 4 48 30 31 3 [5,] 5 38 1 18 41 [6,] 6 19 11 49 45
$dist [,1] [,2] [,3] [,4] [,5] [1,] 0 0.1000000 0.1414214 0.1414214 0.1414214 [2,] 0 0.1414214 0.1414214 0.1414214 0.1732051 [3,] 0 0.1414214 0.2449490 0.2645751 0.2645751 [4,] 0 0.1414214 0.1732051 0.2236068 0.2449490 [5,] 0 0.1414214 0.1414214 0.1732051 0.1732051 [6,] 0 0.3316625 0.3464102 0.3605551 0.3741657
If for some reason you specify
ret_nnwhile supplying precomputed nearest neighbor data to
nn_method, the returned data should be identical to what you passed in, and the list item names will be
As discussed under the Mixed Data Types section, you can apply multiple distance metrics to different parts of matrix or data frame input data. if you do this, then
ret_nnwill return all the neighbor data. The list under
nnwill now contain as many items as metrics, in the order they were specified. For instance, if the
metric = list("euclidean" = c("Petal.Width", "Petal.Length"), "cosine" = c("Sepal.Width", "Sepal.Length"))
nnlist will contain two list entries. The first will be called
euclideanand the second
If you have access to multiple distance metrics, you may also provide multiple precomputed neighbor data to
nn_methodin the same format: a list of lists, where each sublist has the same format as described above (i.e. the two matrices,
dist). The names of the list items are ignored, so you don't need to set them. Roughly, do something like this:
The different neighbor data must all have the same number of neighbors, i.e. the number of columns in all the matrices must be the same.
If you are using supervised UMAP with a numericy, then you can also pass nearest neighbor data toy, using the same format as above. In this case the nearest neighbors should be with respect to the data iny.
Note that you cannot pass categoricalyas nearest neighbor data. This is because the processing of the data goes through a different code path that doesn't directly calculate nearest neighbors: ifyis a factor, when there are only a small number of levels, the number of neighbors of an item can be vastly larger thann_neighbors.
Nearest neighbor data foryis not returned fromumapfor re-use.