Carry out dimensionality reduction of a dataset using the Uniform Manifold Approximation and Projection (UMAP) method (McInnes et al., 2018). Some of the following help text is lifted verbatim from the Python reference implementation at https://github.com/lmcinnes/umap.

## Usage

```
umap(
X,
n_neighbors = 15,
n_components = 2,
metric = "euclidean",
n_epochs = NULL,
learning_rate = 1,
scale = FALSE,
init = "spectral",
init_sdev = NULL,
spread = 1,
min_dist = 0.01,
set_op_mix_ratio = 1,
local_connectivity = 1,
bandwidth = 1,
repulsion_strength = 1,
negative_sample_rate = 5,
a = NULL,
b = NULL,
nn_method = NULL,
n_trees = 50,
search_k = 2 * n_neighbors * n_trees,
approx_pow = FALSE,
y = NULL,
target_n_neighbors = n_neighbors,
target_metric = "euclidean",
target_weight = 0.5,
pca = NULL,
pca_center = TRUE,
pcg_rand = TRUE,
fast_sgd = FALSE,
ret_model = FALSE,
ret_nn = FALSE,
ret_extra = c(),
n_threads = NULL,
n_sgd_threads = 0,
grain_size = 1,
tmpdir = tempdir(),
verbose = getOption("verbose", TRUE),
batch = FALSE,
opt_args = NULL,
epoch_callback = NULL,
pca_method = NULL,
binary_edge_weights = FALSE,
dens_scale = NULL,
seed = NULL,
nn_args = list()
)
```

## Arguments

- X
Input data. Can be a

`data.frame`

,`matrix`

,`dist`

object or`sparseMatrix`

. Matrix and data frames should contain one observation per row. Data frames will have any non-numeric columns removed, although factor columns will be used if explicitly included via`metric`

(see the help for`metric`

for details). A sparse matrix is interpreted as a distance matrix, and is assumed to be symmetric, so you can also pass in an explicitly upper or lower triangular sparse matrix to save storage. There must be at least`n_neighbors`

non-zero distances for each row. Both implicit and explicit zero entries are ignored. Set zero distances you want to keep to an arbitrarily small non-zero value (e.g.`1e-10`

).`X`

can also be`NULL`

if pre-computed nearest neighbor data is passed to`nn_method`

, and`init`

is not`"spca"`

or`"pca"`

.- n_neighbors
The size of local neighborhood (in terms of number of neighboring sample points) used for manifold approximation. Larger values result in more global views of the manifold, while smaller values result in more local data being preserved. In general values should be in the range

`2`

to`100`

.- n_components
The dimension of the space to embed into. This defaults to

`2`

to provide easy visualization, but can reasonably be set to any integer value in the range`2`

to`100`

.- metric
Type of distance metric to use to find nearest neighbors. For

`nn_method = "annoy"`

this can be one of:`"euclidean"`

(the default)`"cosine"`

`"manhattan"`

`"hamming"`

`"correlation"`

(a distance based on the Pearson correlation)`"categorical"`

(see below)

For

`nn_method = "hnsw"`

this can be one of:`"euclidean"`

`"cosine"`

`"correlation"`

If rnndescent is installed and

`nn_method = "nndescent"`

is specified then many more metrics are avaiable, including:`"braycurtis"`

`"canberra"`

`"chebyshev"`

`"dice"`

`"hamming"`

`"hellinger"`

`"jaccard"`

`"jensenshannon"`

`"kulsinski"`

`"rogerstanimoto"`

`"russellrao"`

`"sokalmichener"`

`"sokalsneath"`

`"spearmanr"`

`"symmetrickl"`

`"tsss"`

`"yule"`

For more details see the package documentation of

`rnndescent`

. For`nn_method = "fnn"`

, the distance metric is always "euclidean".If

`X`

is a data frame or matrix, then multiple metrics can be specified, by passing a list to this argument, where the name of each item in the list is one of the metric names above. The value of each list item should be a vector giving the names or integer ids of the columns to be included in a calculation, e.g.`metric = list(euclidean = 1:4, manhattan = 5:10)`

.Each metric calculation results in a separate fuzzy simplicial set, which are intersected together to produce the final set. Metric names can be repeated. Because non-numeric columns are removed from the data frame, it is safer to use column names than integer ids.

