Type: | Package |
Title: | Visualise Clusterings at Different Resolutions |
Version: | 0.5.1 |
Date: | 2023-11-05 |
Maintainer: | Luke Zappia <luke@lazappi.id.au> |
Description: | Deciding what resolution to use can be a difficult question when approaching a clustering analysis. One way to approach this problem is to look at how samples move as the number of clusters increases. This package allows you to produce clustering trees, a visualisation for interrogating clusterings as resolution increases. |
License: | GPL-3 |
Encoding: | UTF-8 |
LazyData: | true |
URL: | https://github.com/lazappi/clustree, https://lazappi.github.io/clustree/ |
BugReports: | https://github.com/lazappi/clustree/issues |
VignetteBuilder: | knitr |
Depends: | R (≥ 3.5), ggraph |
Imports: | checkmate, igraph, dplyr, grid, ggplot2 (≥ 3.4.0), viridis, methods, rlang, tidygraph, ggrepel |
Suggests: | testthat (≥ 2.1.0), knitr, rmarkdown, SingleCellExperiment, Seurat (≥ 2.3.0), covr, SummarizedExperiment, pkgdown, spelling |
RoxygenNote: | 7.2.3 |
Language: | en-GB |
NeedsCompilation: | no |
Packaged: | 2023-11-05 18:40:36 UTC; luke.zappia |
Author: | Luke Zappia |
Repository: | CRAN |
Date/Publication: | 2023-11-05 19:10:02 UTC |
Clustree
Description
Deciding what resolution to use can be a difficult question when approaching a clustering analysis. One way to approach this problem is to look at how samples move as the number of clusters increases. This package allows you to produce clustering trees, a visualisation for interrogating clusterings as resolution increases.
Add node labels
Description
Add node labels to a clustering tree plot with the specified aesthetics.
Usage
add_node_labels(
node_label,
node_colour,
node_label_size,
node_label_colour,
node_label_nudge,
allowed
)
Arguments
node_label |
the name of a metadata column for node labels |
node_colour |
either a value indicating a colour to use for all nodes or the name of a metadata column to colour nodes by |
node_label_size |
size of node label text |
node_label_colour |
colour of node_label text |
node_label_nudge |
numeric value giving nudge in y direction for node labels |
allowed |
vector of allowed node attributes to use as aesthetics |
Add node points
Description
Add node points to a clustering tree plot with the specified aesthetics.
Usage
add_node_points(node_colour, node_size, node_alpha, allowed)
Arguments
node_colour |
either a value indicating a colour to use for all nodes or the name of a metadata column to colour nodes by |
node_size |
either a numeric value giving the size of all nodes or the name of a metadata column to use for node sizes |
node_alpha |
either a numeric value giving the alpha of all nodes or the name of a metadata column to use for node transparency |
allowed |
vector of allowed node attributes to use as aesthetics |
Aggregate metadata
Description
Aggregate a metadata column to get a summarized value for a cluster node
Usage
aggr_metadata(node_data, col_name, col_aggr, metadata, is_cluster)
Arguments
node_data |
data.frame containing information about a set of cluster nodes |
col_name |
the name of the metadata column to aggregate |
col_aggr |
string naming a function used to aggregate the column |
metadata |
data.frame providing metadata on samples |
is_cluster |
logical vector indicating which rows of metadata are in the node to be summarized |
Value
data.frame with aggregated data
Assert colour node aesthetics
Description
Raise error if an incorrect set of colour node parameters has been supplied.
Usage
assert_colour_node_aes(
node_aes_name,
prefix,
metadata,
node_aes,
node_aes_aggr,
min,
max
)
Arguments
node_aes_name |
name of the node aesthetic to check |
prefix |
string indicating columns containing clustering information |
metadata |
data.frame containing metadata on each sample that can be used as node aesthetics |
node_aes |
value of the node aesthetic to check |
node_aes_aggr |
aggregation function associated with the node aesthetic |
min |
minimum numeric value allowed |
max |
maximum numeric value allowed |
Assert node aesthetics
Description
Raise error if an incorrect set of node parameters has been supplied.
