Usage
We will give an example of how to use this packge hereafter.
Simulation data generation
We generate simulated data with five row clusters and four column clusters via the function simu_data_generation. The simulated data matrix Sim is a similarity matrix of two group of samples X1 and X2. The first group of samples X1 is comprised of 100 samples with 100 features, belonging to 5 clusters, and each cluster consists of 20 samples with mean {10,20,30,40,50} and variance 1. The second group of samples X2 is comprised of 80 samples with 100 features, belonging to 4 clusters, and each cluster consists of 20 samples with mean {5,10,15,20,25} and variance 1. The data can be generated by running:
simu_data = simu_data_generation()Structure of the simulated data: The simulation data has clear data structure, as shown in the Heatmap:
OSNMTF: Factorize the simulation data into the row coefficient matrix, the association matrix and the column coefficient matrix with orthogonal and sparsity constraints.
# Factorize the matrix with OSNMTF
OSNMTF_res <- OSNMTF(simu_data,k=5,l=4)
# Get the row coefficient matrix
row_coef <- OSNMTF_res[[1]][[1]]
# Get the association matrix
asso_matrix <- OSNMTF_res[[1]][[2]]
# Get the column coefficient matrix
column_coef <- OSNMTF_res[[1]][[3]]
# Get the row cluster results
row_cluster <- OSNMTF_res[[2]][[1]]
# Get the column cluster results
column_cluster <- OSNMTF_res[[2]][[2]]Structure of the association matrix: The association matrix has the same data structure as the simulation data, as shown in the Heatmap:
Cluster number evaluation: Evaluate the proper row and column cluster number with the metric average residue.
# Specify your desired cluster number evaluation interval by your prior knowledge of the data
ASR_matrix <- matrix(0,5,5)
for (i in 1:5)
{
rankk <- i+2
for (j in 1:5)
{
rankl <- j+2
temp_res <- OSNMTF(simu_data,k=rankk,l=rankl)
row_clu1 <- temp_res[[2]][[1]]
col_clu1 <- temp_res[[2]][[2]]
# MNSR_matrix[i,j] <- MNSR(row_clu1,col_clu1,simi_matr1)
ASR_matrix[i,j] <- ASR(row_clu1,col_clu1,simu_data)
}
}Results of the average residue: The average residue is shown in the 3D Histgram:
The larger the value, the better the corresponding cluster number. It can be found that (5,4) is the best with regard to the average residue metric, which is consistent with our data structure.