Factor columns can also be used by specifying the metric name

`"categorical"`

. Factor columns are treated different from numeric columns and although multiple factor columns can be specified in a vector, each factor column specified is processed individually. If you specify a non-factor column, it will be coerced to a factor.For a given data block, you may override the

`pca`

and`pca_center`

arguments for that block, by providing a list with one unnamed item containing the column names or ids, and then any of the`pca`

or`pca_center`

overrides as named items, e.g.`metric = list(euclidean = 1:4, manhattan = list(5:10, pca_center = FALSE))`

. This exists to allow mixed binary and real-valued data to be included and to have PCA applied to both, but with centering applied only to the real-valued data (it is typical not to apply centering to binary data before PCA is applied).- n_epochs
Number of epochs to use during the optimization of the embedded coordinates. By default, this value is set to

`500`

for datasets containing 10,000 vertices or less, and`200`

otherwise. If`n_epochs = 0`

, then coordinates determined by`"init"`

will be returned.- learning_rate
Initial learning rate used in optimization of the coordinates.

- scale
Scaling to apply to

`X`

if it is a data frame or matrix:`"none"`

or`FALSE`

or`NULL`

No scaling.`"Z"`

or`"scale"`

or`TRUE`

Scale each column to zero mean and variance 1.`"maxabs"`

Center each column to mean 0, then divide each element by the maximum absolute value over the entire matrix.`"range"`

Range scale the entire matrix, so the smallest element is 0 and the largest is 1.`"colrange"`

Scale each column in the range (0,1).

For UMAP, the default is

`"none"`

.- init
Type of initialization for the coordinates. Options are:

`"spectral"`

Spectral embedding using the normalized Laplacian of the fuzzy 1-skeleton, with Gaussian noise added.`"normlaplacian"`

. Spectral embedding using the normalized Laplacian of the fuzzy 1-skeleton, without noise.`"random"`

. Coordinates assigned using a uniform random distribution between -10 and 10.`"lvrandom"`

. Coordinates assigned using a Gaussian distribution with standard deviation 1e-4, as used in LargeVis (Tang et al., 2016) and t-SNE.`"laplacian"`

. Spectral embedding using the Laplacian Eigenmap (Belkin and Niyogi, 2002).`"pca"`

. The first two principal components from PCA of`X`

if`X`

is a data frame, and from a 2-dimensional classical MDS if`X`

is of class`"dist"`

.`"spca"`

. Like`"pca"`

, but each dimension is then scaled so the standard deviation is 1e-4, to give a distribution similar to that used in t-SNE. This is an alias for`init = "pca", init_sdev = 1e-4`

.`"agspectral"`

An "approximate global" modification of`"spectral"`

which all edges in the graph to a value of 1, and then sets a random number of edges (`negative_sample_rate`

edges per vertex) to 0.1, to approximate the effect of non-local affinities.A matrix of initial coordinates.

For spectral initializations, (

`"spectral"`

,`"normlaplacian"`

,`"laplacian"`

,`"agspectral"`

), if more than one connected component is identified, no spectral initialization is attempted. Instead a PCA-based initialization is attempted. If`verbose = TRUE`

the number of connected components are logged to the console. The existence of multiple connected components implies that a global view of the data cannot be attained with this initialization. Increasing the value of`n_neighbors`

may help.- init_sdev
If non-

`NULL`

, scales each dimension of the initialized coordinates (including any user-supplied matrix) to this standard deviation. By default no scaling is carried out, except when`init = "spca"`

, in which case the value is`0.0001`

. Scaling the input may help if the unscaled versions result in initial coordinates with large inter-point distances or outliers. This usually results in small gradients during optimization and very little progress being made to the layout. Shrinking the initial embedding by rescaling can help under these circumstances. Scaling the result of`init = "pca"`

is usually recommended and`init = "spca"`

as an alias for`init = "pca", init_sdev = 1e-4`

but for the spectral initializations the scaled versions usually aren't necessary unless you are using a large value of`n_neighbors`

(e.g.`n_neighbors = 150`

or higher). For compatibility with recent versions of the Python UMAP package, if you are using`init = "spectral"`