Usage
assert_node_aes(node_aes_name, prefix, metadata, node_aes, node_aes_aggr)
Arguments
node_aes_name |
name of the node aesthetic to check |
prefix |
string indicating columns containing clustering information |
metadata |
data.frame containing metadata on each sample that can be used as node aesthetics |
node_aes |
value of the node aesthetic to check |
node_aes_aggr |
aggregation function associated with the node aesthetic |
Assert numeric node aesthetics
Description
Raise error if an incorrect set of numeric node parameters has been supplied.
Usage
assert_numeric_node_aes(
node_aes_name,
prefix,
metadata,
node_aes,
node_aes_aggr,
min,
max
)
Arguments
node_aes_name |
name of the node aesthetic to check |
prefix |
string indicating columns containing clustering information |
metadata |
data.frame containing metadata on each sample that can be used as node aesthetics |
node_aes |
value of the node aesthetic to check |
node_aes_aggr |
aggregation function associated with the node aesthetic |
min |
minimum numeric value allowed |
max |
maximum numeric value allowed |
Build tree graph
Description
Build a tree graph from a set of clusterings, metadata and associated aesthetics
Usage
build_tree_graph(
clusterings,
prefix,
count_filter,
prop_filter,
metadata,
node_aes_list
)
Arguments
clusterings |
numeric matrix containing clustering information, each column contains clustering at a separate resolution |
prefix |
string indicating columns containing clustering information |
count_filter |
count threshold for filtering edges in the clustering graph |
prop_filter |
in proportion threshold for filtering edges in the clustering graph |
metadata |
data.frame containing metadata on each sample that can be used as node aesthetics |
node_aes_list |
nested list containing node aesthetics |
Value
tidygraph::tbl_graph object containing the tree graph
Calculate SC3 stability
Description
Calculate the SC3 stability index for every cluster at every resolution in a
set of clusterings. The index varies from 0 to 1, where 1 suggests that a
cluster is more stable across resolutions. See calc_sc3_stability_cluster()
for more details.
Usage
calc_sc3_stability(clusterings)
Arguments
clusterings |
numeric matrix containing clustering information, each column contains clustering at a separate resolution |
Value
matrix with stability score for each cluster
Calculate single SC3 stability
Description
Calculate the SC3 stability index for a single cluster in a set of clusterings. The index varies from 0 to 1, where 1 suggests that a cluster is more stable across resolutions.
Usage
calc_sc3_stability_cluster(clusterings, res, cluster)
Arguments
clusterings |
numeric matrix containing clustering information, each column contains clustering at a separate resolution |
res |
resolution of the cluster to calculate stability for |
cluster |
index of the cluster to calculate stability for |
Details
This index was originally introduced in the SC3
package for clustering
single-cell RNA-seq data. Clusters are awarded increased stability if they
share the same samples as a cluster at another resolution and penalised at
higher resolutions. We use a slightly different notation to describe the
score but the results are the same:
s(c_{k, i}) =
\frac{1}{size(L) + 1}
\sum_{l \in L}
\sum_{j \in N_l}
\frac{size(c_{k, i} \cap c_{l, j})}{size(c_{l, j}) * size(N_l) ^ 2}
Where:
-
c_{x, y}
is clustery
at resolutionx
-
k
is the resolution of the cluster we want to score -
i
is the index of the cluster we want to score -
L
is the set of all resolutions exceptk
-
l
is a resolution inL
-
N_l
is the set of clusters at resolutionl
that share samples withc_{k, i}
-
j
is a cluster inN_l
Value
SC3 stability index
See Also
The documentation for the calculate_stability
function in the
SC3 package
Check node aes list
Description
Warn if node aesthetic names are incorrect
Usage
check_node_aes_list(node_aes_list)
Arguments
node_aes_list |
List of node aesthetics |
Value
Corrected node aesthetics list
Plot a clustering tree
Description
Creates a plot of a clustering tree showing the relationship between clusterings at different resolutions.
Usage
clustree(x, ...)
## S3 method for class 'matrix'
clustree(
x,
prefix,
suffix = NULL,
metadata = NULL,
count_filter = 0,
prop_filter = 0.1,
layout = c("tree", "sugiyama"),
use_core_edges = TRUE,
highlight_core = FALSE,
node_colour = prefix,
node_colour_aggr = NULL,
node_size = "size",
node_size_aggr = NULL,
node_size_range = c(4, 15),
node_alpha = 1,
node_alpha_aggr = NULL,
node_text_size = 3,
scale_node_text = FALSE,
node_text_colour = "black",
node_text_angle = 0,
node_label = NULL,
node_label_aggr = NULL,
node_label_size = 3,
node_label_nudge = -0.2,
edge_width = 1.5,
edge_arrow = TRUE,
edge_arrow_ends = c("last", "first", "both"),
show_axis = FALSE,
return = c("plot", "graph", "layout"),
...
