R/ndr.R

In nda: Generalized Network-Based Dimensionality Reduction and Analysis

#-----------------------------------------------------------------------------#
#                                                                             #
#  GENERALIZED NETWORK-BASED DIMENSIONALITY REDUCTION AND ANALYSIS (GNDA)     #
#                                                                             #
#  Written by: Zsolt T. Kosztyan*, Marcell T. Kurbucz, Attila I. Katona,      #
#              Zahid Khan                                                     #
#              *Department of Quantitative Methods                            #
#              University of Pannonia, Hungary                                #
#              kosztyan.zsolt@gtk.uni-pannon.hu                               #
#                                                                             #
# Last modified: February 2024                                                #
#-----------------------------------------------------------------------------#
#### GENERALIZED NETWORK-BASED DIMENSIONALITY REDUCTION AND ANALYSIS (GNDA) ###
#' @export
ndr<-function(r,covar=FALSE,cor_method=1,cor_type=1,min_R=0,min_comm=2,Gamma=1,
              null_modell_type=4,mod_mode=6,min_evalue=0,
              min_communality=0,com_communalities=0,use_rotation=FALSE,
              rotation="oblimin"){

  cl<-match.call()
  if (!requireNamespace("energy", quietly = TRUE)) {
    stop(
      "Package \"energy\" must be installed to use this function.",
      call. = FALSE
    )
  }
  if (!requireNamespace("psych", quietly = TRUE)) {
    stop(
      "Package \"psych\" must be installed to use this function.",
      call. = FALSE
    )
  }
  if (!requireNamespace("igraph", quietly = TRUE)) {
    stop(
      "Package \"igraph\" must be installed to use this function.",
      call. = FALSE
    )
  }
  if (!requireNamespace("stats", quietly = TRUE)) {
    stop(
      "Package \"stats\" must be installed to use this function.",
      call. = FALSE
    )
  }
  if (!requireNamespace("ppcor", quietly = TRUE)) {
    stop(
      "Package \"ppcor\" must be installed to use this function.",
      call. = FALSE
    )
  }
  if (!requireNamespace("leidenAlg", quietly = TRUE)) {
    stop(
      "Package \"leidenAlg\" must be installed to use this function.",
      call. = FALSE
    )
  }
  DATA<-r
  X<-r

  # Prepare correlation matrix

  if (covar==FALSE){
    if (cor_type==1){ # Bivariate correlations
      COR=switch(
        cor_method,
        "1"=stats::cor(X),
        "2"=stats::cor(X,method="spearman"),
        "3"=stats::cor(X,method="kendall"),
        "4"=dCor(X)
      )
    }else{
      if (cor_type==2){ # Partial correlations
        COR=switch(
          cor_method,
          "1"=ppcor::pcor(X)$estimate,
          "2"=ppcor::pcor(X,method="spearman")$estimate,
          "3"=ppcor::pcor(X,method="kendall")$estimate,
          "4"=pdCor(X)
        )
      }else{ # Semi-partial correlations
        COR=switch(
          cor_method,
          "1"=ppcor::spcor(X)$estimate,
          "2"=ppcor::spcor(X,method="spearman")$estimate,
          "3"=ppcor::spcor(X,method="kendall")$estimate,
          "4"=spdCor(X)
        )
      }
    }
  }else{
    COR<-X
  }
  COR[is.na(COR)]<-0
  issymm<-isSymmetric(as.matrix(COR))

  R<-COR^2
  R<-as.data.frame(R)
  colnames(R)<-colnames(r)
  rownames(R)<-colnames(r)
  remove(COR)

  R<-R-diag(nrow(R))

  R[R<min_R]<-0

  ## Calculate null modell

  kin<-colSums(R)
  kout<-rowSums(R)
  l=sum(R)
  N<-(kout %*% t(kin))/l

  # Calculate modularity

  coords<-matrix(1,nrow(R),1)