, then you should also set`init_sdev = "range"`

, which will range scale each of the columns containing the initial data between 0-10. This is not set by default to maintain backwards compatibility with previous versions of uwot.- spread
The effective scale of embedded points. In combination with

`min_dist`

, this determines how clustered/clumped the embedded points are.- min_dist
The effective minimum distance between embedded points. Smaller values will result in a more clustered/clumped embedding where nearby points on the manifold are drawn closer together, while larger values will result on a more even dispersal of points. The value should be set relative to the

`spread`

value, which determines the scale at which embedded points will be spread out.- set_op_mix_ratio
Interpolate between (fuzzy) union and intersection as the set operation used to combine local fuzzy simplicial sets to obtain a global fuzzy simplicial sets. Both fuzzy set operations use the product t-norm. The value of this parameter should be between

`0.0`

and`1.0`

; a value of`1.0`

will use a pure fuzzy union, while`0.0`

will use a pure fuzzy intersection.- local_connectivity
The local connectivity required – i.e. the number of nearest neighbors that should be assumed to be connected at a local level. The higher this value the more connected the manifold becomes locally. In practice this should be not more than the local intrinsic dimension of the manifold.

- bandwidth
The effective bandwidth of the kernel if we view the algorithm as similar to Laplacian Eigenmaps. Larger values induce more connectivity and a more global view of the data, smaller values concentrate more locally.

- repulsion_strength
Weighting applied to negative samples in low dimensional embedding optimization. Values higher than one will result in greater weight being given to negative samples.

- negative_sample_rate
The number of negative edge/1-simplex samples to use per positive edge/1-simplex sample in optimizing the low dimensional embedding.

- a
More specific parameters controlling the embedding. If

`NULL`

these values are set automatically as determined by`min_dist`

and`spread`

.- b
More specific parameters controlling the embedding. If

`NULL`

these values are set automatically as determined by`min_dist`

and`spread`

.- nn_method
Method for finding nearest neighbors. Options are:

`"fnn"`

. Use exact nearest neighbors via the FNN package.`"annoy"`

Use approximate nearest neighbors via the RcppAnnoy package.`"hnsw"`

Use approximate nearest neighbors with the Hierarchical Navigable Small World (HNSW) method (Malkov and Yashunin, 2018) via the RcppHNSW package.`RcppHNSW`

is not a dependency of this package: this option is only available if you have installed`RcppHNSW`

yourself. Also, HNSW only supports the following arguments for`metric`

and`target_metric`

:`"euclidean"`

,`"cosine"`

and`"correlation"`

.`"nndescent"`

Use approximate nearest neighbors with the Nearest Neighbor Descent method (Dong et al., 2011) via the rnndescent package.`rnndescent`

is not a dependency of this package: this option is only available if you have installed`rnndescent`

yourself.

By default, if

`X`

has less than 4,096 vertices, the exact nearest neighbors are found. Otherwise, approximate nearest neighbors are used. You may also pass pre-calculated nearest neighbor data to this argument. It must be one of two formats, either a list consisting of two elements:`"idx"`

. A`n_vertices x n_neighbors`

matrix containing the integer indexes of the nearest neighbors in`X`

. Each vertex is considered to be its own nearest neighbor, i.e.`idx[, 1] == 1:n_vertices`

.`"dist"`

. A`n_vertices x n_neighbors`

matrix containing the distances of the nearest neighbors.

or a sparse distance matrix of type

`dgCMatrix`

, with dimensions`n_vertices x n_vertices`

. Distances should be arranged by column, i.e. a non-zero entry in row`j`

of the`i`

th column indicates that the`j`

th observation in`X`

is a nearest neighbor of the`i`

th observation with the distance given by the value of that element. The`n_neighbors`

parameter is ignored when using precomputed nearest neighbor data. If using the sparse distance matrix input, each column can contain a different number of neighbors.- n_trees
Number of trees to build when constructing the nearest neighbor index. The more trees specified, the larger the index, but the better the results. With

`search_k`

, determines the accuracy of the Annoy nearest neighbor search. Only used if the`nn_method`

is`"annoy"`

. Sensible values are between`10`

to`100`

.- search_k
Number of nodes to search during the neighbor retrieval. The larger k, the more the accurate results, but the longer the search takes. With