)
## S3 method for class 'data.frame'
clustree(x, prefix, ...)
## S3 method for class 'SingleCellExperiment'
clustree(x, prefix, exprs = "counts", ...)
## S3 method for class 'seurat'
clustree(x, prefix = "res.", exprs = c("data", "raw.data", "scale.data"), ...)
## S3 method for class 'Seurat'
clustree(
x,
prefix = paste0(assay, "_snn_res."),
exprs = c("data", "counts", "scale.data"),
assay = NULL,
...
)
Arguments
x |
object containing clustering data |
... |
extra parameters passed to other methods |
prefix |
string indicating columns containing clustering information |
suffix |
string at the end of column names containing clustering information |
metadata |
data.frame containing metadata on each sample that can be used as node aesthetics |
count_filter |
count threshold for filtering edges in the clustering graph |
prop_filter |
in proportion threshold for filtering edges in the clustering graph |
layout |
string specifying the "tree" or "sugiyama" layout, see
|
use_core_edges |
logical, whether to only use core tree (edges with maximum in proportion for a node) when creating the graph layout, all (unfiltered) edges will still be displayed |
highlight_core |
logical, whether to increase the edge width of the core network to make it easier to see |
node_colour |
either a value indicating a colour to use for all nodes or the name of a metadata column to colour nodes by |
node_colour_aggr |
if |
node_size |
either a numeric value giving the size of all nodes or the name of a metadata column to use for node sizes |
node_size_aggr |
if |
node_size_range |
numeric vector of length two giving the maximum and minimum point size for plotting nodes |
node_alpha |
either a numeric value giving the alpha of all nodes or the name of a metadata column to use for node transparency |
node_alpha_aggr |
if |
node_text_size |
numeric value giving the size of node text if
|
scale_node_text |
logical indicating whether to scale node text along with the node size |
node_text_colour |
colour value for node text (and label) |
node_text_angle |
the rotation of the node text |
node_label |
additional label to add to nodes |
node_label_aggr |
if |
node_label_size |
numeric value giving the size of node label text |
node_label_nudge |
numeric value giving nudge in y direction for node labels |
edge_width |
numeric value giving the width of plotted edges |
edge_arrow |
logical indicating whether to add an arrow to edges |
edge_arrow_ends |
string indicating which ends of the line to draw arrow
heads if |
show_axis |
whether to show resolution axis |
return |
string specifying what to return, either "plot" (a |
exprs |
source of gene expression information to use as node aesthetics,
for |
assay |
name of assay to pull expression and clustering data from for
|
Details
Data sources
Plotting a clustering tree requires information about which cluster each
sample has been assigned to at different resolutions. This information can
be supplied in various forms, as a matrix, data.frame or more specialised
object. In all cases the object provided must contain numeric columns with
the naming structure PXS
where P
is a prefix indicating that the column
contains clustering information, X
is a numeric value indicating the
clustering resolution and S
is any additional suffix to be removed. For
SingleCellExperiment
objects this information must be in the colData
slot
and for Seurat
objects it must be in the meta.data
slot. For all objects
except matrices any additional columns can be used as aesthetics, for
matrices an additional metadata data.frame can be supplied if required.
Filtering
Edges in the graph can be filtered by adjusting the count_filter
and
prop_filter
parameters. The count_filter
removes any edges that represent
less than that number of samples, while the prop_filter
removes edges that
represent less than that proportion of cells in the node it points towards.
Node aesthetics
The aesthetics of the plotted nodes can be controlled in various ways. By
default the colour indicates the clustering resolution, the size indicates
the number of samples in that cluster and the transparency is set to 100%.
Each of these can be set to a specific value or linked to a supplied metadata
column. For a SingleCellExperiment
or Seurat
object the names of genes
can also be used. If a metadata column is used than an aggregation function
must also be supplied to combine the samples in each cluster. This function
must take a vector of values and return a single value.
