| Title: | R Toolbox for Unsupervised Spectral Clustering |
|---|---|
| Description: | Toolbox containing a variety of spectral clustering tools functions. Among the tools available are the hierarchical spectral clustering algorithm, the Shi and Malik clustering algorithm, the Perona and Freeman algorithm, the non-normalized clustering, the Von Luxburg algorithm, the Partition Around Medoids clustering algorithm, a multi-level clustering algorithm, recursive clustering and the fast method for all clustering algorithm. As well as other tools needed to run these algorithms or useful for unsupervised spectral clustering. This toolbox aims to gather the main tools for unsupervised spectral classification. See <http://mawenzi.univ-littoral.fr/> for more information and documentation. |
| Authors: | Emilie Poisson-Caillault [aut, cre, cph], Alain Lefebvre [ctb], Erwan Vincent [aut], Pierre-Alexandre Hebert [ctb] |
| Maintainer: | Emilie Poisson-Caillault <[email protected]> |
| License: | GPL (>= 2) |
| Version: | 1.0 |
| Built: | 2025-01-30 06:55:19 UTC |
| Source: | CRAN |
Function to check if a similarity matrix is Gram or not
checking.gram.similarityMatrix(W, flagDiagZero = FALSE, verbose = FALSE)checking.gram.similarityMatrix(W, flagDiagZero = FALSE, verbose = FALSE)
W |
Gram Similarity Matrix or not. |
flagDiagZero |
if True, Put zero on the similarity matrix W. |
verbose |
To output the verbose in the terminal. |
a Gram similarity matrix
Emilie Poisson Caillault and Erwan Vincent
### Example 1: 2 disks of the same size n<-100 ; r1<-1 x<-(runif(n)-0.5)*2; y<-(runif(n)-0.5)*2 keep1<-which((x*2+y*2)<(r1*2)) disk1<-data.frame(x+3*r1,y)[keep1,] disk2 <-data.frame(x-3*r1,y)[keep1,] sameTwoDisks <- rbind(disk1,disk2) W <- compute.similarity.ZP(scale(sameTwoDisks)) W <- checking.gram.similarityMatrix(W) ### Example 2: Speed and Stopping Distances of Cars W <- compute.similarity.ZP(scale(cars)) W <- checking.gram.similarityMatrix(W)### Example 1: 2 disks of the same size n<-100 ; r1<-1 x<-(runif(n)-0.5)*2; y<-(runif(n)-0.5)*2 keep1<-which((x*2+y*2)<(r1*2)) disk1<-data.frame(x+3*r1,y)[keep1,] disk2 <-data.frame(x-3*r1,y)[keep1,] sameTwoDisks <- rbind(disk1,disk2) W <- compute.similarity.ZP(scale(sameTwoDisks)) W <- checking.gram.similarityMatrix(W) ### Example 2: Speed and Stopping Distances of Cars W <- compute.similarity.ZP(scale(cars)) W <- checking.gram.similarityMatrix(W)
Function which select the number of cluster to compute thanks to a selected method
compute.kclust( eigenValues, method = "default", Kmax = 20, tolerence = 1, threshold = 0.9, verbose = FALSE )compute.kclust( eigenValues, method = "default", Kmax = 20, tolerence = 1, threshold = 0.9, verbose = FALSE )
eigenValues |
The eigenvalues of the laplacian matrix. |
method |
The method that will be used. "default" to let the function choose the most suitable method. "PEV" for the Principal EigenValue method. "GAP" for the GAP method. |
Kmax |
The maximum number of cluster which is allowed. |
tolerence |
The tolerance allowed for the Principal EigenValue method. |
threshold |
The threshold to select the dominant eigenvalue for the GAP method. |
verbose |
To output the verbose in the terminal. |
a vector which contain the number of cluster to compute.
Emilie Poisson Caillault and Erwan Vincent
### Example 1: 2 disks of the same size n<-100 ; r1<-1 x<-(runif(n)-0.5)*2; y<-(runif(n)-0.5)*2 keep1<-which((x*2+y*2)<(r1*2)) disk1<-data.frame(x+3*r1,y)[keep1,] disk2 <-data.frame(x-3*r1,y)[keep1,] sameTwoDisks <- rbind(disk1,disk2) W <- compute.similarity.ZP(scale(sameTwoDisks)) W <- checking.gram.similarityMatrix(W) eigVal <- compute.laplacian.NJW(W,verbose = TRUE)$eigen$values K <- compute.kclust(eigVal, method="default", Kmax=20, tolerence=0.99, threshold=0.9, verbose=TRUE) ### Example 2: Speed and Stopping Distances of Cars W <- compute.similarity.ZP(scale(cars)) W <- checking.gram.similarityMatrix(W) eigVal <- compute.laplacian.NJW(W,verbose = TRUE)$eigen$values K <- compute.kclust(eigVal, method="default", Kmax=20, tolerence=0.99, threshold=0.9, verbose=TRUE)### Example 1: 2 disks of the same size n<-100 ; r1<-1 x<-(runif(n)-0.5)*2; y<-(runif(n)-0.5)*2 keep1<-which((x*2+y*2)<(r1*2)) disk1<-data.frame(x+3*r1,y)[keep1,] disk2 <-data.frame(x-3*r1,y)[keep1,] sameTwoDisks <- rbind(disk1,disk2) W <- compute.similarity.ZP(scale(sameTwoDisks)) W <- checking.gram.similarityMatrix(W) eigVal <- compute.laplacian.NJW(W,verbose = TRUE)$eigen$values K <- compute.kclust(eigVal, method="default", Kmax=20, tolerence=0.99, threshold=0.9, verbose=TRUE) ### Example 2: Speed and Stopping Distances of Cars W <- compute.similarity.ZP(scale(cars)) W <- checking.gram.similarityMatrix(W) eigVal <- compute.laplacian.NJW(W,verbose = TRUE)$eigen$values K <- compute.kclust(eigVal, method="default", Kmax=20, tolerence=0.99, threshold=0.9, verbose=TRUE)
Function which select the number of cluster to compute thanks to a selected method
compute.kclust2( eigenValues, method = "default", Kmax = 20, tolerence = 1, threshold = 0.9, verbose = FALSE )compute.kclust2( eigenValues, method = "default", Kmax = 20, tolerence = 1, threshold = 0.9, verbose = FALSE )
eigenValues |
The eigenvalues of the laplacian matrix. |
method |
The method that will be used. "default" to let the function choose the most suitable method. "PEV" for the Principal EigenValue method. "GAP" for the GAP method. |
Kmax |
The maximum number of cluster which is allowed. |
tolerence |
The tolerance allowed for the Principal EigenValue method. |
threshold |
The threshold to select the dominant eigenvalue for the GAP method. |
verbose |
To output the verbose in the terminal. |
a vector which contain the number of cluster to compute.