  Gamma<-1
  null_modell_type<-4

  MTX=switch(
    null_modell_type,
    "1"=R-N*Gamma,
    "2"=R-matrix(mean(R[R>0])*Gamma,nrow(R),ncol(R)),
    "3"=R-matrix(min_R*Gamma,nrow(R),ncol(R)),
    "4"=R
  )
  MTX[MTX<0]<-0
  cor_method<-1 # Non-linear correlation only used for the correlation graph
  if (issymm==TRUE) {
    modular=switch(
      mod_mode,
      "1"=igraph::cluster_louvain(igraph::graph_from_adjacency_matrix(as.matrix(MTX),
                                                          mode = "undirected", weighted = TRUE, diag = FALSE)),
      "2"=igraph::cluster_fast_greedy(igraph::graph_from_adjacency_matrix(as.matrix(MTX),
                                                              mode = "undirected", weighted = TRUE, diag = FALSE)),
      "3"=igraph::cluster_leading_eigen(igraph::graph_from_adjacency_matrix(as.matrix(MTX),
                                                                mode = "undirected", weighted = TRUE, diag = FALSE)),
      "4"=igraph::cluster_infomap(igraph::graph_from_adjacency_matrix(as.matrix(MTX),
                                                          mode = "undirected", weighted = TRUE, diag = FALSE)),
      "5"=igraph::cluster_walktrap(igraph::graph_from_adjacency_matrix(as.matrix(MTX),
                                                           mode = "undirected", weighted = TRUE, diag = FALSE)),
      "6"=leidenAlg::leiden.community(igraph::graph_from_adjacency_matrix(as.matrix(MTX),
                                                              mode = "directed", weighted = TRUE, diag = FALSE))
    )
  }else{
    modular=switch(
      mod_mode,
      "1"=igraph::cluster_louvain(igraph::graph_from_adjacency_matrix(as.matrix(MTX),
                                                          mode = "max", weighted = TRUE, diag = FALSE)),
      "2"=igraph::cluster_fast_greedy(igraph::graph_from_adjacency_matrix(as.matrix(MTX),
                                                              mode = "max", weighted = TRUE, diag = FALSE)),
      "3"=igraph::cluster_leading_eigen(igraph::graph_from_adjacency_matrix(as.matrix(MTX),
                                                                mode = "max", weighted = TRUE, diag = FALSE)),
      "4"=igraph::cluster_infomap(igraph::graph_from_adjacency_matrix(as.matrix(MTX),
                                                          mode = "directed", weighted = TRUE, diag = FALSE)),
      "5"=igraph::cluster_walktrap(igraph::graph_from_adjacency_matrix(as.matrix(MTX),
                                                           mode = "directed", weighted = TRUE, diag = FALSE)),
      "6"=leidenAlg::leiden.community(igraph::graph_from_adjacency_matrix(as.matrix(MTX),
                                                                      mode = "directed", weighted = TRUE, diag = FALSE))
    )
  }

  S<-as.numeric(modular$membership)

  # igraph::sizes(modular)

  for (i in 1: max(S)){
    if (nrow(as.matrix(coords[S==i]))<min_comm){
      coords[S==i]<-0
    }
  }

  S[coords==0]<-0

  # Estimate latent variables

  M<-sort(unique(S))
  if (min(M)>0)
  {
    M2=min(M):(length(M))
  }else{
    M2=min(M):(length(M)-1)
  }
  S<-M2[match(S,M)]
  M<-M2
  if (M[1]==0){
    M<-M[-1]
  }

  if (covar==FALSE){
    r<-X;
    is.na(r)<-sapply(r, is.infinite)
    r[is.na(r)]<-0
  }
  # Feature selection (1) - Drop peripheric items
  Coords<-c(1:nrow(as.matrix(S)))
  L<-matrix(0,nrow(DATA),nrow(as.matrix(M))) # Factor scores

  EVCs<-list()
  DATAs<-list()
  for (i in 1:nrow(as.matrix(M))){
    Coordsi<-Coords[(S==M[i])&(coords==1)]
    if (issymm==TRUE) {
      EVC<-as.matrix(igraph::eigen_centrality(igraph::graph_from_adjacency_matrix(
        as.matrix(R[Coordsi,Coordsi]), mode = "undirected",
        weighted = TRUE, diag = FALSE))$vector)
    }else{
      EVC<-as.matrix(igraph::eigen_centrality(igraph::graph_from_adjacency_matrix(
        as.matrix(R[Coordsi,Coordsi]), mode = "directed",
        weighted = TRUE, diag = FALSE))$vector)
    }
    if ((nrow(as.matrix(EVC[EVC>min_evalue]))>2)&(nrow(EVC)>2)){
      L[,i]<-as.matrix(rowSums(r[,
                                 Coordsi[EVC>min_evalue]] * EVC[EVC>min_evalue]))
      coords[Coordsi[EVC<=min_evalue]]<-0
      coords[Coordsi[EVC<=min_evalue]]<-0
      S[Coordsi[EVC<=min_evalue]]<-0
    }else{
      L[,i]<-as.matrix(rowSums(r[,Coordsi] * EVC))
    }
    EVCs[[i]]=EVC[EVC>min_evalue]
    DATAs[[i]]=r[,S==M[i]];
  }
  if (ncol(L)>1 && use_rotation==TRUE){
    L<-psych::principal(L,nfactors = dim(L)[2],
                        rotate = rotation)$scores
  }else{
    L<-scale(L)
  }

