Package 'SC3'

Title: Single-Cell Consensus Clustering
Description: A tool for unsupervised clustering and analysis of single cell RNA-Seq data.
Authors: Vladimir Kiselev
Maintainer: Vladimir Kiselev <[email protected]>
License: GPL-3
Version: 1.35.0
Built: 2024-10-31 04:44:16 UTC
Source: https://github.com/bioc/SC3

Help Index


Cell type annotations for data extracted from a publication by Yan et al.

Description

Cell type annotations for data extracted from a publication by Yan et al.

Usage

ann

Format

An object of class data.frame with 90 rows and 1 columns.

Source

http://dx.doi.org/10.1038/nsmb.2660

Each row corresponds to a single cell from 'yan' dataset


Calculate a distance matrix

Description

Distance between the cells, i.e. columns, in the input expression matrix are calculated using the Euclidean, Pearson and Spearman metrics to construct distance matrices.

Usage

calculate_distance(data, method)

Arguments

data

expression matrix

method

one of the distance metrics: 'spearman', 'pearson', 'euclidean'

Value

distance matrix


Calculate the stability index of the obtained clusters when changing k

Description

Stability index shows how stable each cluster is accross the selected range of k. The stability index varies between 0 and 1, where 1 means that the same cluster appears in every solution for different k.

Usage

calculate_stability(consensus, k)

Arguments

consensus

consensus item of the sc3 slot of an object of 'SingleCellExperiment' class

k

number of clusters k

Details

Imagine a given cluster is split into N clusters when k is changed (all possible values of k are provided via ks argument in the main sc3 function). In each of the new clusters there are given_cells of the given cluster and also some extra_cells from other clusters. Then we define stability as follows:

1ksN2ksNgiven_cellsgiven_cells+extra_cells\frac{1}{ks*N^2}\sum_{ks}\sum_{N}\frac{given\_cells}{given\_cells + extra\_cells}

Where one N corrects for the number of clusters and the other N is a penalty for splitting the cluster. ks corrects for the range of k.

Value

a numeric vector containing a stability index of each cluster


Calculate consensus matrix

Description

Consensus matrix is calculated using the Cluster-based Similarity Partitioning Algorithm (CSPA). For each clustering solution a binary similarity matrix is constructed from the corresponding cell labels: if two cells belong to the same cluster, their similarity is 1, otherwise the similarity is 0. A consensus matrix is calculated by averaging all similarity matrices.

Usage

consensus_matrix(clusts)

Arguments

clusts

a matrix containing clustering solutions in columns

Value

consensus matrix


Consensus matrix computation

Description

Computes consensus matrix given cluster labels

Usage

consmx(dat)

Arguments

dat

a matrix containing clustering solutions in columns


Compute Euclidean distance matrix by rows

Description

Used in consmx function

Usage

ED1(x)

Arguments

x

A numeric matrix.


Compute Euclidean distance matrix by columns

Description

Used in sc3-funcs.R distance matrix calculation and within the consensus clustering.

Usage

ED2(x)

Arguments

x

A numeric matrix.


Estimate the optimal k for k-means clustering

Description

The function finds the eigenvalues of the sample covariance matrix. It will then return the number of significant eigenvalues according to the Tracy-Widom test.

Usage

estkTW(dataset)

Arguments

dataset

processed input expression matrix.

Value

an estimated number of clusters k


Calculate the area under the ROC curve for a given gene.

Description

For a given gene a binary classifier is constructed based on the mean cluster expression values (these are calculated using the cell labels). The classifier prediction is then calculated using the gene expression ranks. The area under the receiver operating characteristic (ROC) curve is used to quantify the accuracy of the prediction. A p-value is assigned to each gene by using the Wilcoxon signed rank test.

Usage

get_auroc(gene, labels)

Arguments

gene

expression data of a given gene

labels

cell labels correspodning to the expression values of the gene


Wrapper for calculating biological properties

Description

Wrapper for calculating biological properties

Usage

get_biolgy(dataset, labels, regime)

Arguments

dataset

expression matrix

labels

cell labels corresponding clusters

regime

defines what biological analysis to perform. "marker" for marker genes, "de" for differentiall expressed genes and "outl" for outlier cells

Value

results of either


Find differentially expressed genes

Description

Differential expression is calculated using the non-parametric Kruskal-Wallis test. A significant p-value indicates that gene expression in at least one cluster stochastically dominates one other cluster. Note that the calculation of differential expression after clustering can introduce a bias in the distribution of p-values, and thus we advise to use the p-values for ranking the genes only.

