R/data.Normalization.r

In clusterSim: Searching for Optimal Clustering Procedure for a Data Set

.abs<-function(x){
  return (abs(x[!is.na(x)]))
}

data.Normalization<-function (x, type = "n0", normalization = "column", ...) 
{
    bycolumn = T
    if (normalization == "row") 
        bycolumn = F
    if (is.vector(x) && !is.list(x)) {
        if (is.numeric(resul <- x)) {
            resul <- switch(type, n0 = x, n1 = (x - mean(x, ...))/sd(x, 
                ...), n2 = (x - median(x, ...))/mad(x, ...), 
                n3 = (x - mean(x, ...))/(max(x, ...) - min(x, 
                  ...)), n3a = (x - median(x, ...))/(max(x, ...) - 
                  min(x, ...)), n4 = (x - min(x, ...))/(max(x, 
                  ...) - min(x, ...)), n5 = (x - mean(x, ...))/(max(.abs((x) - 
                  mean(x, ...)))), n5a = (x - median(x, ...))/(max(.abs((x) - 
                  median(x, ...)))), n6 = x/sd(x, ...), n6a = x/mad(x, 
                  ...), n7 = x/(max(x, ...) - min(x, ...)), n8 = x/max(x, 
                  ...), n9 = x/mean(x, ...), n9a = x/median(x, 
                  ...), n10 = x/sum(x, ...), n11 = x/(sum(x^2, 
                  ...)^0.5), n12 = (x - mean(x, ...))/(sum((x - 
                  mean(x, ...))^2, ...)^0.5), n12a = (x - median(x, 
                  ...))/(sum((x - median(x, ...))^2, ...)^0.5), 
                n13 = (x - ((max(x, ...) + min(x, ...))/2))/((max(x, 
                  ...) - min(x, ...))/2))
            params <- switch(type, n0 = c(0, 1), n1 = c(mean(x, 
                ...), sd(x, ...)), n2 = c(median(x, ...), mad(x, 
                ...)), n3 = c(mean(x, ...), max(x, ...) - min(x, 
                ...)), n3a = c(median(x, ...), max(x, ...) - 
                min(x, ...)), n4 = c(min(x, ...), max(x, ...) - 
                min(x, ...)), n5 = c(mean(x, ...), max(.abs((x) - 
                mean(x, ...)))), n5a = c((median(x, ...)), (max(.abs((x) - 
                median(x, ...))))), n6 = c(0, sd(x, ...)), n6a = c(0, 
                mad(x, ...)), n7 = c(0, (max(x, ...) - min(x, 
                ...))), n8 = c(0, max(x, ...)), n9 = c(0/mean(x, 
                ...)), n9a = c(0/median(x, ...)), n10 = c(0/sum(x, 
                ...)), n11 = c(0, (sum(x^2, ...)^0.5)), n12 = c((mean(x, 
                ...)), (sum((x - mean(x, ...))^2, ...)^0.5)), 
                n12a = c((median(x, ...)), (sum((x - median(x, 
                  ...))^2, ...)^0.5)), n13 = c((((max(x, ...) + 
                  min(x, ...))/2)), ((max(x, ...) - min(x, ...))/2)))
            center <- params[1]
            scale <- params[2]
        }
        else warning("Data not numeric, normalization not applicable")
        names(resul) <- names(x)
    }
    else if (is.data.frame(x)) {
        resul <- NULL
        params <- NULL
        if (bycolumn) {
            for (nn in names(x)) {
                if (is.numeric(x[, nn])) {
                  resul <- switch(type, n0 = cbind(resul, (x[, 
                    nn])), n1 = cbind(resul, (x[, nn] - mean(x[, 
                    nn], ...))/(sd(x[, nn], ...))), n2 = cbind(resul, 
                    (x[, nn] - median(x[, nn], ...))/(mad(x[, 
                      nn], ...))), n3 = cbind(resul, (x[, nn] - 
                    mean(x[, nn], ...))/(max(x[, nn], ...) - 
                    min(x[, nn], ...))), n3a = cbind(resul, (x[, 
                    nn] - median(x[, nn], ...))/(max(x[, nn], 
                    ...) - min(x[, nn], ...))), n4 = cbind(resul, 
                    (x[, nn] - min(x[, nn], ...))/(max(x[, nn], 
                      ...) - min(x[, nn], ...))), n5 = cbind(resul, 
                    (x[, nn] - mean(x[, nn], ...))/(max(.abs(x[, 
                      nn] - mean(x[, nn], ...))))), n5a = cbind(resul, 
                    (x[, nn] - median(x[, nn], ...))/(max(.abs(x[, 
                      nn] - median(x[, nn], ...))))), n6 = cbind(resul, 
                    (x[, nn])/sd(x[, nn], ...)), n6a = cbind(resul, 
                    (x[, nn])/mad(x[, nn], ...)), n7 = cbind(resul, 
                    (x[, nn])/(max(x[, nn], ...) - min(x[, nn], 
