make_sigma {graphsim}

Generate Sigma (\Sigma) Matrix

Description

Compute the Sigma (\Sigma) matrix from an igraph structure or pre-computed matrix. These are compatible with rmvnorm and generate_expression. By default data is generated with a mean of 0 and standard deviation of 1 for each gene (with correlations between derived from the graph structure). Thus where the Sigma (\Sigma) matrix has diagonals of 1 (for the variance of each gene) then the symmetric non-diagonal terms (for covariance) determine the correlations between each gene in the output from generate_expression.

Usage

make_sigma_mat_adjmat(mat, state = NULL, cor = 0.8, sd = 1)

make_sigma_mat_comm(mat, state = NULL, cor = 0.8, sd = 1)

make_sigma_mat_laplacian(mat, state = NULL, cor = 0.8, sd = 1)

make_sigma_mat_graph(
  graph,
  state = NULL,
  cor = 0.8,
  sd = 1,
  comm = FALSE,
  laplacian = FALSE,
  directed = FALSE
)

make_sigma_mat_dist_adjmat(
  mat,
  state = NULL,
  cor = 0.8,
  sd = 1,
  absolute = FALSE
)

make_sigma_mat_dist_graph(
  graph,
  state = NULL,
  cor = 0.8,
  sd = 1,
  absolute = FALSE
)

Arguments

mat

precomputed adjacency, laplacian, commonlink, or scaled distance matrix (generated by make_distance).

state

numeric vector. Vector of length E(graph). Sign used to calculate state matrix, may be an integer state or inferred directly from expected correlations for each edge. May be applied a scalar across all edges or as a vector for each edge respectively. May also be entered as text for "activating" or "inhibiting" or as integers for activating (0,1) or inhibiting (-1,2). Compatible with inputs for plot_directed. Also takes a pre-computed state matrix from make_state if applied to the same graph multiple times.

cor

numeric. Simulated maximum correlation/covariance of two adjacent nodes. Default to 0.8.

sd

standard deviations of each gene. Defaults to 1. May be entered as a scalar applying to all genes or a vector with a separate value for each.

graph

An igraph object. May be directed or weighted.

comm

logical whether a common link matrix is used to compute sigma. Defaults to FALSE (adjacency matrix).

laplacian

logical whether a Laplacian matrix is used to compute sigma. Defaults to FALSE (adjacency matrix).

directed

logical. Whether directed information is passed to the distance matrix.

absolute

logical. Whether distances are scaled as the absolute difference from the diameter (maximum possible). Defaults to TRUE. The alternative is to calculate a relative difference from the diameter for a geometric decay in distance.

Value

a numeric covariance matrix of values in the range [-1, 1]

Author(s)

Tom Kelly [e-mail]

See Also

See also generate_expression for computing the simulated data, make_distance for computing distance from a graph object, and make_state for resolving inhibiting states.

See also plot_directed for plotting graphs or heatmap.2 for plotting matrices.

See also make_laplacian, make_commonlink, or make_adjmatrix for computing input matrices.

See also igraph for handling graph objects.

Other graphsim functions: generate_expression(), make_adjmatrix, make_commonlink, make_distance, make_laplacian, make_state, plot_directed()

Other generate simulated expression functions: generate_expression(), make_distance, make_state

Examples

# construct a synthetic graph module
library("igraph")
graph_test_edges <- rbind(c("A", "B"), c("B", "C"), c("B", "D"))
graph_test <- graph.edgelist(graph_test_edges, directed = TRUE)
# compute sigma (\eqn{\Sigma}) matrix for toy example
sigma_matrix <- make_sigma_mat_graph(graph_test, cor = 0.8)
sigma_matrix

# compute sigma (\eqn{\Sigma}) matrix  from adjacency matrix for toy example
adjacency_matrix <- make_adjmatrix_graph(graph_test)
sigma_matrix <- make_sigma_mat_adjmat(adjacency_matrix, cor = 0.8)
sigma_matrix

# compute sigma (\eqn{\Sigma}) matrix from shared edges for toy example
common_link_matrix <- make_commonlink_graph(graph_test)
sigma_matrix <- make_sigma_mat_comm(common_link_matrix, cor = 0.8)
sigma_matrix

# compute sigma (\eqn{\Sigma}) matrix from Laplacian for toy example
laplacian_matrix <- make_laplacian_graph(graph_test)
sigma_matrix <- make_sigma_mat_laplacian(laplacian_matrix, cor = 0.8)
sigma_matrix

# compute sigma (\eqn{\Sigma}) matrix from distance matrix for toy example
distance_matrix <- make_distance_graph(graph_test, absolute = FALSE)
sigma_matrix <- make_sigma_mat_dist_adjmat(distance_matrix, cor = 0.8)
sigma_matrix

# compute sigma (\eqn{\Sigma}) matrix from geometric distance directly from toy example graph
sigma_matrix <- make_sigma_mat_dist_graph(graph_test, cor = 0.8)
sigma_matrix

# compute sigma (\eqn{\Sigma}) matrix from absolute distance directly from toy example graph
sigma_matrix <- make_sigma_mat_dist_graph(graph_test, cor = 0.8, absolute = TRUE)
sigma_matrix