Emilie Poisson Caillault and Erwan Vincent
Function which select the number of cluster to compute thanks to a selected method
compute.laplacian.NJW(W, verbose = FALSE)compute.laplacian.NJW(W, verbose = FALSE)
W |
Gram Similarity Matrix. |
verbose |
To output the verbose in the terminal. |
returns a list containing the following elements:
Lsym: a NJW laplacian matrix
eigen: a list that contain the eigenvectors ans eigenvalues
diag: a diagonal matrix used for the laplacian matrix
Emilie Poisson Caillault and Erwan Vincent
### Example 1: 2 disks of the same size n<-100 ; r1<-1 x<-(runif(n)-0.5)*2; y<-(runif(n)-0.5)*2 keep1<-which((x*2+y*2)<(r1*2)) disk1<-data.frame(x+3*r1,y)[keep1,] disk2 <-data.frame(x-3*r1,y)[keep1,] sameTwoDisks <- rbind(disk1,disk2) W <- compute.similarity.ZP(scale(sameTwoDisks)) W <- checking.gram.similarityMatrix(W) res <- compute.laplacian.NJW(W,verbose = TRUE) ### Example 2: Speed and Stopping Distances of Cars W <- compute.similarity.ZP(scale(cars)) W <- checking.gram.similarityMatrix(W) res <- compute.laplacian.NJW(W,verbose = TRUE)### Example 1: 2 disks of the same size n<-100 ; r1<-1 x<-(runif(n)-0.5)*2; y<-(runif(n)-0.5)*2 keep1<-which((x*2+y*2)<(r1*2)) disk1<-data.frame(x+3*r1,y)[keep1,] disk2 <-data.frame(x-3*r1,y)[keep1,] sameTwoDisks <- rbind(disk1,disk2) W <- compute.similarity.ZP(scale(sameTwoDisks)) W <- checking.gram.similarityMatrix(W) res <- compute.laplacian.NJW(W,verbose = TRUE) ### Example 2: Speed and Stopping Distances of Cars W <- compute.similarity.ZP(scale(cars)) W <- checking.gram.similarityMatrix(W) res <- compute.laplacian.NJW(W,verbose = TRUE)
Recherche du nb de cluster par selon le critere du gap
compute.nbCluster.gap(val, seuil = 0, fig = FALSE)compute.nbCluster.gap(val, seuil = 0, fig = FALSE)
val |
#valeur propre d'une matrice de similarite |
seuil |
seuil |
fig |
booleen |
Kli
Emilie Poisson Caillault v13/10/2015
Calcule matrice de similarite gaussienn
compute.similarity.gaussien(points, sigma)compute.similarity.gaussien(points, sigma)
points |
matrice pointsxattributs |
sigma |
sigma |
mat
Emilie Poisson Caillault v13/10/2015
sigma local, attention risque matrice non semi-def positive
compute.similarity.ZP(points, vois = 7)compute.similarity.ZP(points, vois = 7)
points |
matrice pointsxattributs |
vois |
nombre de voisin qui seront selectionnes |
mat
Emilie Poisson Caillault v13/10/2015
This function will sample the data before performing a classification function on the samples and then applying K nearest neighbours.
fastClustering( dataFrame, smplPoint, stopCriteria = 0.99, neighbours = 7, similarity = TRUE, clustFunction, ... )fastClustering( dataFrame, smplPoint, stopCriteria = 0.99, neighbours = 7, similarity = TRUE, clustFunction, ... )
dataFrame |
The dataFrame. |
smplPoint |
maximum of sample number for reduction. |
stopCriteria |
criterion for minimizing intra-group distance and select final smplPoint. |
neighbours |
number of points that will be selected for the similarity computation. |
similarity |
if True, will use the similarity matrix for the clustering function. |
clustFunction |
the clustering function to apply on data. |
... |
additional arguments for the clustering function. |
returns a list containing the following elements:
results: clustering results
sample: dataframe containing the sample used
quantLabels: quantization labels
clustLabels: results labels
kmeans: kmeans quantization results
Emilie Poisson Caillault and Erwan Vincent
### Example 1: 2 disks of the same size n<-100 ; r1<-1 x<-(runif(n)-0.5)*2; y<-(runif(n)-0.5)*2 keep1<-which((x*2+y*2)<(r1*2)) disk1<-data.frame(x+3*r1,y)[keep1,] disk2 <-data.frame(x-3*r1,y)[keep1,] sameTwoDisks <- rbind(disk1,disk2) res <- fastClustering(scale(sameTwoDisks),smplPoint = 500, stopCriteria = 0.99, neighbours = 7, similarity = TRUE, clustFunction = UnormalizedSC, K = 2) plot(sameTwoDisks, col = as.factor(res$clustLabels)) ### Example 2: Speed and Stopping Distances of Cars res <- fastClustering(scale(iris[,-5]),smplPoint = 500, stopCriteria = 0.99, neighbours = 7, similarity = TRUE, clustFunction = spectralPAM, K = 3) plot(iris, col = as.factor(res$clustLabels)) table(res$clustLabels,iris$Species)### Example 1: 2 disks of the same size n<-100 ; r1<-1 x<-(runif(n)-0.5)*2; y<-(runif(n)-0.5)*2 keep1<-which((x*2+y*2)<(r1*2)) disk1<-data.frame(x+3*r1,y)[keep1,] disk2 <-data.frame(x-3*r1,y)[keep1,] sameTwoDisks <- rbind(disk1,disk2) res <- fastClustering(scale(sameTwoDisks),smplPoint = 500, stopCriteria = 0.99, neighbours = 7, similarity = TRUE, clustFunction = UnormalizedSC, K = 2) plot(sameTwoDisks, col = as.factor(res$clustLabels)) ### Example 2: Speed and Stopping Distances of Cars res <- fastClustering(scale(iris[,-5]),smplPoint = 500, stopCriteria = 0.99, neighbours = 7, similarity = TRUE, clustFunction = spectralPAM, K = 3) plot(iris, col = as.factor(res$clustLabels)) table(res$clustLabels,iris$Species)
The function, for a given dataFrame, will separate the data using the Fast NJW clustering in several levels.
