Help for package GSD

Type:

Package

Title:

Graph Signal Decomposition

Version:

1.0.0

Date:

2024-02-04

Author:

Hyeonglae Cho [aut], Hee-Seok Oh [aut], Donghoh Kim [aut, cre]

Maintainer:

Donghoh Kim <donghoh.kim@gmail.com>

Description:

Graph signals residing on the vertices of a graph have recently gained prominence in research in various fields. Many methodologies have been proposed to analyze graph signals by adapting classical signal processing tools. Recently, several notable graph signal decomposition methods have been proposed, which include graph Fourier decomposition based on graph Fourier transform, graph empirical mode decomposition, and statistical graph empirical mode decomposition. This package efficiently implements multiscale analysis applicable to various fields, and offers an effective tool for visualizing and decomposing graph signals. For the detailed methodology, see Ortega et al. (2018) <doi:10.1109/JPROC.2018.2820126>, Shuman et al. (2013) <doi:10.1109/MSP.2012.2235192>, Tremblay et al. (2014) https://www.eurasip.org/Proceedings/Eusipco/Eusipco2014/HTML/papers/1569922141.pdf, and Cho et al. (2024) "Statistical graph empirical mode decomposition by graph denoising and boundary treatment".

Depends:

R (≥ 3.5.0), igraph, Matrix, EbayesThresh, ggplot2

License:

GPL-2 | GPL-3 [expanded from: GPL (≥ 2)]

Encoding:

UTF-8

NeedsCompilation:

Packaged:

2024-02-04 14:02:32 UTC; donghohkim

Repository:

CRAN

Date/Publication:

2024-02-05 20:40:13 UTC

Weighted Adjacency Matrix

Description

This function produces weighted adjacency matrix by Gaussian kernel.

Usage

adjmatrix(xy, method = c("dist", "neighbor"), alpha)

Arguments

xy

matrix or data.frame containing vertex coordinate x, y.

method

When method="dist", edge weights are calculated by Gaussian kernel for connecting vertices within distance alpha. When method="neighbor", edge weights are calcaulated by Gaussian kernel for connecting alpha neighboring vertices.

alpha

specifies distance between vertices when method="dist", and the number of neighboring vertices when method="neighbor".

Details

This function produces a sparse weighted adjacency matrix by Gaussian kernel based on the distance between vertices.

Value

a sparse weighted adjacency matrix

References

Zeng, J., Cheung, G., and Ortega, A. (2017). Bipartite approximation for graph wavelet signal decomposition. IEEE Transactions on Signal Processing, 65(20), 5466–5480. doi:10.1109/TSP.2017.2733489

Examples

## 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
A1 <- adjmatrix(xy, method = "dist", 0.04) 

## weighted adjacency matrix by Gaussian kernel 
## for connecting seven neighboring vertices
A2 <- adjmatrix(xy, method="neighbor", 7)

Finding Local Extrema of a Graph Signal

Description

This function finds the local extrema of a graph signal identifying the edge between neighboring vertices.

Usage

gextrema(ad_mat, signal)

Arguments

ad_mat

an weighted adjacency matrix.

signal

a graph signal.

Details

This function finds the local extrema of a graph signal identifying the edge between neighboring vertices.

Value

maxima_list

vertex index of local maxima of a signal.

minima_list

vertex index of local minima of a signal.

n_extrema

the number of local maxima and local minima of a signal.

References

Tremblay, N., Borgnat, P., and Flandrin, P. (2014). Graph empirical mode decomposition. 22nd European Signal Processing Conference (EUSIPCO), 2350–2354.

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")

# local extrema
gextrema(A, signal)

# local extrema using graph object
gextrema(as_adjacency_matrix(gsig, attr="weight"), V(gsig)$z)

Graph Fourier Decomposition

Description

This function performs the graph Fourier decomposition.

Usage

gfdecomp(graph, K)

Arguments

graph

an igraph graph object with vertex attributes of coordinates x, y, a signal z, and edge attribute of weight.

K

specifies the number of frequency components.

Details

This function performs the graph Fourier decomposition.

Value

fc

list of frequency components according to the frequencies with fc[[1]] the lowest-frequency component.

residue

residue signal after extracting frequency components.

