In Nisus-Liu/GRA: Grey Relational Analysis(GRA)

Grey Relational Analysis include two important function. First function: grey relational degree, which is similar to orrelation coefficient, if you want to evaluate some units, please transpose data frame before using this function. Second funtion: grey clustering, like hierarchical clustering, see hclust.

Grey Relational Degree

There are two usage of grey relational degree. This algorithm is to measure similarity of two variables, just like cor. You can transpose your data set if you want to evaluate some units.

• One is to inspect correlation of two variables, data type like:

| reference | v1 | v2 | v3 | |-----------|----|----|----| | 1.2 | 1.8|0.9 | 8.4| | 0.11 | 0.3|0.5 | 0.2| | 1.3 | 0.7|0.12|0.98| | 1.9 |1.09|2.8 |0.99|

reference: reference variable, grey relational degree between reference and v1... approximately measures the similarity of reference and v1.

• Another is to evaluate good or bad about some units.

| units | v1 | v2 | v3 | |-----------|----|----|----| | jiangsu | 1.8|0.9 | 8.4| | zhejiang | 0.3|0.5 | 0.2| | anhui | 0.7|0.12|0.98| | fujian |1.09|2.8 |0.99|

Example

#' @title Grey Relational Analysis(GRA)
#' @description first function: grey relational degree, which is similar to orrelation coefficient, if you want to evaluate some unit, please transpose data frame before using this function.
#' second funtion: grey clustering, like hierarchical clustering, see \code{hclust}.
#' @param df a data frame with standardized data which can aviod the effects of dimensions. Note: it must
#' includes reference sequence.
#' @param referColNum the number of reference sequence in \code{df}.
#' @param distingCoeff distinguishing coefficient, the smaller the higher distinguish.
#' @param cluster logical value, indicates whether to cluster, default is \code{FALSE}. Note: this algorithm clusters by column(most clustering method are by row) because it is
#' base on grey relational degree algorithm(mode like correlation coefficient, not evaluating mode).
#' @param clusterMethod method of cluster.

#' @examples

#' ## generate data
#' refer = c(1,1,1,1)
#' liaoning = c(0.064, 0.082,0.978,0.423)
#' shandong = c(0.101,0.3,1,0.917)
#' jiangsu = c(0.114,0.14,0.943, 0.315)
#' zhejiang = c(0.102,0.147,0.934,0.395)
#' fujian = c(0.022,0.053,0.927,0.061)
#' guangdong = c(1,1,0.012,1)
#' economyCompare = data.frame(refer, liaoning, shandong, jiangsu, zhejiang, fujian, guangdong)
#' rownames(economyCompare) = c("indGV", "indVA", "profit", "incomeTax")

#' ## Grey Relational Degree
#' greyRelDegree = GRA(economyCompare)
#' greyRelDegree

#' ## Grey Clustering
#' GRA(economyCompare, cluster = T)


GRA = function(df, referColNum = 1, distingCoeff = 0.5, cluster = FALSE, clusterMethod = "single")  {

  # 异常控制 #
  if (any(is.na(df))) stop("'df' have NA" )
  if (distingCoeff<0 | distingCoeff>1) stop("'distingCoeff' must be in range of [0,1]" )
  if (referColNum<0 | referColNum>ncol(df)) stop("'referColNum' out of range")


  y = df[referColNum]
  nr = nrow(y)
  X = df[-referColNum]
  nc = ncol(X)


  diff = X  #设置差学列矩阵空间

  for (i in 1:nc) {
    diff[i] = abs(y-X[i])
  }

  mi = min(diff)
  mx = max(diff)


  #计算关联系数#
  relations = (mi+distingCoeff*mx) / (diff + distingCoeff*mx)

  #计算关联度#
  # 暂时简单处理, 等权
  relDegree = rep(NA, nc)
  for (i in 1:nc) {
    relDegree[i] = mean(relations[,i])  # 等权
  }


  #排序: 按关联度大到小#
  X_order = X[order(relDegree, decreasing = TRUE)]
  relationalDegree = relDegree[order(relDegree, decreasing = TRUE)]
  relDes = rep(NA, nc) #分配空间  关联关系描述(说明谁和谁的关联度)
  X_names = names(X_order)
  for (i in 1:nc) {
    relDes[i] = paste(names(df)[referColNum], X_names[i], sep = "~")
  }
  names(relationalDegree) = relDes

  # greyRelDegree = list(relationalDegree = relationalDegree, X_order = X_order)


  if (cluster) {

    greyRelDegree = GRA(economyCompare, referColNum = 1, distingCoeff = 0.5)


    # relationalDegree = greyRelDegree$relationalDegree
    # X = X_order



    nc = length(relationalDegree)

    # 得到差异率矩阵 #
    grey_diff = matrix(0, nrow = nc, ncol = nc)
    for (i in 1:nc) {
      for(j in 1:nc)  {

        grey_diff[i,j] = abs(relationalDegree[i] - relationalDegree[j]) / relationalDegree[j]
      }
    }
    #得到距离矩阵#
    grey_dist = matrix(0, nrow = nc, ncol = nc)
    for (i in 1:nc) {
      for (j in 1:nc) {
        grey_dist[i,j] = grey_diff[i,j]+grey_diff[j,i]
      }
    }

    # 得到灰色相关系数矩阵 #
    grey_dist_max = max(grey_dist)
    grey_correl = matrix(0, nrow = nc, ncol = nc)
    for (i in 1:nc) {
      for (j in 1:nc) {
        grey_correl[i,j] = 1 - grey_dist[i,j] / grey_dist_max
      }
    }

    rownames(grey_correl) = names(X_order)
    colnames(grey_correl) = names(X_order)
    grey_correl


    d = as.dist(1-grey_correl)  # 得到无对角线的下三角矩阵(数值意义反向了, 值越小表示越相关 )
    # 主对角线其实表示了各个对象的相近程度, 画图的时候, 相近的对象放在一起

    hc = hclust(d, method = clusterMethod)  # 系统聚类(分层聚类)函数, single: 单一连接(最短距离法/最近邻) 
    # hc$height, 是上面矩阵的对角元素升序
    # hc$order, 层次树图上横轴个体序号
    plot(hc,hang=-1)  #hang: 设置标签悬挂位置

  }

  #output#

  if (cluster)  {
    lst = list(relationalDegree=relationalDegree, greyCorrelCoeff = grey_correl, X = X_order, referColumn = y)

  }
  else {
    lst = list(relationalDegree=relationalDegree, X = X_order, referColumn = y)
  }

  return(lst)

}

## generate data
refer = c(1,1,1,1)
liaoning = c(0.064, 0.082,0.978,0.423)
shandong = c(0.101,0.3,1,0.917)
jiangsu = c(0.114,0.14,0.943, 0.315)
zhejiang = c(0.102,0.147,0.934,0.395)
fujian = c(0.022,0.053,0.927,0.061)
guangdong = c(1,1,0.012,1)
economyCompare = data.frame(refer, liaoning, shandong, jiangsu, zhejiang, fujian, guangdong)
rownames(economyCompare) = c("indGV", "indVA", "profit", "incomeTax")

## Grey Relational Degree
greyRelDegree = GRA(economyCompare)
greyRelDegree

Grey Clustering

Example

## Grey Clustering
GRA(economyCompare, cluster = T)

Nisus-Liu/GRA documentation built on May 3, 2019, 5:03 p.m.