# compute sigma (\eqn{\Sigma}) matrix from geometric distance with sd = 2
sigma_matrix <- make_sigma_mat_dist_graph(graph_test, cor = 0.8, sd = 2)
sigma_matrix

# construct a synthetic graph network
graph_structure_edges <- rbind(c("A", "C"), c("B", "C"), c("C", "D"), c("D", "E"),
                               c("D", "F"), c("F", "G"), c("F", "I"), c("H", "I"))
graph_structure <- graph.edgelist(graph_structure_edges, directed = TRUE)

# compute sigma (\eqn{\Sigma}) matrix from geometric distance directly from synthetic graph network
sigma_matrix_graph_structure <- make_sigma_mat_dist_graph(graph_structure,
                                                          cor = 0.8, absolute = FALSE)
sigma_matrix_graph_structure
# visualise matrix
library("gplots")
heatmap.2(sigma_matrix_graph_structure, scale = "none", trace = "none",
                     col = colorpanel(50, "white", "red"))

# compute sigma (\eqn{\Sigma}) matrix from geometric distance directly from
# synthetic graph network with inhibitions
edge_state <- c(1, 1, -1, 1, 1, 1, 1, -1)
# pass edge state as a parameter
sigma_matrix_graph_structure_inhib <- make_sigma_mat_dist_graph(graph_structure, 
                                                                state = edge_state,
                                                                cor = 0.8,
                                                                absolute = FALSE)
sigma_matrix_graph_structure_inhib
# visualise matrix
library("gplots")
heatmap.2(sigma_matrix_graph_structure_inhib, scale = "none", trace = "none",
          col = colorpanel(50, "blue", "white", "red"))

# compute sigma (\eqn{\Sigma}) matrix from geometric distance directly from 
# synthetic graph network with inhibitions
E(graph_structure)$state <-  c(1, 1, -1, 1, 1, 1, 1, -1)
# pass edge state as a graph attribute
sigma_matrix_graph_structure_inhib <- make_sigma_mat_dist_graph(graph_structure,
                                                                cor = 0.8,
                                                                absolute = FALSE)
sigma_matrix_graph_structure_inhib
# visualise matrix
library("gplots")
heatmap.2(sigma_matrix_graph_structure_inhib, scale = "none", trace = "none",
          col = colorpanel(50, "blue", "white", "red"))

# import graph from package for reactome pathway
# TGF-\eqn{\Beta} receptor signaling activates SMADs (R-HSA-2173789)
TGFBeta_Smad_graph <- identity(TGFBeta_Smad_graph)

# compute sigma (\eqn{\Sigma}) matrix from geometric distance directly from TGF-\eqn{\Beta} pathway
TFGBeta_Smad_state <- E(TGFBeta_Smad_graph)$state
table(TFGBeta_Smad_state)
# states are edge attributes
 sigma_matrix_TFGBeta_Smad_inhib <- make_sigma_mat_dist_graph(TGFBeta_Smad_graph,
                                                              cor = 0.8,
                                                              absolute = FALSE)
# visualise matrix
library("gplots")
heatmap.2(sigma_matrix_TFGBeta_Smad_inhib, scale = "none", trace = "none",
          col = colorpanel(50, "blue", "white", "red"))

# compute sigma (\eqn{\Sigma}) matrix from geometric distance directly from TGF-\eqn{\Beta} pathway
TGFBeta_Smad_graph <- remove.edge.attribute(TGFBeta_Smad_graph, "state")
# compute with states removed (all negative)
sigma_matrix_TFGBeta_Smad <- make_sigma_mat_dist_graph(TGFBeta_Smad_graph,
                                                       state = -1,
                                                       cor = 0.8,
                                                       absolute = FALSE)
# visualise matrix
library("gplots")
heatmap.2(sigma_matrix_TFGBeta_Smad, scale = "none", trace = "none",
          col = colorpanel(50, "white", "red"))
# compute with states removed (all positive)
sigma_matrix_TFGBeta_Smad <- make_sigma_mat_dist_graph(TGFBeta_Smad_graph,
                                                       state = 1,
                                                       cor = 0.8,
                                                       absolute = FALSE)
# visualise matrix
library("gplots")
heatmap.2(sigma_matrix_TFGBeta_Smad, scale = "none", trace = "none",
          col = colorpanel(50, "white", "red"))

#restore edge attributes
TGFBeta_Smad_graph <- set_edge_attr(TGFBeta_Smad_graph, "state",
                                    value = TFGBeta_Smad_state)
TFGBeta_Smad_state <- E(TGFBeta_Smad_graph)$state
# states are edge attributes
 sigma_matrix_TFGBeta_Smad_inhib <- make_sigma_mat_dist_graph(TGFBeta_Smad_graph,
                                                              cor = 0.8,
                                                              absolute = FALSE)
# visualise matrix
library("gplots")
heatmap.2(sigma_matrix_TFGBeta_Smad_inhib, scale = "none", trace = "none",
          col = colorpanel(50, "blue", "white", "red"))