`n_trees`

, determines the accuracy of the Annoy nearest neighbor search. Only used if the`nn_method`

is`"annoy"`

.- approx_pow
If

`TRUE`

, use an approximation to the power function in the UMAP gradient, from https://martin.ankerl.com/2012/01/25/optimized-approximative-pow-in-c-and-cpp/. Ignored if`dens_scale`

is non-`NULL`

.- y
Optional target data for supervised dimension reduction. Can be a vector, matrix or data frame. Use the

`target_metric`

parameter to specify the metrics to use, using the same syntax as`metric`

. Usually either a single numeric or factor column is used, but more complex formats are possible. The following types are allowed:Factor columns with the same length as

`X`

.`NA`

is allowed for any observation with an unknown level, in which case UMAP operates as a form of semi-supervised learning. Each column is treated separately.Numeric data.

`NA`

is*not*allowed in this case. Use the parameter`target_n_neighbors`

to set the number of neighbors used with`y`

. If unset,`n_neighbors`

is used. Unlike factors, numeric columns are grouped into one block unless`target_metric`

specifies otherwise. For example, if you wish columns`a`

and`b`

to be treated separately, specify`target_metric = list(euclidean = "a", euclidean = "b")`

. Otherwise, the data will be effectively treated as a matrix with two columns.Nearest neighbor data, consisting of a list of two matrices,

`idx`

and`dist`

. These represent the precalculated nearest neighbor indices and distances, respectively. This is the same format as that expected for precalculated data in`nn_method`

. This format assumes that the underlying data was a numeric vector. Any user-supplied value of the`target_n_neighbors`

parameter is ignored in this case, because the the number of columns in the matrices is used for the value. Multiple nearest neighbor data using different metrics can be supplied by passing a list of these lists.

Unlike

`X`

, all factor columns included in`y`

are automatically used.- target_n_neighbors
Number of nearest neighbors to use to construct the target simplicial set. Default value is

`n_neighbors`

. Applies only if`y`

is non-`NULL`

and`numeric`

.- target_metric
The metric used to measure distance for

`y`

if using supervised dimension reduction. Used only if`y`

is numeric.- target_weight
Weighting factor between data topology and target topology. A value of 0.0 weights entirely on data, a value of 1.0 weights entirely on target. The default of 0.5 balances the weighting equally between data and target. Only applies if

`y`

is non-`NULL`

.- pca
If set to a positive integer value, reduce data to this number of columns using PCA. Doesn't applied if the distance

`metric`

is`"hamming"`

, or the dimensions of the data is larger than the number specified (i.e. number of rows and columns must be larger than the value of this parameter). If you have > 100 columns in a data frame or matrix, reducing the number of columns in this way may substantially increase the performance of the nearest neighbor search at the cost of a potential decrease in accuracy. In many t-SNE applications, a value of 50 is recommended, although there's no guarantee that this is appropriate for all settings.- pca_center
If

`TRUE`

, center the columns of`X`

before carrying out PCA. For binary data, it's recommended to set this to`FALSE`

.- pcg_rand
If

`TRUE`

, use the PCG random number generator (O'Neill, 2014) during optimization. Otherwise, use the faster (but probably less statistically good) Tausworthe "taus88" generator. The default is`TRUE`

.- fast_sgd
If

`TRUE`

, then the following combination of parameters is set:`pcg_rand = TRUE`

,`n_sgd_threads = "auto"`

and`approx_pow = TRUE`

. The default is`FALSE`

. Setting this to`TRUE`

will speed up the stochastic optimization phase, but give a potentially less accurate embedding, and which will not be exactly reproducible even with a fixed seed. For visualization,`fast_sgd = TRUE`

will give perfectly good results. For more generic dimensionality reduction, it's safer to leave`fast_sgd = FALSE`

. If`fast_sgd = TRUE`

, then user-supplied values of`pcg_rand`

,`n_sgd_threads`

, and`approx_pow`

are ignored.- ret_model
If

`TRUE`

, then return extra data that can be used to add new data to an existing embedding via`umap_transform`

. The embedded coordinates are returned as the list item`embedding`

. If`FALSE`

, just return the coordinates. This parameter can be used in conjunction with`ret_nn`

and`ret_extra`

. Note that some settings are incompatible with the production of a UMAP model: external neighbor data (passed via a list to`nn_method`

