| Title: | Data Cloud Geometry (DCG): Using Random Walks to Find Community Structure in Social Network Analysis |
|---|---|
| Description: | Data cloud geometry (DCG) applies random walks in finding community structures for social networks. Fushing, VanderWaal, McCowan, & Koehl (2013) (<doi:10.1371/journal.pone.0056259>). |
| Authors: | Chen Chen [aut], Jian Jin [aut], Jessica Vandeleest [aut, cre], Brianne Beisner [aut], Brenda McCowan [aut, cph], Hsieh Fushing [aut, cph] |
| Maintainer: | Jessica Vandeleest <[email protected]> |
| License: | GPL (>= 2) |
| Version: | 0.9.3 |
| Built: | 2024-07-12 06:38:41 UTC |
| Source: | CRAN |
as.SimilarityMatrix convert an adjacency matrix to a similarity matrix.Convert a matrix to a similarity matrix.
as.SimilarityMatrix convert an adjacency matrix to a similarity matrix.
as.SimilarityMatrix(mat)as.SimilarityMatrix(mat)
mat |
a symmetric adjacency matrix |
a similarity matrix.
symmetricMatrix <- as.symmetricAdjacencyMatrix(monkeyGrooming, weighted = TRUE, rule = "weak") similarityMatrix <- as.SimilarityMatrix(symmetricMatrix)symmetricMatrix <- as.symmetricAdjacencyMatrix(monkeyGrooming, weighted = TRUE, rule = "weak") similarityMatrix <- as.SimilarityMatrix(symmetricMatrix)
as.symmetricAdjacencyMatrix convert an edgelist or a raw matrix to a symmetric adjacency matrix.
as.symmetricAdjacencyMatrix(Data, weighted = FALSE, rule = "weak")as.symmetricAdjacencyMatrix(Data, weighted = FALSE, rule = "weak")
Data |
either a dataframe or a matrix, representing raw interactions using either an edgelist or a matrix. Frequency of interactions for each dyad can be represented either by multiple occurrences of the dyad for a 2-column edgelist, or by a third column specifying the frequency of the interaction for a 3-column edgelist. |
weighted |
If the edgelist is a 3-column edgelist in which weight was
specified by frequency, use |
rule |
a character vector of length 1, being one of " |
There are ways of symmetrizing a matrix.
The "weak" rule symmetrize the matrix by building an edge
between nodes [i, j] and [j, i] if there is an edge
either from i to j OR from j to i.
The "strong" rule symmetrize the matrix by building an edge
between nodes [i, j] and [j, i] if there is an edge
BOTH from i to j AND from j to i.
The "upper" and the "lower" rule symmetrize the matrix
by using the "upper" or the "lower" triangle respectively.
Note, when using a 3-column edgelist (e.g. a weighted edgelist) to represent raw interactions, each dyad must be unique. If more than one rows are found with the same Initiator and recipient, sum of the frequencies will be taken to represent the freqency of interactions between this unique dyad. A warning message will prompt your attention to the accuracy of your raw data when duplicated dyads were found in a three-column edgelist.
a named matrix with the [i,j]th entry equal to the
number of times i grooms j.
symmetricMatrix <- as.symmetricAdjacencyMatrix(monkeyGrooming, weighted = TRUE, rule = "weak")symmetricMatrix <- as.symmetricAdjacencyMatrix(monkeyGrooming, weighted = TRUE, rule = "weak")
getEigenvalueList get eigenvalues from ensemble matricesgenerate eigenvalues for all ensemble matrices
getEigenvalueList get eigenvalues from ensemble matrices
getEigenvalueList(EnsList)getEigenvalueList(EnsList)
EnsList |
a list of ensemble matrices |
a list of eigenvalues for each of the ensemble matrix in the ensemble matrices list.
getEns get ensemble matrix from given similarity matrix and temperaturegenerate ensemble matrix
getEns get ensemble matrix from given similarity matrix and temperature
getEns(simMat, temperature, MaxIt = 1000, m = 5)getEns(simMat, temperature, MaxIt = 1000, m = 5)
simMat |
a similarity matrix |
temperature |
a numeric vector of length 1, indicating the temperature used to transform the similarity matrix to ensemble matrix |
MaxIt |
number of iterations for regulated random walks |
m |
maxiumnum number of time a node can be visited during random walks |
This function involves two steps.