Usage

get_de_genes(dataset, labels)

Arguments

dataset

expression matrix

labels

cell labels corresponding to the columns of the expression matrix

Value

a numeric vector containing the differentially expressed genes and correspoding p-values

Examples

d <- get_de_genes(yan[1:10,], as.numeric(ann[,1]))
head(d)

Calculate marker genes

Description

Find marker genes in the dataset. The get_auroc is used to calculate marker values for each gene.

Usage

get_marker_genes(dataset, labels)

Arguments

dataset

expression matrix

labels

cell labels corresponding clusters

Value

data.frame containing the marker genes, corresponding cluster indexes and adjusted p-values

Examples

d <- get_marker_genes(yan[1:10,], as.numeric(ann[,1]))
d

Find cell outliers in each cluster.

Description

Outlier cells in each cluster are detected using robust distances, calculated using the minimum covariance determinant (MCD), namely using covMcd. The outlier score shows how different a cell is from all other cells in the cluster and it is defined as the differences between the square root of the robust distance and the square root of the 99.99

Usage

get_outl_cells(dataset, labels)

Arguments

dataset

expression matrix

labels

cell labels corresponding to the columns of the expression matrix

Value

a numeric vector containing the cell labels and correspoding outlier scores ordered by the labels

Examples

d <- get_outl_cells(yan[1:10,], as.numeric(ann[,1]))
head(d)

Get processed dataset used by SC3 clustering

Description

Takes data from the logcounts slot, removes spike-ins and applies the gene filter.

Usage

get_processed_dataset(object)

Arguments

object

an object of SingleCellExperiment class


Reorder and subset gene markers for plotting on a heatmap

Description

Reorders the rows of the input data.frame based on the sc3_k_markers_clusts column and also keeps only the top 10 genes for each value of sc3_k_markers_clusts.

Usage

markers_for_heatmap(markers)

Arguments

markers

a data.frame object with the following colnames: sc3_k_markers_clusts, sc3_k_markers_auroc, sc3_k_markers_padj.


Graph Laplacian calculation

Description

Calculate graph Laplacian of a symmetrix matrix

Usage

norm_laplacian(A)

Arguments

A

symmetric matrix


Get differentiall expressed genes from an object of SingleCellExperiment class

Description

This functions returns all marker gene columns from the phenoData slot of the input object corresponding to the number of clusters k. Additionally, it rearranges genes by the cluster index and order them by the area under the ROC curve value inside of each cluster.

Usage

organise_de_genes(object, k, p_val)

Arguments

object

an object of SingleCellExperiment class

k

number of cluster

p_val

p-value threshold


Get marker genes from an object of SingleCellExperiment class

Description

This functions returns all marker gene columns from the phenoData slot of the input object corresponding to the number of clusters k. Additionally, it rearranges genes by the cluster index and order them by the area under the ROC curve value inside of each cluster.

Usage

organise_marker_genes(object, k, p_val, auroc)

Arguments

object

an object of SingleCellExperiment class

k

number of cluster

p_val

p-value threshold

auroc

area under the ROC curve threshold


A helper function for the SVM analysis

Description

Defines train and study cell indeces based on the svm_num_cells and svm_train_inds input parameters

Usage

prepare_for_svm(N, svm_num_cells = NULL, svm_train_inds = NULL, svm_max)

Arguments

N

number of cells in the input dataset

svm_num_cells

number of random cells to be used for training

svm_train_inds

indeces of cells to be used for training

svm_max

define the maximum number of cells below which SVM is not run

Value

A list of indeces of the train and the study cells


Reindex cluster labels in ascending order

Description

Given an hclust object and the number of clusters k this function reindex the clusters inferred by cutree(hc, k)[hc$order], so that they appear in ascending order. This is particularly useful when plotting heatmaps in which the clusters should be numbered from left to right.

Usage

reindex_clusters(hc, k)

Arguments

hc

an object of class hclust

k

number of cluster to be inferred from hc

Examples

hc <- hclust(dist(USArrests), 'ave')
cutree(hc, 10)[hc$order]
reindex_clusters(hc, 10)[hc$order]

Run all steps of SC3 in one go

Description

This function is a wrapper that executes all steps of SC3 analysis in one go.