), and factor columns that were included via the`metric`

parameter. In the latter case, the model produced is based only on the numeric data. A transformation using new data is possible, but the factor columns in the new data are ignored. Note that setting`ret_model = TRUE`

forces the use of the approximate nearest neighbors method. Because small datasets would otherwise use exact nearest neighbor calculations, setting`ret_model = TRUE`

means that different results may be returned for small datasets in terms of both the returned nearest neighbors (if requested) and the final embedded coordinates, compared to`ret_model = FALSE`

, even if the random number seed is fixed. To avoid this, explicitly set`nn_method = "annoy"`

in the`ret_model = FALSE`

case.- ret_nn
If

`TRUE`

, then in addition to the embedding, also return nearest neighbor data that can be used as input to`nn_method`

to avoid the overhead of repeatedly calculating the nearest neighbors when manipulating unrelated parameters (e.g.`min_dist`

,`n_epochs`

,`init`

). See the "Value" section for the names of the list items. If`FALSE`

, just return the coordinates. Note that the nearest neighbors could be sensitive to data scaling, so be wary of reusing nearest neighbor data if modifying the`scale`

parameter. This parameter can be used in conjunction with`ret_model`

and`ret_extra`

.- ret_extra
A vector indicating what extra data to return. May contain any combination of the following strings:

`"model"`

Same as setting`ret_model = TRUE`

.`"nn"`

Same as setting`ret_nn = TRUE`

.`"fgraph"`

the high dimensional fuzzy graph (i.e. the fuzzy simplicial set of the merged local views of the input data). The graph is returned as a sparse symmetric N x N matrix of class dgCMatrix-class, where a non-zero entry (i, j) gives the membership strength of the edge connecting vertex i and vertex j. This can be considered analogous to the input probability (or similarity or affinity) used in t-SNE and LargeVis. Note that the graph is further sparsified by removing edges with sufficiently low membership strength that they would not be sampled by the probabilistic edge sampling employed for optimization and therefore the number of non-zero elements in the matrix is dependent on`n_epochs`

. If you are only interested in the fuzzy input graph (e.g. for clustering), setting`n_epochs = 0`

will avoid any further sparsifying. Be aware that setting `binary_edge_weights = TRUE` will affect this graph (all non-zero edge weights will be 1).`"sigma"`

the normalization value for each observation in the dataset when constructing the smoothed distances to each of its neighbors. This gives some sense of the local density of each observation in the high dimensional space: higher values of`sigma`

indicate a higher dispersion or lower density.

- n_threads
Number of threads to use (except during stochastic gradient descent). Default is half the number of concurrent threads supported by the system. For nearest neighbor search, only applies if

`nn_method = "annoy"`

. If`n_threads > 1`

, then the Annoy index will be temporarily written to disk in the location determined by`tempfile`

.- n_sgd_threads
Number of threads to use during stochastic gradient descent. If set to > 1, then be aware that if

`batch = FALSE`

, results will*not*be reproducible, even if`set.seed`

is called with a fixed seed before running. Set to`"auto"`

to use the same value as`n_threads`

.- grain_size
The minimum amount of work to do on each thread. If this value is set high enough, then less than

`n_threads`

or`n_sgd_threads`

will be used for processing, which might give a performance improvement if the overhead of thread management and context switching was outweighing the improvement due to concurrent processing. This should be left at default (`1`

) and work will be spread evenly over all the threads specified.- tmpdir
Temporary directory to store nearest neighbor indexes during nearest neighbor search. Default is

`tempdir`

. The index is only written to disk if`n_threads > 1`

and`nn_method = "annoy"`

; otherwise, this parameter is ignored.- verbose
If

`TRUE`

, log details to the console.- batch
If

`TRUE`

, then embedding coordinates are updated at the end of each epoch rather than during the epoch. In batch mode, results are reproducible with a fixed random seed even with`n_sgd_threads > 1`

, at the cost of a slightly higher memory use. You may also have to modify`learning_rate`

and increase`n_epochs`

, so whether this provides a speed increase over the single-threaded optimization is likely to be dataset and hardware-dependent.- opt_args
A list of optimizer parameters, used when