  C=switch(
    cor_method,
    "1"=stats::cor(L),
    "2"=stats::cor(L,method="spearman"),
    "3"=stats::cor(L,method="kendall"),
    "4"=dCor(L)
  )
  CoordsS<-Coords[S!=0]
  CoordsC<-c(1:nrow(as.matrix(CoordsS)))
  if (covar==FALSE){
    LOADING=switch(
      cor_method,
      "1"=stats::cor(r[,S>0],L),
      "2"=stats::cor(r[,S>0],L,method="spearman"),
      "3"=stats::cor(r[,S>0],L,method="kendall"),
      "4"=dCor(r[,S>0],L)
    )
  }else{
    LOADING<-matrix(0,length(S),nrow(as.matrix(M))) # Factor scores
    for (i in 1:nrow(as.matrix(M))){
      LOADING[Coords[S==i],i]<-EVCs[[i]]
    }
    LOADING<-as.matrix(LOADING[Coords[S!=0],])
    rownames(LOADING)<-names(as.data.frame(r))[S>0]
  }
  COMMUNALITY<-t(apply(LOADING^2,1,max))

  # Feature selection (2) - Drop items with low communality

  COMMUNALITY<-t(apply(LOADING^2,1,max))
  COMMUNALITY[is.na(COMMUNALITY)]<-0
  max_it<-100
  it<-1
  while ((min(COMMUNALITY)<min_communality)&&(it<max_it)){
    it<-it+1
    COMMUNALITY<-t(apply(LOADING^2,1,max))
    COMMUNALITY[is.na(COMMUNALITY)]<-0
    CoordsS<-Coords[S!=0]
    CoordsC<-c(1:nrow(as.matrix(CoordsS)))
    s<-S[S!=0]
    coordsS<-coords[S!=0]
    for (i in 1:nrow(as.matrix(M))){
      Coordsi<-Coords[(S==M[i])&(coords==1)]
      CoordsiC<-CoordsC[(s==M[i])&(coordsS==1)]
      COM<-COMMUNALITY[CoordsiC]
      com_min<-min(COM)
      if (sum(COM>min_communality)>=2){
        S[Coordsi[COM<=min_communality]]<-0
        coords[Coordsi[COM<=min_communality]]<-0
        EVC<-EVCs[[i]]
        EVC<-EVC[COM>min_communality]
        EVCs[[i]]<-EVC
        L[,i]<-as.matrix(rowSums(r[,Coordsi[COM>min_communality]] * EVC))
      }else{
        EVC<-EVCs[[i]]
        L[,i]<-as.matrix(rowSums(r[,Coordsi] * EVC))
      }
    }
    if (ncol(L)>1 && use_rotation==TRUE){
      L<-psych::principal(L,nfactors = dim(L)[2],
                          rotate = rotation)$scores
    }else{
      L<-scale(L)
    }
    C=switch(
      cor_method,
      "1"=stats::cor(L),
      "2"=stats::cor(L,method="spearman"),
      "3"=stats::cor(L,method="kendall"),
      "4"=dCor(L)
    )
    if (covar==FALSE){
      LOADING=switch(
        cor_method,
        "1"=stats::cor(r[,S>0],L),
        "2"=stats::cor(r[,S>0],L,method="spearman"),
        "3"=stats::cor(r[,S>0],L,method="kendall"),
        "4"=dCor(r[,S>0],L)
      )
    }else{
      LOADING<-matrix(0,length(S),nrow(as.matrix(M))) # Factor scores
      for (i in 1:nrow(as.matrix(M))){
        LOADING[Coords[S==i],i]<-EVCs[[i]]
      }
      LOADING<-as.matrix(LOADING[Coords[S!=0],])
      rownames(LOADING)<-names(as.data.frame(r))[S>0]
    }
    COMMUNALITY<-t(apply(LOADING^2,1,max))
  }