Usage

sc3.SingleCellExperiment(object, ks, gene_filter, pct_dropout_min,
  pct_dropout_max, d_region_min, d_region_max, svm_num_cells, svm_train_inds,
  svm_max, n_cores, kmeans_nstart, kmeans_iter_max, k_estimator, biology,
  rand_seed)

## S4 method for signature 'SingleCellExperiment'
sc3(object, ks = NULL, gene_filter = TRUE,
  pct_dropout_min = 10, pct_dropout_max = 90, d_region_min = 0.04,
  d_region_max = 0.07, svm_num_cells = NULL, svm_train_inds = NULL,
  svm_max = 5000, n_cores = NULL, kmeans_nstart = NULL,
  kmeans_iter_max = 1e+09, k_estimator = FALSE, biology = FALSE,
  rand_seed = 1)

Arguments

object

an object of SingleCellExperiment class.

ks

a range of the number of clusters k used for SC3 clustering. Can also be a single integer.

gene_filter

a boolen variable which defines whether to perform gene filtering before SC3 clustering.

pct_dropout_min

if gene_filter = TRUE, then genes with percent of dropouts smaller than pct_dropout_min are filtered out before clustering.

pct_dropout_max

if gene_filter = TRUE, then genes with percent of dropouts larger than pct_dropout_max are filtered out before clustering.

d_region_min

defines the minimum number of eigenvectors used for kmeans clustering as a fraction of the total number of cells. Default is 0.04. See SC3 paper for more details.

d_region_max

defines the maximum number of eigenvectors used for kmeans clustering as a fraction of the total number of cells. Default is 0.07. See SC3 paper for more details.

svm_num_cells

number of randomly selected training cells to be used for SVM prediction. The default is NULL.

svm_train_inds

a numeric vector defining indeces of training cells that should be used for SVM training. The default is NULL.

svm_max

define the maximum number of cells below which SVM is not run.

n_cores

defines the number of cores to be used on the user's machine. If not set, 'SC3' will use all but one cores of your machine.

kmeans_nstart

nstart parameter passed to kmeans function. Can be set manually. By default it is 1000 for up to 2000 cells and 50 for more than 2000 cells.

kmeans_iter_max

iter.max parameter passed to kmeans function.

k_estimator

boolean parameter, defines whether to estimate an optimal number of clusters k. If user has already defined the ks parameter the estimation does not affect the user's paramater.

biology

boolean parameter, defines whether to compute differentially expressed genes, marker genes and cell outliers.

rand_seed

sets the seed of the random number generator. SC3 is a stochastic method, so setting the rand_seed to a fixed values can be used for reproducibility purposes.

Value

an object of SingleCellExperiment class


Calculate DE genes, marker genes and cell outliers.

Description

This function calculates differentially expressed (DE) genes, marker genes and cell outliers based on the consensus SC3 clusterings.

Usage

sc3_calc_biology.SingleCellExperiment(object, ks, regime)

## S4 method for signature 'SingleCellExperiment'
sc3_calc_biology(object, ks = NULL,
  regime = NULL)

Arguments

object

an object of SingleCellExperiment class

ks

a continuous range of integers - the number of clusters k to be used for SC3 clustering. Can also be a single integer.

regime

defines what biological analysis to perform. "marker" for marker genes, "de" for differentiall expressed genes and "outl" for outlier cells

Details

DE genes are calculated using get_de_genes. Results of the DE analysis are saved as new columns in the featureData slot of the input object. The column names correspond to the adjusted p-values of the genes and have the following format: sc3_k_de_padj, where k is the number of clusters.

Marker genes are calculated using get_marker_genes. Results of the marker gene analysis are saved as three new columns (for each k) to the featureData slot of the input object. The column names correspond to the SC3 cluster labels, to the adjusted p-values of the genes and to the area under the ROC curve and have the following format: sc3_k_markers_clusts, sc3_k_markers_padj and sc3_k_markers_auroc, where k is the number of clusters.

Outlier cells are calculated using get_outl_cells. Results of the cell outlier analysis are saved as new columns in the phenoData slot of the input object. The column names correspond to the log2(outlier_score) and have the following format: sc3_k_log2_outlier_score, where k is the number of clusters.

Additionally, biology item is added to the sc3 slot and is set to TRUE indicating that the biological analysis of the dataset has been performed.

Value

an object of SingleCellExperiment class


Calculate consensus matrix.