It first generate similarity matrices of different variances
by taking the raw similarity matrix to the power of each
temperature. Then it called the function EstClust to perform random walks in the network to identify clusters.
a matrix.
getEnsList get ensemble matrices from given similarity matrix at all temperatures
getEnsList(simMat, temperatures, MaxIt = 1000, m = 5)getEnsList(simMat, temperatures, MaxIt = 1000, m = 5)
simMat |
a similarity matrix |
temperatures |
temperatures selected |
MaxIt |
number of iterations for regulated random walks |
m |
maxiumnum number of time a node can be visited during random walks |
This step is crucial in finding community structure based on the similarity matrix of the social network.
For each temperatures, the similarity matrix was taken to the power of temperature as saved as a new similarity matrix.
This allows the random walk to explore the similarity matrix at various variations.
Random walks are then performed in similarity matrices of various temperatures.
In order to prevent random walks being stucked in a locale, the parameter m was set (to 5 by default) to remove a node after m times of visits of the node.
An ensemble matrix is generated at each temperature in which values represent likelihood of two nodes being in the same community.
a list of ensemble matrices
Fushing, H., & McAssey, M. P. (2010). Time, temperature, and data cloud geometry. Physical Review E, 82(6), 061110.
Chen, C., & Fushing, H. (2012). Multiscale community geometry in a network and its application. Physical Review E, 86(4), 041120.
Fushing, H., Wang, H., VanderWaal, K., McCowan, B., & Koehl, P. (2013). Multi-scale clustering by building a robust and self correcting ultrametric topology on data points. PloS one, 8(2), e56259.
symmetricMatrix <- as.symmetricAdjacencyMatrix(monkeyGrooming, weighted = TRUE, rule = "weak") Sim <- as.SimilarityMatrix(symmetricMatrix) temperatures <- temperatureSample(start = 0.01, end = 20, n = 20, method = 'random') ## Not run: # Note: It takes a while to run the getEnsList example. Ens_list <- getEnsList(Sim, temperatures, MaxIt = 1000, m = 5) ## End(Not run)symmetricMatrix <- as.symmetricAdjacencyMatrix(monkeyGrooming, weighted = TRUE, rule = "weak") Sim <- as.SimilarityMatrix(symmetricMatrix) temperatures <- temperatureSample(start = 0.01, end = 20, n = 20, method = 'random') ## Not run: # Note: It takes a while to run the getEnsList example. Ens_list <- getEnsList(Sim, temperatures, MaxIt = 1000, m = 5) ## End(Not run)
GetSim get similarity matrix from a distance matrixGetSim get similarity matrix from a distance matrix
GetSim(D, T)GetSim(D, T)
D |
A distance matrix |
T |
Temperature. |
the similarity matrix is calculated at each temperature T.
Fushing, H., & McAssey, M. P. (2010). Time, temperature, and data cloud geometry. Physical Review E, 82(6), 061110.
Chen, C., & Fushing, H. (2012). Multiscale community geometry in a network and its application. Physical Review E, 86(4), 041120.
Fushing, H., Wang, H., VanderWaal, K., McCowan, B., & Koehl, P. (2013). Multi-scale clustering by building a robust and self correcting ultrametric topology on data points. PloS one, 8(2), e56259.
A dataset containing grooming edgelist among monkeys.
monkeyGroomingmonkeyGrooming
A data frame with 1595 rows and 2 variables:
Grooming Initiator ID
Grooming Recipient ID
Grooming Frequency
...
plotCLUSTERS plot all cluster treesgenerate tree plots for each ensemble matrix
plotCLUSTERS plot all cluster trees
plotCLUSTERS(EnsList, mfrow, mar = c(1, 1, 1, 1), line = -1.5, cex = 0.5, ...)plotCLUSTERS(EnsList, mfrow, mar = c(1, 1, 1, 1), line = -1.5, cex = 0.5, ...)