Layout
The clustering tree can be displayed using either the Reingold-Tilford tree
layout algorithm or the Sugiyama layout algorithm for layered directed
acyclic graphs. These layouts were selected as the are the algorithms
available in the igraph
package designed for trees. The Reingold-Tilford
algorithm places children below their parents while the Sugiyama places
nodes in layers while trying to minimise the number of crossing edges. See
igraph::layout_as_tree()
and igraph::layout_with_sugiyama()
for more
details. When use_core_edges
is TRUE
(default) only the core tree of the
maximum in proportion edges for each node are used for constructing the
layout. This can often lead to more attractive layouts where the core tree is
more visible.
Value
a ggplot
object (default), a tbl_graph
object or a ggraph
layout object depending on the value of return
Examples
data(nba_clusts)
clustree(nba_clusts, prefix = "K")
Overlay a clustering tree
Description
Creates a plot of a clustering tree overlaid on a scatter plot of individual samples.
Usage
clustree_overlay(x, ...)
## S3 method for class 'matrix'
clustree_overlay(
x,
prefix,
metadata,
x_value,
y_value,
suffix = NULL,
count_filter = 0,
prop_filter = 0.1,
node_colour = prefix,
node_colour_aggr = NULL,
node_size = "size",
node_size_aggr = NULL,
node_size_range = c(4, 15),
node_alpha = 1,
node_alpha_aggr = NULL,
edge_width = 1,
use_colour = c("edges", "points"),
alt_colour = "black",
point_size = 3,
point_alpha = 0.2,
point_shape = 18,
label_nodes = FALSE,
label_size = 3,
plot_sides = FALSE,
side_point_jitter = 0.45,
side_point_offset = 1,
...
)
## S3 method for class 'data.frame'
clustree_overlay(x, prefix, ...)
## S3 method for class 'SingleCellExperiment'
clustree_overlay(
x,
prefix,
x_value,
y_value,
exprs = "counts",
red_dim = NULL,
...
)
## S3 method for class 'seurat'
clustree_overlay(
x,
x_value,
y_value,
prefix = "res.",
exprs = c("data", "raw.data", "scale.data"),
red_dim = NULL,
...
)
## S3 method for class 'Seurat'
clustree_overlay(
x,
x_value,
y_value,
prefix = paste0(assay, "_snn_res."),
exprs = c("data", "counts", "scale.data"),
red_dim = NULL,
assay = NULL,
...
)
Arguments
x |
object containing clustering data |
... |
extra parameters passed to other methods |
prefix |
string indicating columns containing clustering information |
metadata |
data.frame containing metadata on each sample that can be used as node aesthetics |
x_value |
numeric metadata column to use as the x axis |
y_value |
numeric metadata column to use as the y axis |
suffix |
string at the end of column names containing clustering information |
count_filter |
count threshold for filtering edges in the clustering graph |
prop_filter |
in proportion threshold for filtering edges in the clustering graph |
node_colour |
either a value indicating a colour to use for all nodes or the name of a metadata column to colour nodes by |
node_colour_aggr |
if |
node_size |
either a numeric value giving the size of all nodes or the name of a metadata column to use for node sizes |
node_size_aggr |
if |
node_size_range |
numeric vector of length two giving the maximum and minimum point size for plotting nodes |
node_alpha |
either a numeric value giving the alpha of all nodes or the name of a metadata column to use for node transparency |
node_alpha_aggr |
if |
edge_width |
numeric value giving the width of plotted edges |
use_colour |
one of "edges" or "points" specifying which element to apply the colour aesthetic to |
alt_colour |
colour value to be used for edges or points (whichever is
NOT given by |
point_size |
numeric value giving the size of sample points |
point_alpha |
numeric value giving the alpha of sample points |
point_shape |
numeric value giving the shape of sample points |
label_nodes |
logical value indicating whether to add labels to clustering graph nodes |
label_size |
numeric value giving the size of node labels is
|
plot_sides |
logical value indicating whether to produce side on plots |
side_point_jitter |
numeric value giving the y-direction spread of points in side plots |
side_point_offset |
numeric value giving the y-direction offset for points in side plots |
exprs |
source of gene expression information to use as node aesthetics,
for |
red_dim |
dimensionality reduction to use as a source for x_value and y_value |
assay |
name of assay to pull expression and clustering data from for
|
Details
Data sources
Plotting a clustering tree requires information about which cluster each
sample has been assigned to at different resolutions. This information can
be supplied in various forms, as a matrix, data.frame or more specialised
object. In all cases the object provided must contain numeric columns with
the naming structure PXS
where P
is a prefix indicating that the column
contains clustering information, X
is a numeric value indicating the
clustering resolution and S
is any additional suffix to be removed. For
SingleCellExperiment
objects this information must be in the colData
slot
and for Seurat
objects it must be in the meta.data
slot. For all objects
except matrices any additional columns can be used as aesthetics.