References

Ortega, A., Frossard, P., Kovačević, J., Moura, J. M. F., and Vandergheynst, P. (2018). Graph signal processing: overview, challenges, and applications. Proceedings of the IEEE 106, 808–828. doi:10.1109/JPROC.2018.2820126

Shuman, D. I., Narang, S. K., Frossard, P., Ortega, A., and Vandergheynst, P. (2013). The emerging field of signal processing on graphs: Extending high-dimensional data analysis to networks and other irregular domains. IEEE Signal Processing Magazine, 30(3), 83–98. doi:10.1109/MSP.2012.2235192

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 of absolute values of the graph Fourier coefficients vs the eigenvalues 
gftplot(gsig)
gftplot(gsig, K=5, size=3)
outgft <- gftplot(gsig, K=5, plot=FALSE)
outgft$eigenvalues

# graph Fourier decomposition 
out <- gfdecomp(gsig, K=4)
names(out)

# display of a signal, the extracted low- and high-frequency components by GFD
gplot(gsig, size=3) 
gplot(gsig, out$fc[[1]]+out$fc[[2]], size=3) 
gplot(gsig, out$fc[[3]]+out$fc[[4]], size=3)

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.

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)

Interpolation of a Graph Signal

Description

This function interpolates a graph signal utilizing the Laplacian matrix.

Usage

ginterpolating(ad_mat, signal, vertices)

Arguments

ad_mat

an weighted adjacency matrix.

signal

a graph signal.

vertices

specifies vertices for the observed signal. A signal on vertices and Laplacian matrix is used for interpolating a signal outside vertices.

Details

This function interpolates a graph signal utilizing the Laplacian matrix.

Value

a signal with interpolated points.

References

Tremblay, N., Borgnat, P., and Flandrin, P. (2014). Graph empirical mode decomposition. 22nd European Signal Processing Conference (EUSIPCO), 2350–2354.

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")

# local extrema using graph object
extremaout <- gextrema(as_adjacency_matrix(gsig, attr="weight"), V(gsig)$z)
maxima <- extremaout$maxima_list; minima <- extremaout$minima_list

# Interpolation of upper, lower and mean envelope
uenvelope <- ginterpolating(as_adjacency_matrix(gsig, attr="weight"), 
    V(gsig)$z, maxima)
lenvelope <- ginterpolating(as_adjacency_matrix(gsig, attr="weight"), 
    V(gsig)$z, minima) 
menvelope <- (uenvelope + lenvelope) / 2

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

# display mean envelope
gplot(gsig, menvelope, size=3, legend=FALSE)

Plot of a Graph Signal

Description

This function displays a signal on a graph using a color palette.

Usage

gplot(graph, signal = NULL, size = 1, limits = range(V(graph)$z), 
    gpalette = NULL, legend = 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 to be displayed over object graph using a color palette. When signal=NULL, a signal z of object graph is used.

size

specifies point size of vertex.

limits

specifies color palette limits.

gpalette

specifies a character vector of color palette. When gpalette=NULL, c('#00008D', '#002AFF', '#00D4FF', '#2AFFD4', '#FFFF00', '#FF8D00', '#FF0000') is used as default palette.

legend

if legend=FALSE, the legend is not included.

Details

This function displays a signal on a graph using a color palette.

Value

plot of a signal over a graph using package ggplot2.

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 with legend
gplot(gsig, size=3, legend=TRUE) 

# display a signal over graph without legend
gplotout <- gplot(gsig, size=3, legend=FALSE) 
gplotout

# adding labels using ggplot2 package
gplotout + 
  theme(axis.title=element_text(), 
    plot.title=element_text(hjust = 0.5, vjust = 0)) + 
    labs(x="x", y="y", title="visualization of a composite signal")

# deleting axis title, text and ticks using ggplot2 package
gplotout + 
  theme(axis.title=element_blank(),
        axis.text=element_blank(),
        axis.ticks=element_blank())

# display high-frequency component
gplot(gsig, signal1, size=3, legend=FALSE) 

# display low-frequency component
gplot(gsig, signal2, size=3, legend=FALSE)

Graph Object with a Signal

Description

This function constructs an igraph graph object with several vertex and edge attributes.

Usage

gsignal(vertex, edge, edgetype = c("matrix", "list"))

Arguments

vertex

matrix or data.frame containing vertex information. The first two columns are vertex coordinate x, y, and the third column is a signal z on each vertex.

edge

When edgetype="matrix", a square weighted adjacency matrix. This can be a sparse matrix created with Matrix package. When edgetype="list", matrix or data.frame of edge list with three columns. The first two columns are edge lists and the third column is an edge weight.

edgetype

edges and weights information are provided by "matrix" or "list".