  # Feature selection (3) - Drop items with high common communalities

  l<-FALSE
  while(l==FALSE){
    l<-TRUE
    CCs<-matrix(0,nrow(as.matrix(LOADING)),1)
    if (ncol(LOADING)>1){
      CoordsC=Coords[S!=0]
      L2<-LOADING^2
      nL2<-nrow(L2)
      for (I in 1:nL2){
        CJ<-max(L2[I,])
        CJ2<-max(L2[I,L2[I,]!=CJ]) #2nd maximal value;
        if ((CJ>=CJ2+com_communalities)||(CJ>2*CJ2)){

        }else{
          CCs[I]<-1
        }
      }
    }
    if (sum(CCs)>0){
      Coords_real<-CoordsC[CCs==1]
      COM<-COMMUNALITY[CCs==1]
      com<-sort(COM,index.return=TRUE)
      O_COM<-com[[1]]
      P_COM<-com[[2]]
      remove(com)
      Coords_real=Coords_real[P_COM]
      l<-TRUE
      i<-1
      if (nrow(as.matrix(S[S==S[Coords_real[i]]]))>2){
        l<-FALSE
        S[Coords_real]<-0
        coords[Coords_real]<-0
      }
      i<-i+1
    }
    for (i in 1:nrow(as.matrix(M))){
      Coordsi=Coords[(S==M[i])&(coords==1)]
      if (issymm==TRUE) {
        EVC<-as.matrix(igraph::eigen_centrality(igraph::graph_from_adjacency_matrix(
         as.matrix(R[Coordsi,Coordsi]), mode = "undirected",
          weighted = TRUE, diag = FALSE))$vector)
      }else{
        EVC<-as.matrix(igraph::eigen_centrality(igraph::graph_from_adjacency_matrix(
         as.matrix(R[Coordsi,Coordsi]), mode = "directed",
          weighted = TRUE, diag = FALSE))$vector)
      }
      EVCs[[i]]<-EVC
      result<-NA
      try(result <- as.matrix(rowSums(r[,Coordsi] %*% EVC)),silent=TRUE)
      if (is.null(nrow(is.nan(result)))){
        try(result <- as.matrix(rowSums(r[,Coordsi] * EVC)),silent=TRUE)
      }
      L[,i]<-result
    }
    if (ncol(L)>1 && use_rotation==TRUE){
      L<-psych::principal(L,nfactors = dim(L)[2],
                          rotate = rotation)$scores
    }else{
      L<-scale(L)
    }
    C=switch(
      cor_method,
      "1"=stats::cor(L),
      "2"=stats::cor(L,method="spearman"),
      "3"=stats::cor(L,method="kendall"),
      "4"=dCor(L)
    )
    if (covar==FALSE){
      LOADING=switch(
        cor_method,
        "1"=stats::cor(r[,S>0],L),
        "2"=stats::cor(r[,S>0],L,method="spearman"),
        "3"=stats::cor(r[,S>0],L,method="kendall"),
        "4"=dCor(r[,S>0],L)
      )
    }else{
      LOADING<-matrix(0,length(S),nrow(as.matrix(M))) # Factor scores
      for (i in 1:nrow(as.matrix(M))){
        LOADING[Coords[S==i],i]<-EVCs[[i]]
      }
      LOADING<-as.matrix(LOADING[Coords[S!=0],])
      rownames(LOADING)<-names(as.data.frame(r))[S>0]
    }
    COMMUNALITY<-t(apply(LOADING^2,1,max))
  }

  P<-list()
  P$communality<-COMMUNALITY
  P$loadings<-LOADING
  colnames(P$loadings)<-paste("NDA",1:nrow(as.matrix(M)),sep = "")
  P$uniqueness<-1-COMMUNALITY
  P$factors<-nrow(as.matrix(M))
  if (covar==FALSE){
    P$scores<-L
    rownames(P$scores)<-rownames(DATA)
    colnames(P$scores)<-paste("NDA",1:nrow(as.matrix(M)),sep = "")
  }
  P$n.obs<-nrow(DATA)
  P$R<-R
  P$membership<-S
  P$fn<-"NDA"
  P$Call<-cl
  class(P) <- "nda"
  return(P)
}