Filtering
Edges in the graph can be filtered by adjusting the count_filter
and
prop_filter
parameters. The count_filter
removes any edges that represent
less than that number of samples, while the prop_filter
removes edges that
represent less than that proportion of cells in the node it points towards.
Node aesthetics
The aesthetics of the plotted nodes can be controlled in various ways. By
default the colour indicates the clustering resolution, the size indicates
the number of samples in that cluster and the transparency is set to 100%.
Each of these can be set to a specific value or linked to a supplied metadata
column. For a SingleCellExperiment
or Seurat
object the names of genes
can also be used. If a metadata column is used than an aggregation function
must also be supplied to combine the samples in each cluster. This function
must take a vector of values and return a single value.
Colour aesthetic
The colour aesthetic can be applied to either edges or sample points by
setting use_colour
. If "edges" is selected edges will be coloured according
to the clustering resolution they originate at. If "points" is selected they
will be coloured according to the cluster they are assigned to at the highest
resolution.
Dimensionality reductions
For SingleCellExperiment
and Seurat
objects precomputed dimensionality
reductions can be used for x or y aesthetics. To do so red_dim
must be set
to the name of a dimensionality reduction in reducedDimNames(x)
(for a
SingleCellExperiment
) or x@dr
(for a Seurat
object). x_value
and
y_value
can then be set to red_dimX
when red_dim
matches the red_dim
argument and X
is the column of the dimensionality reduction to use.
Value
a ggplot
object if plot_sides
is FALSE
or a list of ggplot
objects if plot_sides
is TRUE
Examples
data(nba_clusts)
clustree_overlay(nba_clusts, prefix = "K", x_value = "PC1", y_value = "PC2")
Get tree edges
Description
Extract the edges from a set of clusterings
Usage
get_tree_edges(clusterings, prefix)
Arguments
clusterings |
numeric matrix containing clustering information, each column contains clustering at a separate resolution |
prefix |
string indicating columns containing clustering information |
Value
data.frame containing edge information
Get tree nodes
Description
Extract the nodes from a set of clusterings and add relevant attributes
Usage
get_tree_nodes(clusterings, prefix, metadata, node_aes_list)
Arguments
clusterings |
numeric matrix containing clustering information, each column contains clustering at a separate resolution |
prefix |
string indicating columns containing clustering information |
metadata |
data.frame containing metadata on each sample that can be used as node aesthetics |
node_aes_list |
nested list containing node aesthetics |
Value
data.frame containing node information
Clustered NBA positions dataset
Description
NBA positions dataset clustered using k-means with a range of values of k
Usage
nba_clusts
Format
nba_clusts
is a data.frame containing the NBA positions dataset
with additional columns holding k-means clusterings at different values of
k
and the first two principal components
-
Position - Player position
-
TurnoverPct - Turnover percentage
-
ReboundPct - Rebound percentage
-
AssistPct - Assist percentage
-
FieldGoalPct - Field goal percentage
-
K1 - K5 - Results of k-means clustering
-
PC1 - First principal component
-
PC2 - Second principal component
Source
NBA positions downloaded from https://github.com/lazappi/nba_positions.
The source dataset is available from Kaggle at https://www.kaggle.com/drgilermo/nba-players-stats/data?select=Seasons_Stats.csv and was originally scraped from Basketball Reference.
See https://github.com/lazappi/clustree/blob/master/data-raw/nba_clusts.R for details of how clustering was performed.
Overlay node points
Description
Overlay clustering tree nodes on a scatter plot with the specified aesthetics.
