gftplot {GSD}

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) 

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.

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.

See Also

gsignal, gfdecomp.

Examples

#### 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)

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) 

# 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)