Description

This function calculates consensus matrices based on the clustering solutions contained in the kmeans item of the sc3 slot of the metadata(object). It then creates and populates the consensus item of the sc3 slot with consensus matrices, their hierarchical clusterings in hclust objects, and Silhouette indeces of the clusters. It also removes the previously calculated kmeans clusterings from the sc3 slot, as they are not needed for further analysis.

Usage

sc3_calc_consens.SingleCellExperiment(object)

## S4 method for signature 'SingleCellExperiment'
sc3_calc_consens(object)

Arguments

object

an object of SingleCellExperiment class

Details

Additionally, it also adds new columns to the colData slot of the input object. The column names correspond to the consensus cell labels and have the following format: sc3_k_clusters, where k is the number of clusters.

Value

an object of SingleCellExperiment class


Calculate distances between the cells.

Description

This function calculates distances between the cells. It creates and populates the following items of the sc3 slot of the metadata(object):

  • distances - contains a list of distance matrices corresponding to Euclidean, Pearson and Spearman distances.

Usage

sc3_calc_dists.SingleCellExperiment(object)

## S4 method for signature 'SingleCellExperiment'
sc3_calc_dists(object)

Arguments

object

an object of SingleCellExperiment class

Value

an object of SingleCellExperiment class


Calculate transformations of the distance matrices.

Description

This function transforms all distances items of the sc3 slot of the metadata(object) using either principal component analysis (PCA) or by calculating the eigenvectors of the associated graph Laplacian. The columns of the resulting matrices are then sorted in descending order by their corresponding eigenvalues. The first d columns (where d = max(metadata(object)$sc3$n_dim)) of each transformation are then written to the transformations item of the sc3 slot. Additionally, this function also removes the previously calculated distances from the sc3 slot, as they are not needed for further analysis.

Usage

sc3_calc_transfs.SingleCellExperiment(object)

## S4 method for signature 'SingleCellExperiment'
sc3_calc_transfs(object)

Arguments

object

an object of SingleCellExperiment class

Value

an object of SingleCellExperiment class


Estimate the optimal number of cluster k for a scRNA-Seq expression matrix

Description

Uses Tracy-Widom theory on random matrices to estimate the optimal number of clusters k. It creates and populates the k_estimation item of the sc3 slot of the metadata(object).

Usage

sc3_estimate_k.SingleCellExperiment(object)

## S4 method for signature 'SingleCellExperiment'
sc3_estimate_k(object)

Arguments

object

an object of SingleCellExperiment class

Value

an estimated value of k


Write SC3 results to Excel file

Description

This function writes all SC3 results to an excel file.

Usage

sc3_export_results_xls.SingleCellExperiment(object, filename)

## S4 method for signature 'SingleCellExperiment'
sc3_export_results_xls(object,
  filename = "sc3_results.xls")

Arguments

object

an object of SingleCellExperiment class

filename

name of the excel file, to which the results will be written


Opens SC3 results in an interactive session in a web browser.

Description

Runs interactive shiny session of SC3 based on precomputed clusterings.

Usage

sc3_interactive.SingleCellExperiment(object)

## S4 method for signature 'SingleCellExperiment'
sc3_interactive(object)

Arguments

object

an object of SingleCellExperiment class

Value

Opens a browser window with an interactive shiny app and visualize all precomputed clusterings.


kmeans clustering of cells.

Description

This function performs kmeans clustering of the matrices contained in the transformations item of the sc3 slot of the metadata(object). It then creates and populates the following items of the sc3 slot:

  • kmeans - contains a list of kmeans clusterings.

Usage

sc3_kmeans.SingleCellExperiment(object, ks)

## S4 method for signature 'SingleCellExperiment'
sc3_kmeans(object, ks = NULL)

Arguments

object

an object of SingleCellExperiment class

ks

a continuous range of integers - the number of clusters k to be used for SC3 clustering. Can also be a single integer.

Value

an object of SingleCellExperiment class


Plot stability of the clusters

Description

Stability index shows how stable each cluster is accross the selected range of ks. The stability index varies between 0 and 1, where 1 means that the same cluster appears in every solution for different k.