Usage
overlay_node_points(
nodes,
x_value,
y_value,
node_colour,
node_size,
node_alpha
)
Arguments
nodes |
data.frame describing nodes |
x_value |
column of nodes to use for the x position |
y_value |
column of nodes to use for the y position |
node_colour |
either a value indicating a colour to use for all nodes or the name of a metadata column to colour nodes by |
node_size |
either a numeric value giving the size of all nodes or the name of a metadata column to use for node sizes |
node_alpha |
either a numeric value giving the alpha of all nodes or the name of a metadata column to use for node transparency |
Plot overlay side
Description
Plot the side view of a clustree overlay plot. If the ordinary plot shows the tree from above this plot shows it from the side, highlighting either the x or y dimension and the clustering resolution.
Usage
plot_overlay_side(
nodes,
edges,
points,
prefix,
side_value,
graph_attr,
node_size_range,
edge_width,
use_colour,
alt_colour,
point_size,
point_alpha,
point_shape,
label_nodes,
label_size,
y_jitter,
y_offset
)
Arguments
nodes |
data.frame describing nodes |
edges |
data.frame describing edges |
points |
data.frame describing points |
prefix |
string indicating columns containing clustering information |
side_value |
string giving the metadata column to use for the x axis |
graph_attr |
list describing graph attributes |
node_size_range |
numeric vector of length two giving the maximum and minimum point size for plotting nodes |
edge_width |
numeric value giving the width of plotted edges |
use_colour |
one of "edges" or "points" specifying which element to apply the colour aesthetic to |
alt_colour |
colour value to be used for edges or points (whichever is
NOT given by |
point_size |
numeric value giving the size of sample points |
point_alpha |
numeric value giving the alpha of sample points |
point_shape |
numeric value giving the shape of sample points |
label_nodes |
logical value indicating whether to add labels to clustering graph nodes |
label_size |
numeric value giving the size of node labels is
|
y_jitter |
numeric value giving the y-direction spread of points in side plots |
y_offset |
numeric value giving the y-direction offset for points in side plots |
Value
ggplot object
Simulated scRNA-seq dataset
Description
A simulated scRNA-seq dataset generated using the splatter
package and
clustered using the SC3
and Seurat
packages.
Usage
sc_example
Format
sc_example
is a list holding a simulated scRNA-seq dataset. Items
in the list included the simulated counts, normalised log counts,
tSNE dimensionality reduction and cell assignments from SC3
and Seurat
clustering.
Source
# Simulation library("splatter") # Version 1.2.1 sim <- splatSimulate(batchCells = 200, nGenes = 10000, group.prob = c(0.4, 0.2, 0.2, 0.15, 0.05), de.prob = c(0.1, 0.2, 0.05, 0.1, 0.05), method = "groups", seed = 1) sim_counts <- counts(sim)[1:1000, ] # SC3 Clustering library("SC3") # Version 1.7.6 library("scater") # Version 1.6.2 sim_sc3 <- SingleCellExperiment(assays = list(counts = sim_counts)) rowData(sim_sc3)$feature_symbol <- rownames(sim_counts) sim_sc3 <- normalise(sim_sc3) sim_sc3 <- sc3(sim_sc3, ks = 1:8, biology = FALSE, n_cores = 1) sim_sc3 <- runTSNE(sim_sc3) # Seurat Clustering library("Seurat") # Version 2.2.0 sim_seurat <- CreateSeuratObject(sim_counts) sim_seurat <- NormalizeData(sim_seurat, display.progress = FALSE) sim_seurat <- FindVariableGenes(sim_seurat, do.plot = FALSE, display.progress = FALSE) sim_seurat <- ScaleData(sim_seurat, display.progress = FALSE) sim_seurat <- RunPCA(sim_seurat, do.print = FALSE) sim_seurat <- FindClusters(sim_seurat, dims.use = 1:6, resolution = seq(0, 1, 0.1), print.output = FALSE) sc_example <- list(counts = counts(sim_sc3), logcounts = logcounts(sim_sc3), tsne = reducedDim(sim_sc3), sc3_clusters = as.data.frame(colData(sim_sc3)), seurat_clusters = sim_seurat@meta.data)
Store node aesthetics
Description
Store the names of node attributes to use as aesthetics as graph attributes
Usage
store_node_aes(graph, node_aes_list, metadata)
Arguments
graph |
graph to store attributes in |
node_aes_list |
nested list containing node aesthetics |
metadata |
data.frame containing metadata that can be used as aesthetics |
Value
graph with additional attributes