R/mpSTATIS.core.R

In MExPosition: Multi-table ExPosition

mpSTATIS.core <- function (data, num.obs, column.design, num.groups, optimization.option = 'STATIS')
{ 	
##########################################
# Inner Product
##########################################

# Scalar Product Matrices (S)
   scalarProductMatrices = array(0,dim=c(num.obs,num.obs,num.groups))
   from = 1
   for(i in 1:num.groups)
   {   from = sum(column.design[i-1,])+from
       to = from + sum(column.design[i,])-1
       scalarProductMatrices[,,i] = data[,from:to] %*% t(data[,from:to])	
   }

   scalarProductMatrices2 <- array(scalarProductMatrices, dim=c(num.obs*num.obs,num.groups))

#C Matrix
   CMatrix = t(scalarProductMatrices2) %*% scalarProductMatrices2

# RV Matrix
   Norm = sqrt(apply(scalarProductMatrices2^2,2,sum))
   rvMatrix = CMatrix/(t(t(Norm)) %*% Norm)

# eigen decomposition
   C.decomp = corePCA(CMatrix)
   decomp.C = C.decomp$pdq
   
# contribution
   ci = C.decomp$ci
   #rownames(ci)=paste('assessor',1:num.groups)
   if(is.null(rownames(column.design)))
   {  rownames(ci) <- paste("Table", 1:dim(column.design)[1], sep = "")
	   table.names <- rownames(ci)
	 }
   else
   {  rownames(ci) <- rownames(column.design)
	  	table.names <- rownames(ci)
	 }

# contribution
	cj = C.decomp$cj
	rownames(cj) <- rownames(ci)
    
# eigen vectors
   P = decomp.C$p
   rownames(P) <- rownames(ci)

# eigen values
   D= (decomp.C$Dv)

# factor scores
   G = decomp.C$p %*%  diag(sqrt(D))
   rownames(G) <- rownames(P)

# percent of variance explained
   tau <- D/sum(D) * 100
	
# Alpha Weights
   if (optimization.option == "None")
   {	alphaWeights = matrix(1/num.groups,1,num.groups)
   }
	
   if (optimization.option == "Multitable")
   {	alphaWeights = matrix(1,1,num.groups)
   }
	
   if(optimization.option == 'RV_Matrix')
   {    alphaWeights = (corePCA(rvMatrix)$pdq$p)[,1]/sum((corePCA(rvMatrix)$pdq$p)[,1])
   }
	
   if(optimization.option == "STATIS")
   {	alphaWeights = P[,1] / sum(P[,1])	
   }
	
   if(optimization.option == 'STATIS_Power1')
   {	alphaWeights = (CMatrix %*% matrix(1,num.groups,1)) / sum(CMatrix %*% matrix(1,num.groups,1))
   }

##########################################
# Compromise
##########################################

#compromise (S+)
compromiseMatrix = apply(apply(scalarProductMatrices,c(1,2), '*',t(alphaWeights)),c(2,3),sum)

#analyze compromise
PCA.compromise <- corePCA(compromiseMatrix)
compromise.PCA <- PCA.compromise$pdq

#contribution
compromise.ci <- PCA.compromise$ci
rownames(compromise.ci) = rownames(data)

compromise.cj <- PCA.compromise$cj
rownames(compromise.cj) = rownames(data)

#eigen vectors
compromise.P = compromise.PCA$p
rownames(compromise.P) = rownames(data)

#eigen values
compromise.dd = compromise.PCA$Dv

#factor scores
compromise.G = compromise.PCA$p %*% diag(sqrt(compromise.PCA$Dv))
rownames(compromise.G) = rownames(data)

# % of variance explained
compromise.tau <- compromise.PCA$Dv/sum(compromise.PCA$Dv) * 100

##########################################
# Tables: Generalized PCA of X
##########################################	

# column names	
  table.colnames <- colnames(column.design)

# weights and masses
 # M = diag(1/(dim(data)[1]),dim(data)[1],dim(data)[1])
  M = rep(1/(dim(data)[1]),dim(data)[1])
	
  w = c()
  for(i in 1:length(rowSums(column.design)))
  { w = c(w, rep(alphaWeights[i],rowSums(column.design)[i]))
  }

#general PDQ
	pdq.general = corePCA(data,M=M,W=w)
	general.pdq = pdq.general$pdq

# contribution
	table.ci = pdq.general$ci

# contribution
	table.cj = pdq.general$cj
   
# Eigen vectors of the tables
   gpdq.vectors = general.pdq$p
   rownames(gpdq.vectors)=rownames(data)

# Eigen values of the tables 
   gpdq.eigenvalues = (general.pdq$Dv)^2
	
# Inertia
   gpdq.inertia = ((general.pdq$Dv) / sum(general.pdq$Dv))*100

# Loadings of the tables
   gpdq.loadings = general.pdq$q
   rownames(gpdq.loadings) = colnames(data)

# Factor scores of the tables
   gpdq.factorscores =  general.pdq$p %*%  (general.pdq$Dd)
   rownames(gpdq.factorscores)=rownames(data)
   
# Partial Factor Scores
   gpdq.partial = array(0,dim=c(dim(data)[1],dim(gpdq.loadings)[2],num.groups))
   to_partial = 0
   from_partial = 1
   for(i in 1:dim(column.design)[1])
   {   from = sum(column.design[i-1,]) + from_partial
       to = sum(column.design[i,]) + to_partial
       to_partial = to
       from_partial = from
       gpdq.partial[,,i] = data[,from:to] %*% gpdq.loadings[from:to,]
   }
   
   gpdq.partialFS <- matrix(0,dim(data)[1]*num.groups,dim(gpdq.loadings)[2])
   to.total = 0
   for(i in 1:num.groups)
   {	from = to.total + 1
   		to = i*dim(gpdq.partial)[1]
   		to.total = to
   		gpdq.partialFS[from:to,]= gpdq.partial[,,i]
   	}
   	rownames(gpdq.partialFS) = paste(rep(table.names,each=dim(data)[1]),rep(rownames(data)))

##########################################
# Results
##########################################	

res.statis.core <- list(S=scalarProductMatrices, RVMatrix = rvMatrix, C = CMatrix, ci = ci, cj = cj, eigs.vector = P, eigs = D, 
                        fi = G, alphaWeights = alphaWeights, tau = tau,
          
                        compromise = compromiseMatrix, compromise.ci = compromise.ci, compromise.cj = compromise.cj, 
                        compromise.eigs.vector = compromise.P, compromise.eigs = compromise.dd, compromise.fi = compromise.G, 
                        compromise.tau = compromise.tau,
      
                        weights = alphaWeights, masses = M, 
                        table.partial.fi.array = gpdq.partial,table.cj = table.cj, table.ci = table.ci, 
                        table.eigs = gpdq.eigenvalues, table.tau = gpdq.inertia, table.eigs.vector = gpdq.vectors, 
                        table.loadings = gpdq.loadings,  table.fi = gpdq.factorscores,  
                        table.partial.fi = gpdq.partialFS)
    
return (res.statis.core)
}