gftplot: Plot of the absolute values of the graph Fourier coefficients vs the eigenvalues

Description

This function displays the absolute values of the graph Fourier coefficients vs the eigenvalues.

Usage

gftplot(graph, signal = NULL, K = NULL, size = 1, plot=TRUE)

Value

If plot=TRUE, plot of the absolute values of the graph Fourier coefficients vs the eigenvalues for signal over a graph using package ggplot2. If plot=FALSE, a list with components:

absgFCoeffs: the absolute values of the graph Fourier coefficients in decreasing order.
eigenvalues: the eigenvalues according to the absolute values of the graph Fourier coefficients.

Arguments

graph: an igraph graph object with vertex attributes of coordinates x, y, a signal z, and edge attribute of weight.
signal: specifies a signal for the graph Fourier transform. When signal=NULL, a signal z of object graph is used.
K: specifies the number of frequency components.
size: specifies point size.
plot: specifies whether plot is displayed.

Details

This function displays the absolute values of the graph Fourier coefficients vs the eigenvalues for signal. The red color denotes the nonnegative graph Fourier coefficients, and the blue color indicates the negative graph Fourier coefficients.

Examples

Run this code

#### example : composite of two components having different frequencies

## define vertex coordinate
x <- y <- seq(0, 1, length=30)
xy <- expand.grid(x=x, y=y)

## weighted adjacency matrix by Gaussian kernel 
## for connecting vertices within distance 0.04
A <- adjmatrix(xy, method = "dist", 0.04) 

## signal
# high-frequency component
signal1 <- rep(sin(12.5*pi*x - 1.25*pi), 30)

# low-frequency component
signal2 <- rep(sin(5*pi*x - 0.5*pi), 30)

# composite signal
signal0 <- signal1 + signal2

# noisy signal with SNR(signal-to-noise ratio)=5
signal <- signal0 + rnorm(900, 0, sqrt(var(signal0) / 5)) 

# graph with signal
gsig <- gsignal(vertex = cbind(xy, signal), edge = A, edgetype = "matrix")

# display a signal over graph
gplot(gsig, size=3) 

# display of absolute values of the graph Fourier coefficients vs the eigenvalues 
# for signal
gftplot(gsig)
# \donttest{
gftplot(gsig, K=5, size=3)
out <- gftplot(gsig, K=5, plot=FALSE)
names(out)
# }
## signal3
# high-frequency component
signal11 <- c(outer(sin(6*pi*x - 0.5*pi), sin(6*pi*y - 0.5*pi)))

# low-frequency component
signal22 <- c(outer(sin(2*pi*x - 0.5*pi), sin(2*pi*y - 0.5*pi)))

# composite signal
signal00 <- signal11 + signal22

# noisy signal
signal3 <- signal00 + rnorm(900, 0, sqrt(var(signal00) / 5)) 

# display signal3 over graph
gplot(gsig, signal=signal3, size=3) 
# \donttest{
# display of absolute values of the graph Fourier coefficients vs the eigenvalues 
# for signal3
gftplot(gsig, signal=signal3)
gftplot(gsig, signal=signal3, K=10, size=2)
# }