EnsList |
a list in which elements are ensemble matrices. |
mfrow |
A vector of the form |
mar |
plotting parameters with useful defaults ( |
line |
plotting parameters with useful defaults ( |
cex |
plotting parameters with useful defaults ( |
... |
further plotting parameters |
plotCLUSTERS plots all cluster trees with each tree corresponding to each ensemble matrix in the list of ens_list.
EnsList is the output from getEnsList.
mfrow determines the arrangement of multiple plots. It takes the form of
c(nr, nc) with the first parameter being the number of rows and
the second parameter being the number of columns. When deciding parameters for mfrow,
one should take into considerations size of the plotting device and number of cluster plots.
For example, there are 20 cluster plots, mfrow can be set to c(4, 5) or c(2, 10)
depending on the size and shape of the plotting area.
a graph containing all tree plots with each tree plot corresponding to the community structure from each of the ensemble matrix.
Fushing, H., & McAssey, M. P. (2010). Time, temperature, and data cloud geometry. Physical Review E, 82(6), 061110.
Chen, C., & Fushing, H. (2012). Multiscale community geometry in a network and its application. Physical Review E, 86(4), 041120.
Fushing, H., Wang, H., VanderWaal, K., McCowan, B., & Koehl, P. (2013). Multi-scale clustering by building a robust and self correcting ultrametric topology on data points. PloS one, 8(2), e56259.
symmetricMatrix <- as.symmetricAdjacencyMatrix(monkeyGrooming, weighted = TRUE, rule = "weak") Sim <- as.SimilarityMatrix(symmetricMatrix) temperatures <- temperatureSample(start = 0.01, end = 20, n = 20, method = 'random') ## Not run: # for illustration only. skip CRAN check because it ran forever. Ens_list <- getEnsList(Sim, temperatures, MaxIt = 1000, m = 5) ## End(Not run) plotCLUSTERS(EnsList = Ens_list, mfrow = c(2, 10), mar = c(1, 1, 1, 1))symmetricMatrix <- as.symmetricAdjacencyMatrix(monkeyGrooming, weighted = TRUE, rule = "weak") Sim <- as.SimilarityMatrix(symmetricMatrix) temperatures <- temperatureSample(start = 0.01, end = 20, n = 20, method = 'random') ## Not run: # for illustration only. skip CRAN check because it ran forever. Ens_list <- getEnsList(Sim, temperatures, MaxIt = 1000, m = 5) ## End(Not run) plotCLUSTERS(EnsList = Ens_list, mfrow = c(2, 10), mar = c(1, 1, 1, 1))
plotMultiEigenvalues plot eigenvalues to determine number of communities by finding the elbow pointplot eigenvalues
plotMultiEigenvalues plot eigenvalues to determine number of communities by finding the elbow point
plotMultiEigenvalues(Ens_list, mfrow, mar = c(2, 2, 2, 2), line = -1.5, cex = 0.5, ...)plotMultiEigenvalues(Ens_list, mfrow, mar = c(2, 2, 2, 2), line = -1.5, cex = 0.5, ...)
Ens_list |
a list in which elements are numeric vectors representing eigenvalues. |
mfrow |
A vector of the form |
mar |
plotting parameters with useful defaults ( |
line |
plotting parameters with useful defaults ( |
cex |
plotting parameters with useful defaults ( |
... |
further plotting parameters |
plotMultiEigenvalues plot multiple eigenvalue plots. The dark blue colored dots indicate eigenvalue greater than 0.
Each of the ensemble matrices is decomposed into eigenvalues which is used to determine appropriate number of communities.
Plotting out eigenvalues allow us to see where the elbow point is.
The curve starting from the elbow point flatten out. The number of points above (excluding) the elbow point indicates number of communities.
mfrow determines the arrangement of multiple plots. It takes the form of
c(nr, nc) with the first parameter being the number of rows and
the second parameter being the number of columns. When deciding parameters for mfrow,
one should take into considerations size of the plotting device and number of plots.
For example, there are 20 plots, mfrow can be set to c(4, 5) or c(2, 10)
depending on the size and shape of the plotting area.
a pdf file in the working directory containing all eigenvalue plots
Fushing, H., & McAssey, M. P. (2010). Time, temperature, and data cloud geometry. Physical Review E, 82(6), 061110.
