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".

Controls the size of the local neighborhood used for manifold approximation. This is the analogous to n_neighbors in umap. Change this, rather than n_neighbors.

The number of neighbors to use when calculating the perplexity. Usually set to three times the value of the perplexity. Must be at least as large as perplexity.

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.

Type of distance metric to use to find nearest neighbors. One of:

• "euclidean" (the default)

• "cosine"

• "manhattan"

• "hamming"

• "correlation" (a distance based on the Pearson correlation)

• "categorical" (see below)

Only applies if nn_method = "annoy" (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).

Number of epochs to use during the optimization of the embedded coordinates. The default is calculate the number of epochs dynamically based on dataset size, to give the same number of edge samples as the LargeVis defaults. This is usually substantially larger than the UMAP defaults. If n_epochs = 0, then coordinates determined by "init" will be returned.

Initial learning rate used in optimization of the coordinates.

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 lvish, the default is "maxabs", for consistency with LargeVis.

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 and LargeVis. 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"), if more than one connected component is identified, each connected component is initialized separately and the results are merged. 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. Either a PCA-based initialization or increasing the value of n_neighbors may be more appropriate.

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).

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

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

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.

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 precalculated nearest neighbor data to this argument. It must be 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.

Multiple nearest neighbor data (e.g. from two different precomputed metrics) can be passed by passing a list containing the nearest neighbor data lists as items. The n_neighbors parameter is ignored when using precomputed nearest neighbor data.

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.

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".

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.

Number of threads to use during stochastic gradient descent. If set to > 1, then results will not be reproducible, even if 'set.seed' is called with a fixed seed before running. Set to "auto" go use the same value as n_threads.

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.

Type of kernel function to create input probabilities. Can be one of "gauss" (the default) or "knn". "gauss" uses the usual Gaussian weighted similarities. "knn" assigns equal probabilities to every edge in the nearest neighbor graph, and zero otherwise, using perplexity nearest neighbors. The n_neighbors parameter is ignored in this case.

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.

If TRUE, center the columns of X before carrying out PCA. For binary data, it's recommended to set this to FALSE.

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.

If TRUE, then the following combination of parameters is set: pcg_rand = TRUE and n_sgd_threads = "auto". 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 and n_sgd_threads, are ignored.

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.

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

• "nn" same as setting 'ret_nn = TRUE'.

• "P" the high dimensional probability matrix. 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 input probability (or similarity or affinity) of the edge connecting vertex i and vertex j. 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.

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.

If TRUE, log details to the console.