fastMSC( X, levelMax, silMin = 0.7, vois = 7, flagDiagZero = FALSE, method = "default", Kmax = 20, tolerence = 0.99, threshold = 0.7, minPoint = 7, verbose = FALSE )fastMSC( X, levelMax, silMin = 0.7, vois = 7, flagDiagZero = FALSE, method = "default", Kmax = 20, tolerence = 0.99, threshold = 0.7, minPoint = 7, verbose = FALSE )
X |
The dataFrame. |
levelMax |
The maximum depth level. |
silMin |
The minimal silhouette allowed. Below this value, the cluster will be cut again. |
vois |
number of points that will be selected for the similarity computation. |
flagDiagZero |
if True, Put zero on the similarity matrix W. |
method |
The method that will be used. "default" to let the function choose the most suitable method. "PEV" for the Principal EigenValue method. "GAP" for the GAP method. |
Kmax |
The maximum number of cluster which is allowed. |
tolerence |
The tolerance allowed for the Principal EigenValue method. |
threshold |
The threshold to select the dominant eigenvalue for the GAP method. |
minPoint |
The minimum number of points required to compute a cluster. |
verbose |
To output the verbose in the terminal. |
a dataframe containing the results labels of each levels
Emilie Poisson Caillault and Erwan Vincent
### Example 1: 2 disks of the same size n<-100 ; r1<-1 x<-(runif(n)-0.5)*2; y<-(runif(n)-0.5)*2 keep1<-which((x*2+y*2)<(r1*2)) disk1<-data.frame(x+3*r1,y)[keep1,] disk2 <-data.frame(x-3*r1,y)[keep1,] sameTwoDisks <- rbind(disk1,disk2) res <- fastMSC(scale(sameTwoDisks),levelMax=5, silMin=0.7, vois=7, flagDiagZero=TRUE, method = "PEV", Kmax = 20, tolerence = 0.99,threshold = 0.7, minPoint = 7, verbose = TRUE) plot(sameTwoDisks, col = as.factor(res[,ncol(res)])) ### Example 2: Speed and Stopping Distances of Cars res <- fastMSC(scale(iris[,-5]),levelMax=5, silMin=0.7, vois=7, flagDiagZero=TRUE, method = "PEV", Kmax = 20, tolerence = 0.99,threshold = 0.9, minPoint = 7, verbose = TRUE) plot(iris, col = as.factor(res[,ncol(res)])) table(res[,ncol(res)],iris$Species)### Example 1: 2 disks of the same size n<-100 ; r1<-1 x<-(runif(n)-0.5)*2; y<-(runif(n)-0.5)*2 keep1<-which((x*2+y*2)<(r1*2)) disk1<-data.frame(x+3*r1,y)[keep1,] disk2 <-data.frame(x-3*r1,y)[keep1,] sameTwoDisks <- rbind(disk1,disk2) res <- fastMSC(scale(sameTwoDisks),levelMax=5, silMin=0.7, vois=7, flagDiagZero=TRUE, method = "PEV", Kmax = 20, tolerence = 0.99,threshold = 0.7, minPoint = 7, verbose = TRUE) plot(sameTwoDisks, col = as.factor(res[,ncol(res)])) ### Example 2: Speed and Stopping Distances of Cars res <- fastMSC(scale(iris[,-5]),levelMax=5, silMin=0.7, vois=7, flagDiagZero=TRUE, method = "PEV", Kmax = 20, tolerence = 0.99,threshold = 0.9, minPoint = 7, verbose = TRUE) plot(iris, col = as.factor(res[,ncol(res)])) table(res[,ncol(res)],iris$Species)
Hierarchical Clustering
HierarchicalClust( W, K = 5, method = "ward.D2", flagDiagZero = FALSE, verbose = FALSE, ... )HierarchicalClust( W, K = 5, method = "ward.D2", flagDiagZero = FALSE, verbose = FALSE, ... )
W |
Gram Similarity Matrix. |
K |
number of cluster to obtain. |
method |
method that will be used in the hierarchical clustering. |
flagDiagZero |
if True, Put zero on the similarity matrix W. |
verbose |
To output the verbose in the terminal. |
... |
Additional parameter for the hclust function. |
returns a list containing the following elements:
cluster: a vector containing the cluster
Emilie Poisson Caillault and Erwan Vincent
### Example 1: 2 disks of the same size n<-100 ; r1<-1 x<-(runif(n)-0.5)*2; y<-(runif(n)-0.5)*2 keep1<-which((x*2+y*2)<(r1*2)) disk1<-data.frame(x+3*r1,y)[keep1,] disk2 <-data.frame(x-3*r1,y)[keep1,] sameTwoDisks <- rbind(disk1,disk2) W <- compute.similarity.ZP(scale(sameTwoDisks)) res <- HierarchicalClust(W,K=2,method="ward.D2",flagDiagZero=TRUE,verbose=TRUE) plot(sameTwoDisks, col = res$cluster) ### Example 2: Speed and Stopping Distances of Cars W <- compute.similarity.ZP(scale(iris[,-5])) res <- HierarchicalClust(W,K=2,method="ward.D2",flagDiagZero=TRUE,verbose=TRUE) plot(iris, col = res$cluster)### Example 1: 2 disks of the same size n<-100 ; r1<-1 x<-(runif(n)-0.5)*2; y<-(runif(n)-0.5)*2 keep1<-which((x*2+y*2)<(r1*2)) disk1<-data.frame(x+3*r1,y)[keep1,] disk2 <-data.frame(x-3*r1,y)[keep1,] sameTwoDisks <- rbind(disk1,disk2) W <- compute.similarity.ZP(scale(sameTwoDisks)) res <- HierarchicalClust(W,K=2,method="ward.D2",flagDiagZero=TRUE,verbose=TRUE) plot(sameTwoDisks, col = res$cluster) ### Example 2: Speed and Stopping Distances of Cars W <- compute.similarity.ZP(scale(iris[,-5])) res <- HierarchicalClust(W,K=2,method="ward.D2",flagDiagZero=TRUE,verbose=TRUE) plot(iris, col = res$cluster)
Hierarchical Spectral Clustering
HierarchicalSC( W, K = 5, method = "ward.D2", flagDiagZero = FALSE, verbose = FALSE )HierarchicalSC( W, K = 5, method = "ward.D2", flagDiagZero = FALSE, verbose = FALSE )
W |
Gram Similarity Matrix. |
K |
number of cluster to obtain. |
method |
method that will be used in the hierarchical clustering. |
flagDiagZero |
if True, Put zero on the similarity matrix W. |
verbose |
To output the verbose in the terminal. |
returns a list containing the following elements:
cluster: a vector containing the cluster
eigenVect: a vector containing the eigenvectors
eigenVal: a vector containing the eigenvalues
Emilie Poisson Caillault and Erwan Vincent
Sanchez-Garcia, R., Fernnelly, M. and al. (2014). Hierarchical Spectral Clustering of Power Grids. In IEEE Transaction on Power Systems 29.5, pages 2229-2237. ISSN : 0885-8950.