Chen, C., & Fushing, H. (2012). Multiscale community geometry in a network and its application. Physical Review E, 86(4), 041120.
Fushing, H., Wang, H., VanderWaal, K., McCowan, B., & Koehl, P. (2013). Multi-scale clustering by building a robust and self correcting ultrametric topology on data points. PloS one, 8(2), e56259.
symmetricMatrix <- as.symmetricAdjacencyMatrix(monkeyGrooming, weighted = TRUE, rule = "weak") Sim <- as.SimilarityMatrix(symmetricMatrix) temperatures <- temperatureSample(start = 0.01, end = 20, n = 20, method = 'random') ## Not run: # for illustration only. skip CRAN check because it ran forever. Ens_list <- getEnsList(Sim, temperatures, MaxIt = 1000, m = 5) ## End(Not run) plotMultiEigenvalues(Ens_list = Ens_list, mfrow = c(10, 2), mar = c(1, 1, 1, 1))symmetricMatrix <- as.symmetricAdjacencyMatrix(monkeyGrooming, weighted = TRUE, rule = "weak") Sim <- as.SimilarityMatrix(symmetricMatrix) temperatures <- temperatureSample(start = 0.01, end = 20, n = 20, method = 'random') ## Not run: # for illustration only. skip CRAN check because it ran forever. Ens_list <- getEnsList(Sim, temperatures, MaxIt = 1000, m = 5) ## End(Not run) plotMultiEigenvalues(Ens_list = Ens_list, mfrow = c(10, 2), mar = c(1, 1, 1, 1))
plotTrees plot one cluster treegenerate tree plots for selected ensemble matrix
plotTrees plot one cluster tree
plotTheCluster(EnsList, index, ...)plotTheCluster(EnsList, index, ...)
EnsList |
a list in which elements are ensemble matrices. |
index |
an integer. index of which ensemble matrix you want to plot. |
... |
plotting parameters passed to |
a tree plot
temperatureSample generate tempatures based on either random or fixed intervalsgenerate temperatures
temperatureSample generate tempatures based on either random or fixed intervals
temperatureSample(start = 0.01, end = 20, n = 20, method = "random")temperatureSample(start = 0.01, end = 20, n = 20, method = "random")
start |
a numeric vector of length 1, indicating the lowest temperature |
end |
a numeric vector of length 1, indicating the highest temperature |
n |
an integer between 10 to 30, indicating the number of temperatures (more explanations on what temperatures are). |
method |
a character vector indicating the method used in selecting temperatures. It should take either 'random' or 'fixedInterval', case-sensitive. |
In using random walks to find community structure, each normalized similarity matrix is evaluated at different temperatures. This allows greater variations in the normalized similarity matrices. It is recommended to try out 20 - 30 temperatures to allow for a thorough exploration of the matrices. A range of temperatures which lead to stable community structures should be considered as reliable. The temperature in the middle of the range should be selected.
a numeric vector of length n representing temperatures sampled.
Fushing, H., & McAssey, M. P. (2010). Time, temperature, and data cloud geometry. Physical Review E, 82(6), 061110.
Chen, C., & Fushing, H. (2012). Multiscale community geometry in a network and its application. Physical Review E, 86(4), 041120.
Fushing, H., Wang, H., VanderWaal, K., McCowan, B., & Koehl, P. (2013). Multi-scale clustering by building a robust and self correcting ultrametric topology on data points. PloS one, 8(2), e56259.
symmetricMatrix <- as.symmetricAdjacencyMatrix(monkeyGrooming, weighted = TRUE, rule = "weak") Sim <- as.SimilarityMatrix(symmetricMatrix) temperatures <- temperatureSample(start = 0.01, end = 20, n = 20, method = 'random')symmetricMatrix <- as.symmetricAdjacencyMatrix(monkeyGrooming, weighted = TRUE, rule = "weak") Sim <- as.SimilarityMatrix(symmetricMatrix) temperatures <- temperatureSample(start = 0.01, end = 20, n = 20, method = 'random')