Usage

sc3_plot_cluster_stability.SingleCellExperiment(object, k)

## S4 method for signature 'SingleCellExperiment'
sc3_plot_cluster_stability(object, k)

Arguments

object

an object of 'SingleCellExperiment' class

k

number of clusters


Plot consensus matrix as a heatmap

Description

The consensus matrix is a NxN matrix, where N is the number of cells. It represents similarity between the cells based on the averaging of clustering results from all combinations of clustering parameters. Similarity 0 (blue) means that the two cells are always assigned to different clusters. In contrast, similarity 1 (red) means that the two cells are always assigned to the same cluster. The consensus matrix is clustered by hierarchical clustering and has a diagonal-block structure. Intuitively, the perfect clustering is achieved when all diagonal blocks are completely red and all off-diagonal elements are completely blue.

Usage

sc3_plot_consensus.SingleCellExperiment(object, k, show_pdata)

## S4 method for signature 'SingleCellExperiment'
sc3_plot_consensus(object, k,
  show_pdata = NULL)

Arguments

object

an object of 'SingleCellExperiment' class

k

number of clusters

show_pdata

a vector of colnames of the pData(object) table. Default is NULL. If not NULL will add pData annotations to the columns of the output matrix


Plot expression of DE genes of the clusters identified by SC3 as a heatmap

Description

SC3 plots gene expression profiles of the 50 genes with the lowest p-values.

Usage

sc3_plot_de_genes.SingleCellExperiment(object, k, p.val, show_pdata)

## S4 method for signature 'SingleCellExperiment'
sc3_plot_de_genes(object, k, p.val = 0.01,
  show_pdata = NULL)

Arguments

object

an object of 'SingleCellExperiment' class

k

number of clusters

p.val

significance threshold used for the DE genes

show_pdata

a vector of colnames of the pData(object) table. Default is NULL. If not NULL will add pData annotations to the columns of the output matrix


Plot expression matrix used for SC3 clustering as a heatmap

Description

The expression panel represents the original input expression matrix (cells in columns and genes in rows) after the gene filter. Genes are clustered by kmeans with k = 100 (dendrogram on the left) and the heatmap represents the expression levels of the gene cluster centers after log2-scaling.

Usage

sc3_plot_expression.SingleCellExperiment(object, k, show_pdata)

## S4 method for signature 'SingleCellExperiment'
sc3_plot_expression(object, k,
  show_pdata = NULL)

Arguments

object

an object of 'SingleCellExperiment' class

k

number of clusters

show_pdata

a vector of colnames of the pData(object) table. Default is NULL. If not NULL will add pData annotations to the columns of the output matrix


Plot expression of marker genes identified by SC3 as a heatmap.

Description

By default the genes with the area under the ROC curve (AUROC) > 0.85 and with the p-value < 0.01 are selected and the top 10 marker genes of each cluster are visualized in this heatmap.

Usage

sc3_plot_markers.SingleCellExperiment(object, k, auroc, p.val, show_pdata)

## S4 method for signature 'SingleCellExperiment'
sc3_plot_markers(object, k, auroc = 0.85,
  p.val = 0.01, show_pdata = NULL)

Arguments

object

an object of 'SingleCellExperiment' class

k

number of clusters

auroc

area under the ROC curve

p.val

significance threshold used for the DE genes

show_pdata

a vector of colnames of the pData(object) table. Default is NULL. If not NULL will add pData annotations to the columns of the output matrix


Plot silhouette indexes of the cells

Description

A silhouette is a quantitative measure of the diagonality of the consensus matrix. An average silhouette width (shown at the bottom left of the silhouette plot) varies from 0 to 1, where 1 represents a perfectly block-diagonal consensus matrix and 0 represents a situation where there is no block-diagonal structure. The best clustering is achieved when the average silhouette width is close to 1.

Usage

sc3_plot_silhouette.SingleCellExperiment(object, k)

## S4 method for signature 'SingleCellExperiment'
sc3_plot_silhouette(object, k)

Arguments

object

an object of 'SingleCellExperiment' class

k

number of clusters


Prepare the SingleCellExperiment object for SC3 clustering.

Description

This function prepares an object of SingleCellExperiment class for SC3 clustering. It creates and populates the following items of the sc3 slot of the metadata(object):

  • kmeans_iter_max - the same as the kmeans_iter_max argument.

  • kmeans_nstart - the same as the kmeans_nstart argument.

  • n_dim - contains numbers of the number of eigenvectors to be used in kmeans clustering.

  • rand_seed - the same as the rand_seed argument.

  • svm_train_inds - if SVM is used this item contains indexes of the training cells to be used for SC3 clustering and further SVM prediction.