### Example 1: 2 disks of the same size n<-100 ; r1<-1 x<-(runif(n)-0.5)*2; y<-(runif(n)-0.5)*2 keep1<-which((x*2+y*2)<(r1*2)) disk1<-data.frame(x+3*r1,y)[keep1,] disk2 <-data.frame(x-3*r1,y)[keep1,] sameTwoDisks <- rbind(disk1,disk2) W <- compute.similarity.ZP(scale(sameTwoDisks)) res <- HierarchicalSC(W,K=2,method = "ward.D2",flagDiagZero=TRUE,verbose=TRUE) plot(sameTwoDisks, col = res$cluster) plot(res$eigenVect[,1:2], col = res$cluster, main="spectral space", xlim=c(-1,1),ylim=c(-1,1)); points(0,0,pch='+'); plot(res$eigenVal, main="Laplacian eigenvalues",pch='+'); ### Example 2: Speed and Stopping Distances of Cars W <- compute.similarity.ZP(scale(iris[,-5])) res <- HierarchicalSC(W,K=2,method="ward.D2",flagDiagZero=TRUE,verbose=TRUE) plot(iris, col = res$cluster) plot(res$eigenVect[,1:2], col = res$cluster, main="spectral space", xlim=c(-1,1),ylim=c(-1,1)); points(0,0,pch='+'); plot(res$eigenVal, main="Laplacian eigenvalues",pch='+');### Example 1: 2 disks of the same size n<-100 ; r1<-1 x<-(runif(n)-0.5)*2; y<-(runif(n)-0.5)*2 keep1<-which((x*2+y*2)<(r1*2)) disk1<-data.frame(x+3*r1,y)[keep1,] disk2 <-data.frame(x-3*r1,y)[keep1,] sameTwoDisks <- rbind(disk1,disk2) W <- compute.similarity.ZP(scale(sameTwoDisks)) res <- HierarchicalSC(W,K=2,method = "ward.D2",flagDiagZero=TRUE,verbose=TRUE) plot(sameTwoDisks, col = res$cluster) plot(res$eigenVect[,1:2], col = res$cluster, main="spectral space", xlim=c(-1,1),ylim=c(-1,1)); points(0,0,pch='+'); plot(res$eigenVal, main="Laplacian eigenvalues",pch='+'); ### Example 2: Speed and Stopping Distances of Cars W <- compute.similarity.ZP(scale(iris[,-5])) res <- HierarchicalSC(W,K=2,method="ward.D2",flagDiagZero=TRUE,verbose=TRUE) plot(iris, col = res$cluster) plot(res$eigenVect[,1:2], col = res$cluster, main="spectral space", xlim=c(-1,1),ylim=c(-1,1)); points(0,0,pch='+'); plot(res$eigenVal, main="Laplacian eigenvalues",pch='+');
The function use kmeans algorithm to perform data quantization.
kmeansQuantization(dataFrame, maxData, stopCriteria = 0.99)kmeansQuantization(dataFrame, maxData, stopCriteria = 0.99)
dataFrame |
The dataFrame. |
maxData |
maximum of sample number for reduction. |
stopCriteria |
criterion for minimizing intra-group distance and select final smplPoint. |
kmeans result
Emilie Poisson Caillault and Erwan Vincent
The function, for a given dataFrame, will separate the data using the NJW clustering in several levels.
MSC( X, levelMax, silMin = 0.7, vois = 7, flagDiagZero = FALSE, method = "default", Kmax = 20, tolerence = 0.99, threshold = 0.7, minPoint = 7, verbose = FALSE )MSC( X, levelMax, silMin = 0.7, vois = 7, flagDiagZero = FALSE, method = "default", Kmax = 20, tolerence = 0.99, threshold = 0.7, minPoint = 7, verbose = FALSE )
X |
The dataFrame. |
levelMax |
The maximum depth level. |
silMin |
The minimal silhouette allowed. Below this value, the cluster will be cut again. |
vois |
number of points that will be selected for the similarity computation. |
flagDiagZero |
if True, Put zero on the similarity matrix W. |
method |
The method that will be used. "default" to let the function choose the most suitable method. "PEV" for the Principal EigenValue method. "GAP" for the GAP method. |
Kmax |
The maximum number of cluster which is allowed. |
tolerence |
The tolerance allowed for the Principal EigenValue method. |
threshold |
The threshold to select the dominant eigenvalue for the GAP method. |
minPoint |
The minimum number of points required to compute a cluster. |
verbose |
To output the verbose in the terminal. |
returns a list containing the following elements:
cluster: a vector containing the cluster
eigenVect: a vector containing the eigenvectors
eigenVal: a vector containing the eigenvalues
Emilie Poisson Caillault and Erwan Vincent
Grassi, K. (2020) Definition multivariee et multi-echelle d'etats environnementaux par Machine Learning : Caracterisation de la dynamique phytoplanctonique.