`batch = TRUE`

. The default optimization method used is Adam (Kingma and Ba, 2014).`method`

The optimization method to use. Either`"adam"`

or`"sgd"`

(stochastic gradient descent). Default:`"adam"`

.`beta1`

(Adam only). The weighting parameter for the exponential moving average of the first moment estimator. Effectively the momentum parameter. Should be a floating point value between 0 and 1. Higher values can smooth oscillatory updates in poorly-conditioned situations and may allow for a larger`learning_rate`

to be specified, but too high can cause divergence. Default:`0.5`

.`beta2`

(Adam only). The weighting parameter for the exponential moving average of the uncentered second moment estimator. Should be a floating point value between 0 and 1. Controls the degree of adaptivity in the step-size. Higher values put more weight on previous time steps. Default:`0.9`

.`eps`

(Adam only). Intended to be a small value to prevent division by zero, but in practice can also affect convergence due to its interaction with`beta2`

. Higher values reduce the effect of the step-size adaptivity and bring the behavior closer to stochastic gradient descent with momentum. Typical values are between 1e-8 and 1e-3. Default:`1e-7`

.`alpha`

The initial learning rate. Default: the value of the`learning_rate`

parameter.

- epoch_callback
A function which will be invoked at the end of every epoch. Its signature should be:

`(epoch, n_epochs, coords)`

, where:`epoch`

The current epoch number (between`1`

and`n_epochs`

).`n_epochs`

Number of epochs to use during the optimization of the embedded coordinates.`coords`

The embedded coordinates as of the end of the current epoch, as a matrix with dimensions (N,`n_components`

).

- pca_method
Method to carry out any PCA dimensionality reduction when the

`pca`

parameter is specified. Allowed values are:`"irlba"`

. Uses`prcomp_irlba`

from the irlba package.`"rsvd"`

. Uses 5 iterations of`svdr`

from the irlba package. This is likely to give much faster but potentially less accurate results than using`"irlba"`

. For the purposes of nearest neighbor calculation and coordinates initialization, any loss of accuracy doesn't seem to matter much.`"bigstatsr"`

. Uses`big_randomSVD`

from the bigstatsr package. The SVD methods used in`bigstatsr`

may be faster on systems without access to efficient linear algebra libraries (e.g. Windows).**Note**:`bigstatsr`

is*not*a dependency of uwot: if you choose to use this package for PCA, you*must*install it yourself.`"svd"`

. Uses`svd`

for the SVD. This is likely to be slow for all but the smallest datasets.`"auto"`

(the default). Uses`"irlba"`

, unless more than 50 case`"svd"`

is used.

- binary_edge_weights
If

`TRUE`

then edge weights in the input graph are treated as binary (0/1) rather than real valued. This affects the sampling frequency of neighbors and is the strategy used by the PaCMAP method (Wang and co-workers, 2020). Practical (Böhm and co-workers, 2020) and theoretical (Damrich and Hamprecht, 2021) work suggests this has little effect on UMAP's performance.- dens_scale
A value between 0 and 1. If > 0 then the output attempts to preserve relative local density around each observation. This uses an approximation to the densMAP method (Narayan and co-workers, 2021). The larger the value of

`dens_scale`

, the greater the range of output densities that will be used to map the input densities. This option is ignored if using multiple`metric`

blocks.- seed
Integer seed to use to initialize the random number generator state. Combined with

`n_sgd_threads = 1`

or`batch = TRUE`

, this should give consistent output across multiple runs on a given installation. Setting this value is equivalent to calling`set.seed`

, but it may be more convenient in some situations than having to call a separate function. The default is to not set a seed. If`ret_model = TRUE`

, the seed will be stored in the output model and then used to set the seed inside`umap_transform`

.- nn_args
A list containing additional arguments to pass to the nearest neighbor method. For

`nn_method = "annoy"`

, you can specify`"n_trees"`

and`"search_k"`

, and these will override the`n_trees`

and`search_k`

parameters. For`nn_method = "hnsw"`

, you may specify the following arguments:`M`

The maximum number of neighbors to keep for each vertex. Reasonable values are`2`

to`100`

. Higher values give better recall at the cost of more memory. Default value is`16`

.`ef_construction`

A positive integer specifying the size of the dynamic list used during index construction. A higher value will provide better results at the cost of a longer time to build the index. Default is`200`

.`ef`

A positive integer specifying the size of the dynamic list used during search. This cannot be smaller than`n_neighbors`

and cannot be higher than the number of items in the index. Default is`10`

.