Details

This function constructs an igraph graph object with vertex and edge attributes.

Value

an igraph graph object. The vertex attributes are vertex coordinate x, y, and a signal z on each vertex. The edge attribute is weight. These vertex and edge attributes can be identified by names(vertex_attr()) and names(edge_attr()), and are accessible by V(), E(), as_edgelist(), as_adjacency_matrix() or other igraph functions.

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")

# vertex and edge attribute
names(vertex_attr(gsig)); names(edge_attr(gsig))

# edge list
# as_edgelist(gsig, name=FALSE)

# weighted adjacency matrix
# as_adjacency_matrix(gsig, attr="weight")

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

# display a composite graph signal 
gplot(gsig, signal0, size=3)

# display high-frequency component
gplot(gsig, signal1, size=3)

# display low-frequency component
gplot(gsig, signal2, size=3)

Smoothing a Graph Signal

Description

This function denoises a graph signal.

Usage

gsmoothing(ad_mat, signal)

Arguments

ad_mat

an weighted adjacency matrix.

signal

a graph signal.

Details

This function denoises a graph signal utilizing the graph Fourier transform and empirical Bayes thresholding.

Value

a denoised signal.

References

Johnstone, I. and Silverman, B.~W. (2004). Needles and straw in haystacks: empirical Bayes estimates of possibly sparse sequences. The Annals of Statistics, 32, 594–1649. doi:10.1214/009053604000000030

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")

# local extrema using graph object
extremaout <- gextrema(as_adjacency_matrix(gsig, attr="weight"), V(gsig)$z)
maxima <- extremaout$maxima_list; minima <- extremaout$minima_list

# Interpolation of upper, lower and mean envelope
uenvelope <- ginterpolating(as_adjacency_matrix(gsig, attr="weight"), 
  V(gsig)$z, maxima)
lenvelope <- ginterpolating(as_adjacency_matrix(gsig, attr="weight"), 
  V(gsig)$z, minima) 

# smoothing upper, lower and mean envelope
suenvelope <- gsmoothing(A, uenvelope)
slenvelope <- gsmoothing(A, lenvelope) 

smenvelope <- (suenvelope + slenvelope) / 2

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

# display mean envelope
gplot(gsig, smenvelope, size=3, legend=FALSE)

Seoul Subway Ridership Data

Description

This igraph graph object represents the number of subway passengers in Seoul, Korea for January 2021. Consider the subway stations as vertices and railroads between the stations as the edges. The number of passengers for each station is regarded as the graph signal. Seoul subway ridership data can be obtained at https://www.seoulmetro.co.kr.

Usage

data(gsubway)

Format

igraph graph object. The vertex attributes are longitude x, latitude y, and the number of passengers z for each station.

Examples

data(gsubway)

# attributes
names(vertex_attr(gsubway)); names(edge_attr(gsubway)); names(graph_attr(gsubway))

# standardizing the graph signal
V(gsubway)$z <- c(scale(V(gsubway)$z))
 
# statistical graph empirical mode decomposition (SGEMD) with boundary treatment
out <- sgemd(gsubway, nimf=1, smoothing=TRUE, boundary=TRUE, connweight="graph")

# display of a signal, denoised signal by SGEMD
gplot(gsubway, size=3) 
gplot(gsubway, out$residue, size=3)

Statistical Graph Empirical Mode Decomposition

Description

This function performs statistical graph empirical mode decomposition.

Usage

sgemd(graph, nimf, smoothing = FALSE, smlevels = c(1),  
    boundary = FALSE, reflperc = 0.3, reflaver = FALSE, 
    connperc = 0.05, connweight = "boundary", 
    tol = 0.1^3, max.sift = 50, verbose = FALSE)

Arguments

graph

an igraph graph object with vertex attributes of coordinates x, y, a signal z, and edge attribute of weight.

nimf

specifies the maximum number of intrinsic mode functions (IMF).

smoothing

specifies whether intrinsic mode functions are constructed by interpolating or smoothing envelopes. When smoothing =TRUE, denoise envelopes utilizing the graph Fourier transform and empirical Bayes thresholding.

smlevels

specifies which level of the IMF is obtained by smoothing other than interpolation.