### Example 1: 2 disks of the same size n<-100 ; r1<-1 x<-(runif(n)-0.5)*2; y<-(runif(n)-0.5)*2 keep1<-which((x*2+y*2)<(r1*2)) disk1<-data.frame(x+3*r1,y)[keep1,] disk2 <-data.frame(x-3*r1,y)[keep1,] sameTwoDisks <- rbind(disk1,disk2) res <- MSC(scale(sameTwoDisks),levelMax=5, silMin=0.7, vois=7, flagDiagZero=TRUE, method = "default", Kmax = 20, tolerence = 0.99,threshold = 0.7, minPoint = 7, verbose = TRUE) plot(sameTwoDisks, col = as.factor(res[,ncol(res)])) ### Example 2: Speed and Stopping Distances of Cars res <- MSC(scale(iris[,-5]),levelMax=5, silMin=0.7, vois=7, flagDiagZero=TRUE, method = "default", Kmax = 20, tolerence = 0.99,threshold = 0.9, minPoint = 7, verbose = TRUE) plot(iris, col = as.factor(res[,ncol(res)])) table(res[,ncol(res)],iris$Species)### Example 1: 2 disks of the same size n<-100 ; r1<-1 x<-(runif(n)-0.5)*2; y<-(runif(n)-0.5)*2 keep1<-which((x*2+y*2)<(r1*2)) disk1<-data.frame(x+3*r1,y)[keep1,] disk2 <-data.frame(x-3*r1,y)[keep1,] sameTwoDisks <- rbind(disk1,disk2) res <- MSC(scale(sameTwoDisks),levelMax=5, silMin=0.7, vois=7, flagDiagZero=TRUE, method = "default", Kmax = 20, tolerence = 0.99,threshold = 0.7, minPoint = 7, verbose = TRUE) plot(sameTwoDisks, col = as.factor(res[,ncol(res)])) ### Example 2: Speed and Stopping Distances of Cars res <- MSC(scale(iris[,-5]),levelMax=5, silMin=0.7, vois=7, flagDiagZero=TRUE, method = "default", Kmax = 20, tolerence = 0.99,threshold = 0.9, minPoint = 7, verbose = TRUE) plot(iris, col = as.factor(res[,ncol(res)])) table(res[,ncol(res)],iris$Species)
Bi-parted spectral clustering based on Peronna and Freeman algorithm, which separates the data into two distinct clusters
PeronaFreemanSC(W, flagDiagZero = FALSE, verbose = FALSE)PeronaFreemanSC(W, flagDiagZero = FALSE, verbose = FALSE)
W |
Gram Similarity Matrix. |
flagDiagZero |
if True, Put zero on the similarity matrix W. |
verbose |
To output the verbose in the terminal. |
returns a list containing the following elements:
cluster: a vector containing the cluster
eigenVect: a vector containing the eigenvectors
eigenVal: a vector containing the eigenvalues
Emilie Poisson Caillault and Erwan Vincent
Perona, P. and Freeman, W. (1998). A factorization approach to grouping. In European Conference on Computer Vision, pages 655-670
### Example 1: 2 disks of the same size n<-100 ; r1<-1 x<-(runif(n)-0.5)*2; y<-(runif(n)-0.5)*2 keep1<-which((x*2+y*2)<(r1*2)) disk1<-data.frame(x+3*r1,y)[keep1,] disk2 <-data.frame(x-3*r1,y)[keep1,] sameTwoDisks <- rbind(disk1,disk2) W <- compute.similarity.ZP(scale(sameTwoDisks)) res <- PeronaFreemanSC(W,flagDiagZero=TRUE,verbose=TRUE) plot(sameTwoDisks, col = res$cluster) plot(res$eigenVect[,1:2], col = res$cluster, main="spectral space", xlim=c(-1,1),ylim=c(-1,1)); points(0,0,pch='+'); plot(res$eigenVal, main="Laplacian eigenvalues",pch='+'); ### Example 2: Speed and Stopping Distances of Cars W <- compute.similarity.ZP(scale(iris[,-5])) res <- PeronaFreemanSC(W,flagDiagZero=TRUE,verbose=TRUE) plot(iris, col = res$cluster) plot(res$eigenVect[,1:2], col = res$cluster, main="spectral space", xlim=c(-1,1),ylim=c(-1,1)); points(0,0,pch='+'); plot(res$eigenVal, main="Laplacian eigenvalues",pch='+');### Example 1: 2 disks of the same size n<-100 ; r1<-1 x<-(runif(n)-0.5)*2; y<-(runif(n)-0.5)*2 keep1<-which((x*2+y*2)<(r1*2)) disk1<-data.frame(x+3*r1,y)[keep1,] disk2 <-data.frame(x-3*r1,y)[keep1,] sameTwoDisks <- rbind(disk1,disk2) W <- compute.similarity.ZP(scale(sameTwoDisks)) res <- PeronaFreemanSC(W,flagDiagZero=TRUE,verbose=TRUE) plot(sameTwoDisks, col = res$cluster) plot(res$eigenVect[,1:2], col = res$cluster, main="spectral space", xlim=c(-1,1),ylim=c(-1,1)); points(0,0,pch='+'); plot(res$eigenVal, main="Laplacian eigenvalues",pch='+'); ### Example 2: Speed and Stopping Distances of Cars W <- compute.similarity.ZP(scale(iris[,-5])) res <- PeronaFreemanSC(W,flagDiagZero=TRUE,verbose=TRUE) plot(iris, col = res$cluster) plot(res$eigenVect[,1:2], col = res$cluster, main="spectral space", xlim=c(-1,1),ylim=c(-1,1)); points(0,0,pch='+'); plot(res$eigenVal, main="Laplacian eigenvalues",pch='+');
The function, for a given dataFrame, will separate the data using the input clustering method in several levels.