For

`nn_method = "nndescent"`

, you may specify the following arguments:`n_trees`

The number of trees to use in a random projection forest to initialize the search. A larger number will give more accurate results at the cost of a longer computation time. The default of`NULL`

means that the number is chosen based on the number of observations in`X`

.`max_candidates`

The number of potential neighbors to explore per iteration. By default, this is set to`n_neighbors`

or`60`

, whichever is smaller. A larger number will give more accurate results at the cost of a longer computation time.`n_iters`

The number of iterations to run the search. A larger number will give more accurate results at the cost of a longer computation time. By default, this will be chosen based on the number of observations in`X`

. You may also need to modify the convergence criterion`delta`

.`delta`

The minimum relative change in the neighbor graph allowed before early stopping. Should be a value between 0 and 1. The smaller the value, the smaller the amount of progress between iterations is allowed. Default value of`0.001`

means that at least 0.1 neighbor graph must be updated at each iteration.`init`

How to initialize the nearest neighbor descent. By default this is set to`"tree"`

and uses a random project forest. If you set this to`"rand"`

, then a random selection is used. Usually this is less accurate than using RP trees, but for high-dimensional cases, there may be little difference in the quality of the initialization and random initialization will be a lot faster. If you set this to`"rand"`

, then the`n_trees`

parameter is ignored.`pruning_degree_multiplier`

The maximum number of edges per node to retain in the search graph, relative to`n_neighbors`

. A larger value will give more accurate results at the cost of a longer computation time. Default is`1.5`

. This parameter only affects neighbor search when transforming new data with`umap_transform`

.`epsilon`

Controls the degree of the back-tracking when traversing the search graph. Setting this to`0.0`

will do a greedy search with no back-tracking. A larger value will give more accurate results at the cost of a longer computation time. Default is`0.1`

. This parameter only affects neighbor search when transforming new data with`umap_transform`

.`max_search_fraction`

Specifies the maximum fraction of the search graph to traverse. By default, this is set to`1.0`

, so the entire graph (i.e. all items in`X`

) may be visited. You may want to set this to a smaller value if you have a very large dataset (in conjunction with`epsilon`

) to avoid an inefficient exhaustive search of the data in`X`

. This parameter only affects neighbor search when transforming new data with`umap_transform`

.

## Value

A matrix of optimized coordinates, or:

if

`ret_model = TRUE`

(or`ret_extra`

contains`"model"`

), returns a list containing extra information that can be used to add new data to an existing embedding via`umap_transform`

. In this case, the coordinates are available in the list item`embedding`

.**NOTE**: The contents of the`model`

list should*not*be considered stable or part of the public API, and are purposely left undocumented.if

`ret_nn = TRUE`

(or`ret_extra`

contains`"nn"`

), returns the nearest neighbor data as a list called`nn`

. This contains one list for each`metric`

calculated, itself containing a matrix`idx`

with the integer ids of the neighbors; and a matrix`dist`

with the distances. The`nn`

list (or a sub-list) can be used as input to the`nn_method`

parameter.if

`ret_extra`

contains`"fgraph"`

, returns the high dimensional fuzzy graph as a sparse matrix called`fgraph`

, of type dgCMatrix-class.if

`ret_extra`

contains`"sigma"`

, returns a vector of the smooth knn distance normalization terms for each observation as`"sigma"`

and a vector`"rho"`

containing the largest distance to the locally connected neighbors of each observation.if

`ret_extra`

contains`"localr"`

, returns a vector of the estimated local radii, the sum of`"sigma"`

and`"rho"`

.

The returned list contains the combined data from any combination of
specifying `ret_model`

, `ret_nn`

and `ret_extra`

.

