| Title: | Multi-Modal Similarity Matrix Joint Factorization |
| Version: | 1.0 |
| Description: | A new method to implement clustering from multiple modality data of certain samples, the function M2SMjF() jointly factorizes multiple similarity matrices into a shared sub-matrix and several modality private sub-matrices, which is further used for clustering. Along with this method, we also provide function to calculate the similarity matrix and function to evaluate the best cluster number from the original data. |
| Imports: | dplyr, MASS, stats |
| Depends: | R (≥ 3.4.0) |
| License: | GPL-2 | GPL-3 [expanded from: GPL (≥ 2)] |
| Encoding: | UTF-8 |
| LazyData: | true |
| RoxygenNote: | 7.1.1 |
| Suggests: | knitr, rmarkdown |
| VignetteBuilder: | knitr |
| NeedsCompilation: | no |
| Packaged: | 2020-11-20 00:49:57 UTC; DELL |
| Author: | Xiaoyao Yin [aut, cre] |
| Maintainer: | Xiaoyao Yin <yinxy1992@sina.com> |
| Repository: | CRAN |
| Date/Publication: | 2020-11-23 08:40:06 UTC |
calculate the normalized mutual information.
Description
calculate the normalized mutual information of two vectors x and y.
Usage
Cal_NMI(x, y)
Arguments
x |
A vector |
y |
A vector as long as x |
Value
A number between 0 and 1 indicating the normalized mutual information
Author(s)
Xiaoyao Yin
Examples
x <- c(0.1,0.2,0.3,0.4)
y <- c(0.1,0.2,0.3,0.4)
NMI <- Cal_NMI(x,y)
the main part for M2SMJF and clustering result
Description
jointly factorize multiple matrices into a shared sub-matrix and multiple private sub-matrices
Usage
M2SMJF(WL, lambda = 0.25, theta = 10^-4, k)
Arguments
WL |
A list of similarity matrices |
lambda |
A parameter to set the relative weight of the group sparsity constraints |
theta |
A parameter to determine the convergence |
k |
A parameter to specify the cluster number |
Value
A list containing the clustering result
sub_matrices |
a list containing all the sub-matrices |
cluster_res |
the clustering result which is as long as the number of samples |
Author(s)
Xiaoyao Yin
Examples
WL <- simu_data_gen()
res <- M2SMJF(WL,0.25,10^-4,5)
Normalize the input matrix by column
Description
Normalize each column of x to have mean 0 and standard deviation 1.
Usage
Standard_Normalization(x)
Arguments
x |
A sample-feature matrix with rows as samples and columns as features |
Value
A sample-feature matrix with rows as samples and columns as features,each column of the matrix have mean 0 and standard deviation 1
Author(s)
Xiaoyao Yin
Examples
data_list <- simu_data_gen()
x <- data_list[[1]]
data_matrix <- Standard_Normalization(x)
To calculate the similarity matrix
Description
calculate the affinity matrix from the diff matrix with 20 neighbors
Usage
affinityMatrix(Diff, K = 20, sigma = 0.5)
Arguments
Diff |
A diff matrix |
K |
The number of neighbors in consideration |
sigma |
A parameter to determine the scale |
Value
W The similarity matrix
Author(s)
Xiaoyao Yin
Examples
data_list <- simu_data_gen()
Diff <- dist2eu(Standard_Normalization(data_list[[1]]),Standard_Normalization(data_list[[1]]))
simi <- affinityMatrix(Diff,20,0.5)
Calculate the cost
Description
A function to calculate the cost of the objective function
Usage
cost(new_WL_list, init_list, lambda)
Arguments
new_WL_list |
A list of matrices factorized from the similarity matrices list WL |
init_list |
A list containing the updated result in this iteration |
lambda |
A parameter to set the relative weight of the group sparsity constraints |
Value
A number indicating the total cost of the objective function
Author(s)
Xiaoyao Yin
Examples
WL <- simu_data_gen()
WL[[1]] <- affinityMatrix(dist2eu(Standard_Normalization(WL[[1]]),Standard_Normalization(WL[[1]])))
WL[[2]] <- affinityMatrix(dist2eu(Standard_Normalization(WL[[2]]),Standard_Normalization(WL[[2]])))
new_WL_list <- initialize_WL(WL)
k <- 5
lambda <- 0.25
init_list <- initialization(new_WL_list,k)
update_L_list <- update_L(new_WL_list,init_list)
update_alpha_list <- update_alpha(new_WL_list,update_L_list,lambda)
init_list <- update_alpha_list
new_loss <- cost(new_WL_list,init_list,lambda)
Calculate the agreement-based measurement
Description
Calculate the agreement-based measurement of two any pair-wise samples x_i and x_j for binary variables
Usage
dist2bin(X, C)
Arguments
X |
A sample-feature matrix with rows as samples and columns as features |
C |
The same as X |
Value
A matrix whose elements at (i,j) is the agreement-based measurement of two any pair-wise samples x_i and x_j
Author(s)
Xiaoyao Yin
Examples
data_list <- simu_data_gen()
X <- data_list[[1]]
C <- X
Diff <- dist2bin(X,C)
Calculate the chi-squared distance
Description
Calculate the chi-squared distance of two any pair-wise samples x_i and x_j for discrete variables