recursClust( dataFrame, levelMax = 2, clustFunction, similarity = TRUE, vois = 7, flagDiagZero = FALSE, biparted = FALSE, method = "default", tolerence = 0.99, threshold = 0.9, minPoint = 7, verbose = FALSE, ... )recursClust( dataFrame, levelMax = 2, clustFunction, similarity = TRUE, vois = 7, flagDiagZero = FALSE, biparted = FALSE, method = "default", tolerence = 0.99, threshold = 0.9, minPoint = 7, verbose = FALSE, ... )
dataFrame |
The dataFrame. |
levelMax |
The maximum depth level. |
clustFunction |
the clustering function to apply on data. |
similarity |
if True, will use the similarity matrix for the clustering function. |
vois |
number of points that will be selected for the similarity computation. |
flagDiagZero |
if True, Put zero on the similarity matrix W. |
biparted |
if True, the function will not automatically choose the number of clusters to compute. |
method |
The method that will be used. "default" to let the function choose the most suitable method. "PEV" for the Principal EigenValue method. "GAP" for the GAP method. |
tolerence |
The tolerance allowed for the Principal EigenValue method. |
threshold |
The threshold to select the dominant eigenvalue for the GAP method. |
minPoint |
The minimum number of points required to compute a cluster. |
verbose |
To output the verbose in the terminal. |
... |
additional arguments for the clustering function. |
returns a list containing the following elements:
cluster: vector that contain the result of the last level
allLevels: dataframe containing the clustering results of each levels
nbLevels: the number of computed levels
Emilie Poisson Caillault and Erwan Vincent
### Example 1: 2 disks of the same size n<-100 ; r1<-1 x<-(runif(n)-0.5)*2; y<-(runif(n)-0.5)*2 keep1<-which((x*2+y*2)<(r1*2)) disk1<-data.frame(x+3*r1,y)[keep1,] disk2 <-data.frame(x-3*r1,y)[keep1,] sameTwoDisks <- rbind(disk1,disk2) res <- recursClust(scale(sameTwoDisks),levelMax=3, clustFunction =ShiMalikSC, similarity = TRUE, vois = 7, flagDiagZero = FALSE, biparted = TRUE, verbose = TRUE) plot(sameTwoDisks, col = as.factor(res$cluster)) ### Example 2: Speed and Stopping Distances of Cars res <- recursClust(scale(iris[,-5]),levelMax=4, clustFunction = spectralPAM, similarity = TRUE, vois = 7, flagDiagZero = FALSE, biparted = FALSE, method = "PEV", tolerence = 0.99, threshold = 0.9, verbose = TRUE) plot(iris, col = as.factor(res$cluster))### Example 1: 2 disks of the same size n<-100 ; r1<-1 x<-(runif(n)-0.5)*2; y<-(runif(n)-0.5)*2 keep1<-which((x*2+y*2)<(r1*2)) disk1<-data.frame(x+3*r1,y)[keep1,] disk2 <-data.frame(x-3*r1,y)[keep1,] sameTwoDisks <- rbind(disk1,disk2) res <- recursClust(scale(sameTwoDisks),levelMax=3, clustFunction =ShiMalikSC, similarity = TRUE, vois = 7, flagDiagZero = FALSE, biparted = TRUE, verbose = TRUE) plot(sameTwoDisks, col = as.factor(res$cluster)) ### Example 2: Speed and Stopping Distances of Cars res <- recursClust(scale(iris[,-5]),levelMax=4, clustFunction = spectralPAM, similarity = TRUE, vois = 7, flagDiagZero = FALSE, biparted = FALSE, method = "PEV", tolerence = 0.99, threshold = 0.9, verbose = TRUE) plot(iris, col = as.factor(res$cluster))
Recherche du voisin num id le plus proche
search.neighboor(vdist, vois)search.neighboor(vdist, vois)
vdist |
vecteur de distance du point avec d'autres points |
vois |
nombre de voisin a selectionner |
id
Emilie Poisson Caillault v13/10/2015
Bi-parted spectral clustering based on Shi and Malik algorithm, which separates the data into two distinct clusters
ShiMalikSC(W, flagDiagZero = FALSE, verbose = FALSE)ShiMalikSC(W, flagDiagZero = FALSE, verbose = FALSE)
W |
Gram Similarity Matrix. |
flagDiagZero |
if True, Put zero on the similarity matrix W. |
verbose |
To output the verbose in the terminal. |
returns a list containing the following elements:
cluster: a vector containing the cluster
eigenVect: a vector containing the eigenvectors
eigenVal: a vector containing the eigenvalues
Emilie Poisson Caillault and Erwan Vincent
Shi, J and Malik, J. (2000). Normalized cuts and image segmentation. In PAMI, Transactions on Pattern Analysis and Machine Intelligence, pages 888-905
### Example 1: 2 disks of the same size n<-100 ; r1<-1 x<-(runif(n)-0.5)*2; y<-(runif(n)-0.5)*2 keep1<-which((x*2+y*2)<(r1*2)) disk1<-data.frame(x+3*r1,y)[keep1,] disk2 <-data.frame(x-3*r1,y)[keep1,] sameTwoDisks <- rbind(disk1,disk2) W <- compute.similarity.ZP(scale(sameTwoDisks)) res <- ShiMalikSC(W,flagDiagZero=TRUE,verbose=FALSE) plot(sameTwoDisks, col = res$cluster) plot(res$eigenVect[,1:2], col = res$cluster, main="spectral space", xlim=c(-1,1),ylim=c(-1,1)); points(0,0,pch='+'); plot(res$eigenVal, main="Laplacian eigenvalues",pch='+'); ### Example 2: Speed and Stopping Distances of Cars W <- compute.similarity.ZP(scale(iris[,-5])) res <- ShiMalikSC(W,flagDiagZero=TRUE,verbose=TRUE) plot(iris, col = res$cluster) plot(res$eigenVect[,1:2], col = res$cluster, main="spectral space", xlim=c(-1,1),ylim=c(-1,1)); points(0,0,pch='+'); plot(res$eigenVal, main="Laplacian eigenvalues",pch='+');### Example 1: 2 disks of the same size n<-100 ; r1<-1 x<-(runif(n)-0.5)*2; y<-(runif(n)-0.5)*2 keep1<-which((x*2+y*2)<(r1*2)) disk1<-data.frame(x+3*r1,y)[keep1,] disk2 <-data.frame(x-3*r1,y)[keep1,] sameTwoDisks <- rbind(disk1,disk2) W <- compute.similarity.ZP(scale(sameTwoDisks)) res <- ShiMalikSC(W,flagDiagZero=TRUE,verbose=FALSE) plot(sameTwoDisks, col = res$cluster) plot(res$eigenVect[,1:2], col = res$cluster, main="spectral space", xlim=c(-1,1),ylim=c(-1,1)); points(0,0,pch='+'); plot(res$eigenVal, main="Laplacian eigenvalues",pch='+'); ### Example 2: Speed and Stopping Distances of Cars W <- compute.similarity.ZP(scale(iris[,-5])) res <- ShiMalikSC(W,flagDiagZero=TRUE,verbose=TRUE) plot(iris, col = res$cluster) plot(res$eigenVect[,1:2], col = res$cluster, main="spectral space", xlim=c(-1,1),ylim=c(-1,1)); points(0,0,pch='+'); plot(res$eigenVal, main="Laplacian eigenvalues",pch='+');
The function, for a given similarity matrix, will separate the data using a spectral space.It is based on the Jordan and Weiss algorithm. This version uses K-medoid to split the clusters.
