Create a graph (as a sparse symmetric weighted adjacency matrix) representing the similarities between items in a data set. No dimensionality reduction is carried out. By default, the similarities are calculated using the merged fuzzy simplicial set approach in the Uniform Manifold Approximation and Projection (UMAP) method (McInnes et al., 2018), but the approach from LargeVis (Tang et al., 2016) can also be used.
similarity_graph(
X = NULL,
n_neighbors = NULL,
metric = "euclidean",
scale = NULL,
set_op_mix_ratio = 1,
local_connectivity = 1,
nn_method = NULL,
n_trees = 50,
search_k = 2 * n_neighbors * n_trees,
perplexity = 50,
method = "umap",
y = NULL,
target_n_neighbors = n_neighbors,
target_metric = "euclidean",
target_weight = 0.5,
pca = NULL,
pca_center = TRUE,
ret_extra = c(),
n_threads = NULL,
grain_size = 1,
kernel = "gauss",
tmpdir = tempdir(),
verbose = getOption("verbose", TRUE),
pca_method = NULL,
binary_edge_weights = FALSE
)A sparse symmetrized matrix of the similarities between the items in
X or if nn_method contains pre-computed nearest neighbor
data, the items in nn_method. Because of the symmetrization, there
may be more non-zero items in each column than the specified value of
n_neighbors (or pre-computed neighbors in nn_method).
If ret_extra is specified then the return value will be a list
containing:
similarity_graph the similarity graph as a sparse matrix
as described above.
nn (if ret_extra contained "nn") 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.
sigma (if ret_extra contains "sigma"),
a vector of calibrated parameters, one for each item in the input data,
reflecting the local data density for that item. The exact definition of
the values depends on the choice of the method parameter.
rho (if ret_extra contains "sigma"), a
vector containing the largest distance to the locally connected neighbors
of each item in the input data. This will exist only if
method = "umap".
localr (if ret_extra contains "localr") a
vector of the estimated local radii, the sum of "sigma" and
"rho". This will exist only if method = "umap".
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.
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.
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).
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 method "umap", the default is "none". For
"largevis", the default is "maxabs".
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. Ignored if
method = "largevis"
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. Ignored if method = "largevis".
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 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 ith column indicates
that the jth observation in X is a nearest neighbor of the
ith 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.
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".
Used only if method = "largevis". Controls the size
of the local neighborhood used for manifold approximation. Should be a
value between 1 and one less than the number of items in X. If
specified, you should not specify a value for n_neighbors
unless you know what you are doing.
How to generate the similarities between items. One of:
"umap" The UMAP method of McInnes et al. (2018).
"largevis" The LargeVis method of Tang et al. (2016).
Optional target data to add supervised or semi-supervised weighting
to the similarity graph . 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. This parameter is ignored if method = "largevis".
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. This parameter is ignored
if method = "largevis".
The metric used to measure distance for y if
using supervised dimension reduction. Used only if y is numeric.
This parameter is ignored if method = "largevis".
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. This
parameter is ignored if method = "largevis".
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.
A vector indicating what extra data to return. May contain any combination of the following strings:
"nn" 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. See the
"Value" section for the names of the list items. Note that the nearest
neighbors could be sensitive to data scaling, so be wary of reusing
nearest neighbor data if modifying the scale parameter.
"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.
Number of threads to use. 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.
The minimum amount of work to do on each thread. If this
value is set high enough, then less than n_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.
Used only if method = "largevis". Type of kernel
function to create input similiarties. Can be one of "gauss" (the
default) or "knn". "gauss" uses the usual Gaussian weighted
similarities. "knn" assigns equal similiarties. to every edge in the
nearest neighbor graph, and zero otherwise, using perplexity nearest
neighbors. The n_neighbors parameter is ignored in this case.
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.
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.
If TRUE then edge weights of the returned
graph are binary (0/1) rather than reflecting the degree of similarity.
This is equivalent to running umap with the
ret_extra = c("fgraph") parameter, but without the overhead of
calculating (or returning) the optimized low-dimensional coordinates.
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
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
iris30 <- iris[c(1:10, 51:60, 101:110), ]
# return a 30 x 30 sparse matrix with similarity data based on 10 nearest
# neighbors per item
iris30_sim_graph <- similarity_graph(iris30, n_neighbors = 10)
# Default is to use the UMAP method of calculating similarities, but LargeVis
# is also available: for that method, use perplexity instead of n_neighbors
# to control neighborhood size. Use ret_extra = "nn" to return nearest
# neighbor data as well as the similarity graph. Return value is a list
# containing similarity_graph' and 'nn' items.
iris30_lv_graph <- similarity_graph(iris30, perplexity = 10,
method = "largevis", ret_extra = "nn")
# If you have the neighbor information you don't need the original data
iris30_lv_graph_nn <- similarity_graph(nn_method = iris30_lv_graph$nn,
perplexity = 10, method = "largevis")
all(iris30_lv_graph_nn == iris30_lv_graph$similarity_graph)
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