boundary

When boundary=TRUE, a given graph is reflected for boundary treatment.

reflperc

expand a graph by adding specified percentage of a graph at the boundary when boundary=TRUE.

reflaver

specifies the method assigning signal to reflected vertices. When reflaver=TRUE, the signal on reflected vertices is produced by averaging signals on neighboring vertices on a given graph. Otherwise, signal on reflected vertices is the same to the signal on a given graph.

connperc

specifies percentage of a graph for connecting a given graph and reflected graph when boundary=TRUE.

connweight

specifies the method assigning the edge weights for connecting a given graph and reflected graph when boundary=TRUE. The edge weights are calculated by Gaussian kernel considering the relative distance between vertices. When connweight="graph", the relative distance is calculated based on the maximum distance of all the neighboring edges of a given graph. When connweight="boundary", the relative distance is calculated based on the maximum distance of the connected vertices between a given graph and reflected graph.

tol

tolerance for stopping rule of sifting.

max.sift

the maximum number of sifting.

verbose

specifies whether sifting steps are displayed.

Details

This function performs statistical graph empirical mode decomposition utilizing extrema detection of a graph signal.

Value

imf

list of IMF's according to the frequencies with imf[[1]] the highest-frequency IMF.

residue

residue signal after extracting IMF's.

nimf

the number of IMF's.

n_extrema

Each row specifies the number of local maxima and local minima of the remaining signal after extracting the i-th IMF. The first row represents the number of local maxima and local minima of a given signal.

References

Huang, N. E., Shen, Z., Long, S. R., Wu, M. C., Shih, H. H., Zheng, Q., Yen, N.- C., Tung, C. C., and Liu, H. H. (1998). The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis. Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 454(1971), 903–-995. doi:10.1098/rspa.1998.0193

Kim, D., Kim, K. O., and Oh, H.-S. (2012a). Extending the scope of empirical mode decomposition by smoothing. EURASIP Journal on Advances in Signal Processing, 2012, 1–17. doi:10.1186/1687-6180-2012-168

Kim, D., Park, M., and Oh, H.-S. (2012b). Bidimensional statistical empirical mode decomposition. IEEE Signal Processing Letters, 19(4), 191–194. doi:10.1109/LSP.2012.2186566

Tremblay, N., Borgnat, P., and Flandrin, P. (2014). Graph empirical mode decomposition. 22nd European Signal Processing Conference (EUSIPCO), 2350–2354

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")

# graph empirical mode decomposition (GEMD) without boundary treatment
out1 <- sgemd(gsig, nimf=3, smoothing=FALSE, boundary=FALSE)

# denoised signal by GEMD 
dsignal1 <- out1$imf[[2]] + out1$imf[[3]] + out1$residue


# statistical graph empirical mode decomposition (SGEMD) with boundary treatment
out2 <- sgemd(gsig, nimf=3, smoothing=TRUE, boundary=TRUE)
names(out2)

# denoised signal by SGEMD 
dsignal2 <- out2$imf[[2]] + out2$imf[[3]] + out2$residue

# display of a signal, denoised signal, imf2, imf3 and residue by SGEMD
gplot(gsig, size=3) 
gplot(gsig, dsignal2, size=3) 
gplot(gsig, out2$imf[[2]], size=3) 
gplot(gsig, out2$imf[[3]], size=3) 
gplot(gsig, out2$residue, size=3)

Weighted Adjacency Matrix

Description

Usage

Arguments

Details

Value

References

See Also

Examples

Finding Local Extrema of a Graph Signal

Description

Usage

Arguments

Details

Value

References

See Also

Examples

Graph Fourier Decomposition

Description

Usage

Arguments

Details

Value

References

See Also

Examples

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

Description

Usage

Arguments

Details

Value

See Also

Examples

Interpolation of a Graph Signal

Description

Usage

Arguments

Details

Value

References

See Also

Examples

Plot of a Graph Signal

Description

Usage

Arguments

Details

Value

See Also

Examples

Graph Object with a Signal

Description

Usage

Arguments

Details

Value

See Also

Examples

Smoothing a Graph Signal

Description

Usage

Arguments

Details

Value

References

See Also

Examples

Seoul Subway Ridership Data

Description

Usage

Format

Examples

Statistical Graph Empirical Mode Decomposition

Description

Usage

Arguments

Details

Value