Usage
dist2chi(X, C)
Arguments
X |
A sample-feature matrix with rows as samples and columns as features |
C |
The same as X |
Value
A matrix whose elements at (i,j) is the chi-squared distance of two any pair-wise samples x_i and x_j
Author(s)
Xiaoyao Yin
Examples
data_list <- simu_data_gen()
X <- data_list[[1]]
C <- X
Diff <- dist2chi(X,C)
Calculate the Euclidean distance
Description
Calculate the Euclidean distance of two any pair-wise samples x_i and x_j for continuous variables
Usage
dist2eu(X, C)
Arguments
X |
A sample-feature matrix with rows as samples and columns as features |
C |
The same as X |
Value
A matrix whose elements at (i,j) is the Euclidean distance of two any pair-wise samples x_i and x_j
Author(s)
Xiaoyao Yin
Examples
data_list <- simu_data_gen()
X <- data_list[[1]]
C <- X
Diff <- dist2eu(X,C)
initialize the sub-matrix Ci into alpha*Li by SVD
Description
Li takes the first k columns of matrix d in SVD, while alpha is the mean of all the u of SVD result in each modality
Usage
initialization(WL, k)
Arguments
WL |
A list of similarity matrices |
k |
A parameter to specify the cluster number |
Value
A list with N+2 elements, the former N as modality private sub-matrices, the Nth as the shared sub-matrix and the last one as 1
Author(s)
Xiaoyao Yin
Examples
WL <- simu_data_gen()
new_WL_list <- initialize_WL(WL)
k <- 5
init_list <- initialization(new_WL_list,k)
Initialize from the similairty matrix list
Description
Factorize the each of the similairty matrix Si into Ci*t(Ci) by SVD
Usage
initialize_WL(WL)
Arguments
WL |
A list of similarity matrices |
Value
A list as long as WL with elements satisfying res[[i]]
Author(s)
Xiaoyao Yin
Examples
WL <- simu_data_gen()
new_WL_list <- initialize_WL(WL)
Calculate the modularity
Description
A function to calculate the modularity for weighted graph
Usage
new_modularity(init_list, WL)
Arguments
init_list |
A list with N+2 elements, the former N as modality private sub-matrices, the Nth as the shared sub-matrix and the last one as the current loss |
WL |
A list of similarity matrices |
Value
A single value indicating the mudularity of current factorization and clustering
Author(s)
Xiaoyao Yin
Examples
WL <- simu_data_gen()
WL[[1]] <- affinityMatrix(dist2eu(Standard_Normalization(WL[[1]]),Standard_Normalization(WL[[1]])))
WL[[2]] <- affinityMatrix(dist2eu(Standard_Normalization(WL[[2]]),Standard_Normalization(WL[[2]])))
new_WL_list <- initialize_WL(WL)
init_list <- initialization(new_WL_list,5)
res <- M2SMJF(WL,0.25,10^-4,5)
init_list <- res[[1]]
modularity <- new_modularity(init_list,WL)
Generate simulated data
Description
A function to generate simulated data with two modularities and five clusters
Usage
simu_data_gen()
Value
A list with two elements, which are the sample-feature matrices from different modality
Author(s)
Xiaoyao Yin
Examples
data_list <- simu_data_gen()
the function to update Li, for i=1,2,...,N
Description
update the sub-matrix Li, for i=1,2,...,N to convergence to its local minimum gradually
Usage
update_L(WL, init_list)
Arguments
WL |
A list of similarity matrices |
init_list |
A list with N+2 elements, the former N as modality private sub-matrices, the Nth as the shared sub-matrix and the last one as 1 |
Value
A list containing the updated result in this iteration
Author(s)
Xiaoyao Yin
Examples
WL <- simu_data_gen()
WL[[1]] <- affinityMatrix(dist2eu(Standard_Normalization(WL[[1]]),Standard_Normalization(WL[[1]])))
WL[[2]] <- affinityMatrix(dist2eu(Standard_Normalization(WL[[2]]),Standard_Normalization(WL[[2]])))
new_WL_list <- initialize_WL(WL)
k <- 5
init_list <- initialization(new_WL_list,k)
update_L_list <- update_L(WL,init_list)
the function to update alpha
Description
update the sub-matrix alpha to convergence to its local minimum gradually
Usage
update_alpha(WL, update_L_list, lambda)
Arguments
WL |
A list of similarity matrices |
update_L_list |
A list with N+2 elements, the former N as modality private sub-matrices, the Nth as the shared sub-matrix and the last one as the current loss |
lambda |
A parameter to set the relative weight of the group sparsity constraints |
Value
A list containing the updated result in this iteration
Author(s)
Xiaoyao Yin
Examples
WL <- simu_data_gen()
WL[[1]] <- affinityMatrix(dist2eu(Standard_Normalization(WL[[1]]),Standard_Normalization(WL[[1]])))
WL[[2]] <- affinityMatrix(dist2eu(Standard_Normalization(WL[[2]]),Standard_Normalization(WL[[2]])))
new_WL_list <- initialize_WL(WL)
k <- 5
lambda <- 0.25
init_list <- initialization(new_WL_list,k)
update_L_list <- update_L(new_WL_list,init_list)
update_alpha_list <- update_alpha(WL,update_L_list,lambda)