  • svm_study_inds - if SVM is used this item contains indexes of the cells to be predicted by SVM.

  • n_cores - the same as the n_cores argument.

Usage

sc3_prepare.SingleCellExperiment(object, gene_filter, pct_dropout_min,
  pct_dropout_max, d_region_min, d_region_max, svm_num_cells, svm_train_inds,
  svm_max, n_cores, kmeans_nstart, kmeans_iter_max, rand_seed)

## S4 method for signature 'SingleCellExperiment'
sc3_prepare(object, gene_filter = TRUE,
  pct_dropout_min = 10, pct_dropout_max = 90, d_region_min = 0.04,
  d_region_max = 0.07, svm_num_cells = NULL, svm_train_inds = NULL,
  svm_max = 5000, n_cores = NULL, kmeans_nstart = NULL,
  kmeans_iter_max = 1e+09, rand_seed = 1)

Arguments

object

an object of SingleCellExperiment class.

gene_filter

a boolen variable which defines whether to perform gene filtering before SC3 clustering.

pct_dropout_min

if gene_filter = TRUE, then genes with percent of dropouts smaller than pct_dropout_min are filtered out before clustering.

pct_dropout_max

if gene_filter = TRUE, then genes with percent of dropouts larger than pct_dropout_max are filtered out before clustering.

d_region_min

defines the minimum number of eigenvectors used for kmeans clustering as a fraction of the total number of cells. Default is 0.04. See SC3 paper for more details.

d_region_max

defines the maximum number of eigenvectors used for kmeans clustering as a fraction of the total number of cells. Default is 0.07. See SC3 paper for more details.

svm_num_cells

number of randomly selected training cells to be used for SVM prediction. The default is NULL.

svm_train_inds

a numeric vector defining indeces of training cells that should be used for SVM training. The default is NULL.

svm_max

define the maximum number of cells below which SVM is not run.

n_cores

defines the number of cores to be used on the user's machine. If not set, 'SC3' will use all but one cores of your machine.

kmeans_nstart

nstart parameter passed to kmeans function. Default is 1000 for up to 2000 cells and 50 for more than 2000 cells.

kmeans_iter_max

iter.max parameter passed to kmeans function. Default is 1e+09.

rand_seed

sets the seed of the random number generator. SC3 is a stochastic method, so setting the rand_seed to a fixed values can be used for reproducibility purposes.

Value

an object of SingleCellExperiment class


Run the hybrid SVM approach.

Description

This method parallelize SVM prediction for each k (the number of clusters). Namely, for each k, support_vector_machines function is utilized to predict the labels of study cells. Training cells are selected using svm_train_inds item of the sc3 slot of the metadata(object).

Usage

sc3_run_svm.SingleCellExperiment(object, ks)

## S4 method for signature 'SingleCellExperiment'
sc3_run_svm(object, ks = NULL)

Arguments

object

an object of SingleCellExperiment class

ks

a continuous range of integers - the number of clusters k to be used for SC3 clustering. Can also be a single integer.

Details

Results are written to the sc3_k_clusters columns to the colData slot of the input object, where k is the number of clusters.

Value

an object of SingleCellExperiment class


Run support vector machines (SVM) prediction

Description

Train an SVM classifier on a training dataset (train) and then classify a study dataset (study) using the classifier.

Usage

support_vector_machines(train, study, kern)

Arguments

train

training dataset with colnames, corresponding to training labels

study

study dataset

kern

kernel to be used with SVM

Value

classification of the study dataset


Matrix left-multiplied by its transpose

Description

Given matrix A, the procedure returns A'A.

Usage

tmult(x)

Arguments

x

Numeric matrix.


Distance matrix transformation

Description

All distance matrices are transformed using either principal component analysis (PCA) or by calculating the eigenvectors of the graph Laplacian (Spectral). The columns of the resulting matrices are then sorted in descending order by their corresponding eigenvalues.

Usage

transformation(dists, method)

Arguments

dists

distance matrix

method

transformation method: either 'pca' or 'laplacian'

Value

transformed distance matrix


Single cell RNA-Seq data extracted from a publication by Yan et al.

Description

Single cell RNA-Seq data extracted from a publication by Yan et al.

Usage

yan

Format

An object of class data.frame with 20214 rows and 90 columns.

Source

http://dx.doi.org/10.1038/nsmb.2660

Columns represent cells, rows represent genes expression values.