spectralPAM(W, K, flagDiagZero = FALSE, verbose = FALSE)spectralPAM(W, K, flagDiagZero = FALSE, verbose = FALSE)
W |
Gram Similarity Matrix. |
K |
number of cluster to obtain. |
flagDiagZero |
if True, Put zero on the similarity matrix W. |
verbose |
To output the verbose in the terminal. |
returns a list containing the following elements:
cluster: a vector containing the cluster
eigenVect: a vector containing the eigenvectors
eigenVal: a vector containing the eigenvalues
Emilie Poisson Caillault and Erwan Vincent
### Example 1: 2 disks of the same size n<-100 ; r1<-1 x<-(runif(n)-0.5)*2; y<-(runif(n)-0.5)*2 keep1<-which((x*2+y*2)<(r1*2)) disk1<-data.frame(x+3*r1,y)[keep1,] disk2 <-data.frame(x-3*r1,y)[keep1,] sameTwoDisks <- rbind(disk1,disk2) W <- compute.similarity.ZP(scale(sameTwoDisks)) res <- spectralPAM(W,K=2,flagDiagZero=TRUE,verbose=TRUE) plot(sameTwoDisks, col = res$cluster) plot(res$eigenVect[,1:2], col = res$cluster, main="spectral space", xlim=c(-1,1),ylim=c(-1,1)); points(0,0,pch='+'); plot(res$eigenVal, main="Laplacian eigenvalues",pch='+'); abline(h=1,lty="dashed",col="red") ### Example 2: Speed and Stopping Distances of Cars W <- compute.similarity.ZP(scale(iris[-5])) res <- spectralPAM(W,K=2,flagDiagZero=TRUE,verbose=TRUE) plot(iris, col = res$cluster) plot(res$eigenVect[,1:2], col = res$cluster, main="spectral space", xlim=c(-1,1),ylim=c(-1,1)); points(0,0,pch='+'); plot(res$eigenVal, main="Laplacian eigenvalues",pch='+'); abline(h=1,lty="dashed",col="red")### Example 1: 2 disks of the same size n<-100 ; r1<-1 x<-(runif(n)-0.5)*2; y<-(runif(n)-0.5)*2 keep1<-which((x*2+y*2)<(r1*2)) disk1<-data.frame(x+3*r1,y)[keep1,] disk2 <-data.frame(x-3*r1,y)[keep1,] sameTwoDisks <- rbind(disk1,disk2) W <- compute.similarity.ZP(scale(sameTwoDisks)) res <- spectralPAM(W,K=2,flagDiagZero=TRUE,verbose=TRUE) plot(sameTwoDisks, col = res$cluster) plot(res$eigenVect[,1:2], col = res$cluster, main="spectral space", xlim=c(-1,1),ylim=c(-1,1)); points(0,0,pch='+'); plot(res$eigenVal, main="Laplacian eigenvalues",pch='+'); abline(h=1,lty="dashed",col="red") ### Example 2: Speed and Stopping Distances of Cars W <- compute.similarity.ZP(scale(iris[-5])) res <- spectralPAM(W,K=2,flagDiagZero=TRUE,verbose=TRUE) plot(iris, col = res$cluster) plot(res$eigenVect[,1:2], col = res$cluster, main="spectral space", xlim=c(-1,1),ylim=c(-1,1)); points(0,0,pch='+'); plot(res$eigenVal, main="Laplacian eigenvalues",pch='+'); abline(h=1,lty="dashed",col="red")
The function, for a given similarity matrix, will separate the data using a spectral space. It does not normalize the Laplacian matrix compared to other algorithms
UnormalizedSC(W, K = 5, flagDiagZero = FALSE, verbose = FALSE)UnormalizedSC(W, K = 5, flagDiagZero = FALSE, verbose = FALSE)
W |
Gram Similarity Matrix. |
K |
number of cluster to obtain. |
flagDiagZero |
if True, Put zero on the similarity matrix W. |
verbose |
To output the verbose in the terminal. |
returns a list containing the following elements:
cluster: a vector containing the cluster
eigenVect: a vector containing the eigenvectors
eigenVal: a vector containing the eigenvalues
Emilie Poisson Caillault and Erwan Vincent
### Example 1: 2 disks of the same size n<-100 ; r1<-1 x<-(runif(n)-0.5)*2; y<-(runif(n)-0.5)*2 keep1<-which((x*2+y*2)<(r1*2)) disk1<-data.frame(x+3*r1,y)[keep1,] disk2 <-data.frame(x-3*r1,y)[keep1,] sameTwoDisks <- rbind(disk1,disk2) W <- compute.similarity.ZP(scale(sameTwoDisks)) res <- UnormalizedSC(W,K=2,flagDiagZero=TRUE,verbose=TRUE) plot(sameTwoDisks, col = res$cluster) plot(res$eigenVect[,1:2], col = res$cluster, main="spectral space", xlim=c(-1,1),ylim=c(-1,1)); points(0,0,pch='+'); plot(res$eigenVal, main="Laplacian eigenvalues",pch='+'); ### Example 2: Speed and Stopping Distances of Cars W <- compute.similarity.ZP(scale(iris[,-5])) res <- UnormalizedSC(W,K=2,flagDiagZero=TRUE,verbose=TRUE) plot(iris, col = res$cluster) plot(res$eigenVect[,1:2], col = res$cluster, main="spectral space", xlim=c(-1,1),ylim=c(-1,1)); points(0,0,pch='+'); plot(res$eigenVal, main="Laplacian eigenvalues",pch='+');### Example 1: 2 disks of the same size n<-100 ; r1<-1 x<-(runif(n)-0.5)*2; y<-(runif(n)-0.5)*2 keep1<-which((x*2+y*2)<(r1*2)) disk1<-data.frame(x+3*r1,y)[keep1,] disk2 <-data.frame(x-3*r1,y)[keep1,] sameTwoDisks <- rbind(disk1,disk2) W <- compute.similarity.ZP(scale(sameTwoDisks)) res <- UnormalizedSC(W,K=2,flagDiagZero=TRUE,verbose=TRUE) plot(sameTwoDisks, col = res$cluster) plot(res$eigenVect[,1:2], col = res$cluster, main="spectral space", xlim=c(-1,1),ylim=c(-1,1)); points(0,0,pch='+'); plot(res$eigenVal, main="Laplacian eigenvalues",pch='+'); ### Example 2: Speed and Stopping Distances of Cars W <- compute.similarity.ZP(scale(iris[,-5])) res <- UnormalizedSC(W,K=2,flagDiagZero=TRUE,verbose=TRUE) plot(iris, col = res$cluster) plot(res$eigenVect[,1:2], col = res$cluster, main="spectral space", xlim=c(-1,1),ylim=c(-1,1)); points(0,0,pch='+'); plot(res$eigenVal, main="Laplacian eigenvalues",pch='+');
The function, for a given similarity matrix, will separate the data using a spectral space. It uses the Von Luxburg algorithm to do this
VonLuxburgSC(W, K = 5, flagDiagZero = FALSE, verbose = FALSE)VonLuxburgSC(W, K = 5, flagDiagZero = FALSE, verbose = FALSE)
W |
Gram Similarity Matrix. |
K |
number of cluster to obtain. |
flagDiagZero |
if True, Put zero on the similarity matrix W. |
verbose |
To output the verbose in the terminal. |
returns a list containing the following elements:
cluster: a vector containing the cluster
eigenVect: a vector containing the eigenvectors
eigenVal: a vector containing the eigenvalues
Emilie Poisson Caillault and Erwan Vincent
Von Luxburg, U. (2007). A Tutorial on Spectral Clustering. Statistics and Computing, Volume 17(4), pages 395-416
### Example 1: 2 disks of the same size n<-100 ; r1<-1 x<-(runif(n)-0.5)*2; y<-(runif(n)-0.5)*2 keep1<-which((x*2+y*2)<(r1*2)) disk1<-data.frame(x+3*r1,y)[keep1,] disk2 <-data.frame(x-3*r1,y)[keep1,] sameTwoDisks <- rbind(disk1,disk2) W <- compute.similarity.ZP(scale(sameTwoDisks)) res <- VonLuxburgSC(W,K=2,flagDiagZero=TRUE,verbose=TRUE) plot(sameTwoDisks, col = res$cluster) plot(res$eigenVect[,1:2], col = res$cluster, main="spectral space", xlim=c(-1,1),ylim=c(-1,1)); points(0,0,pch='+'); plot(res$eigenVal, main="Laplacian eigenvalues",pch='+'); ### Example 2: Speed and Stopping Distances of Cars W <- compute.similarity.ZP(scale(iris[,-5])) res <- VonLuxburgSC(W,K=2,flagDiagZero=TRUE,verbose=TRUE) plot(iris, col = res$cluster) plot(res$eigenVect[,1:2], col = res$cluster, main="spectral space", xlim=c(-1,1),ylim=c(-1,1)); points(0,0,pch='+'); plot(res$eigenVal, main="Laplacian eigenvalues",pch='+');### Example 1: 2 disks of the same size n<-100 ; r1<-1 x<-(runif(n)-0.5)*2; y<-(runif(n)-0.5)*2 keep1<-which((x*2+y*2)<(r1*2)) disk1<-data.frame(x+3*r1,y)[keep1,] disk2 <-data.frame(x-3*r1,y)[keep1,] sameTwoDisks <- rbind(disk1,disk2) W <- compute.similarity.ZP(scale(sameTwoDisks)) res <- VonLuxburgSC(W,K=2,flagDiagZero=TRUE,verbose=TRUE) plot(sameTwoDisks, col = res$cluster) plot(res$eigenVect[,1:2], col = res$cluster, main="spectral space", xlim=c(-1,1),ylim=c(-1,1)); points(0,0,pch='+'); plot(res$eigenVal, main="Laplacian eigenvalues",pch='+'); ### Example 2: Speed and Stopping Distances of Cars W <- compute.similarity.ZP(scale(iris[,-5])) res <- VonLuxburgSC(W,K=2,flagDiagZero=TRUE,verbose=TRUE) plot(iris, col = res$cluster) plot(res$eigenVect[,1:2], col = res$cluster, main="spectral space", xlim=c(-1,1),ylim=c(-1,1)); points(0,0,pch='+'); plot(res$eigenVal, main="Laplacian eigenvalues",pch='+');