## References

Belkin, M., & Niyogi, P. (2002).
Laplacian eigenmaps and spectral techniques for embedding and clustering.
In *Advances in neural information processing systems*
(pp. 585-591).
http://papers.nips.cc/paper/1961-laplacian-eigenmaps-and-spectral-techniques-for-embedding-and-clustering.pdf

Böhm, J. N., Berens, P., & Kobak, D. (2020).
A unifying perspective on neighbor embeddings along the attraction-repulsion spectrum.
*arXiv preprint* *arXiv:2007.08902*.
https://arxiv.org/abs/2007.08902

Damrich, S., & Hamprecht, F. A. (2021).
On UMAP's true loss function.
*Advances in Neural Information Processing Systems*, *34*.
https://proceedings.neurips.cc/paper/2021/hash/2de5d16682c3c35007e4e92982f1a2ba-Abstract.html

Dong, W., Moses, C., & Li, K. (2011, March).
Efficient k-nearest neighbor graph construction for generic similarity measures.
In *Proceedings of the 20th international conference on World Wide Web*
(pp. 577-586).
ACM.
doi:10.1145/1963405.1963487
.

Kingma, D. P., & Ba, J. (2014).
Adam: A method for stochastic optimization.
*arXiv preprint* *arXiv*:1412.6980.
https://arxiv.org/abs/1412.6980

Malkov, Y. A., & Yashunin, D. A. (2018).
Efficient and robust approximate nearest neighbor search using hierarchical
navigable small world graphs.
*IEEE transactions on pattern analysis and machine intelligence*, *42*(4), 824-836.

McInnes, L., Healy, J., & Melville, J. (2018).
UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction
*arXiv preprint* *arXiv*:1802.03426.
https://arxiv.org/abs/1802.03426

Narayan, A., Berger, B., & Cho, H. (2021).
Assessing single-cell transcriptomic variability through density-preserving data visualization.
*Nature biotechnology*, *39*(6), 765-774.
doi:10.1038/s41587-020-00801-7

O’Neill, M. E. (2014).
*PCG: A family of simple fast space-efficient statistically good
algorithms for random number generation*
(Report No. HMC-CS-2014-0905). Harvey Mudd College.

Tang, J., Liu, J., Zhang, M., & Mei, Q. (2016, April).
Visualizing large-scale and high-dimensional data.
In *Proceedings of the 25th International Conference on World Wide Web*
(pp. 287-297).
International World Wide Web Conferences Steering Committee.
https://arxiv.org/abs/1602.00370

Van der Maaten, L., & Hinton, G. (2008).
Visualizing data using t-SNE.
*Journal of Machine Learning Research*, *9* (2579-2605).
https://www.jmlr.org/papers/v9/vandermaaten08a.html

Wang, Y., Huang, H., Rudin, C., & Shaposhnik, Y. (2021).
Understanding How Dimension Reduction Tools Work: An Empirical Approach to Deciphering t-SNE, UMAP, TriMap, and PaCMAP for Data Visualization.
*Journal of Machine Learning Research*, *22*(201), 1-73.
https://www.jmlr.org/papers/v22/20-1061.html

## Examples

```
iris30 <- iris[c(1:10, 51:60, 101:110), ]
# Non-numeric columns are automatically removed so you can pass data frames
# directly in a lot of cases without pre-processing
iris_umap <- umap(iris30, n_neighbors = 5, learning_rate = 0.5, init = "random", n_epochs = 20)
# Faster approximation to the gradient and return nearest neighbors
iris_umap <- umap(iris30, n_neighbors = 5, approx_pow = TRUE, ret_nn = TRUE, n_epochs = 20)
# Can specify min_dist and spread parameters to control separation and size
# of clusters and reuse nearest neighbors for efficiency
nn <- iris_umap$nn
iris_umap <- umap(iris30, n_neighbors = 5, min_dist = 1, spread = 5, nn_method = nn, n_epochs = 20)
# Supervised dimension reduction using the 'Species' factor column
iris_sumap <- umap(iris30,
n_neighbors = 5, min_dist = 0.001, y = iris30$Species,
target_weight = 0.5, n_epochs = 20
)
# Calculate Petal and Sepal neighbors separately (uses intersection of the resulting sets):
iris_umap <- umap(iris30, metric = list(
"euclidean" = c("Sepal.Length", "Sepal.Width"),
"euclidean" = c("Petal.Length", "Petal.Width")
))
```