                      ...))), n8 = cbind(resul, (x[, nn])/(max(x[, 
                    nn], ...))), n9 = cbind(resul, (x[, nn])/(mean(x[, 
                    nn], ...))), n9a = cbind(resul, (x[, nn])/(median(x[, 
                    nn], ...))), n10 = cbind(resul, (x[, nn])/(sum(x[, 
                    nn], ...))), n11 = cbind(resul, (x[, nn])/(sum(x[, 
                    nn]^2, ...)^0.5)), n12 = cbind(resul, (x[, 
                    nn] - mean(x[, nn], ...))/(sum((x[, nn] - 
                    mean(x[, nn], ...))^2, ...)^0.5)), n12a = cbind(resul, 
                    (x[, nn] - median(x[, nn], ...))/(sum((x[, 
                      nn] - median(x[, nn], ...))^2, ...)^0.5)), 
                    n13 = cbind(resul, (x[, nn] - ((max(x[, nn], 
                      ...) + min(x[, nn], ...))/2))/((max(x[, 
                      nn], ...) - min(x[, nn], ...))/2)))
                  p <- switch(type, n0 = c(0, 1), n1 = c((mean(x[, 
                    nn], ...)), (sd(x[, nn], ...))), n2 = c(median(x[, 
                    nn], ...), (mad(x[, nn], ...))), n3 = c((mean(x[, 
                    nn], ...)), (max(x[, nn], ...) - min(x[, 
                    nn], ...))), n3a = c(median(x[, nn], ...), 
                    (max(x[, nn], ...) - min(x[, nn], ...))), 
                    n4 = c((min(x[, nn], ...)), (max(x[, nn], 
                      ...) - min(x[, nn], ...))), n5 = c((mean(x[, 
                      nn], ...)), (max(.abs(mean(x[, nn], ...))))), 
                    n5a = c((x[, nn] - median(x[, nn], ...)), 
                      (max(.abs(median(x[, nn], ...))))), n6 = c(0, 
                      sd(x[, nn], ...)), n6a = c((0), mad(x[, 
                      nn], ...)), n7 = c(0, max(x[, nn], ...) - 
                      min(x[, nn], ...)), n8 = c(0, (max(x[, 
                      nn], ...))), n9 = c(0, mean(x[, nn], ...)), 
                    n9a = c(0, median(x[, nn], ...)), n10 = c(0, 
                      sum(x[, nn], ...)), n11 = c(0, (sum(x[, 
                      nn]^2, ...)^0.5)), n12 = c((mean(x[, nn], 
                      ...)), (sum((mean(x[, nn], ...))^2, ...)^0.5)), 
                    n12a = c(median(x[, nn], ...), (sum((x[, 
                      nn] - median(x[, nn], ...))^2, ...)^0.5)), 
                    n13 = c(((max(x[, nn], ...) + min(x[, nn], 
                      ...))/2), ((max(x[, nn], ...) - min(x[, 
                      nn], ...))/2)))
                  params <- cbind(params, p)
                }
                else {
                  resul <- cbind(resul, x[, nn], ...)
                  params <- cbind(params, c(NA, NA))
                  warning("Data not numeric, normalization not applicable")
                }
            }
            center <- params[1, ]
            scale <- params[2, ]
        }
        else {
            for (nn in 1:nrow(x)) {
                if (sum(is.na(as.numeric((x[nn, ])))) == 0) {
                  resul <- switch(type, n0 = rbind(resul, (x[nn, 
                    ])), n1 = rbind(resul, (x[nn, ] - mean(as.numeric(x[nn, 
                    ], ...)))/(sd(as.numeric(x[nn, ], ...)))), 
                    n2 = rbind(resul, (x[nn, ] - median(as.numeric(x[nn, 
                      ], ...)))/(mad(as.numeric(x[nn, ], ...)))), 
                    n3 = rbind(resul, (x[nn, ] - mean(as.numeric(x[nn, 
                      ], ...)))/(max(as.numeric(x[nn, ], ...)) - 
                      min(as.numeric(x[nn, ], ...)))), n3a = rbind(resul, 
                      (x[nn, ] - median(as.numeric(x[nn, ], ...)))/(max(as.numeric(x[nn, 
                        ], ...)) - min(as.numeric(x[nn, ], ...)))), 
                    n4 = rbind(resul, (x[nn, ] - min(as.numeric(x[nn, 
                      ], ...)))/(max(as.numeric(x[nn, ], ...)) - 
                      min(as.numeric(x[nn, ], ...)))), n5 = rbind(resul, 
                      (x[nn, ] - mean(as.numeric(x[nn, ], ...)))/(max(.abs(as.numeric(x[nn, 
                        ], ...) - mean(as.numeric(x[nn, ], ...)))))), 
                    n5a = rbind(resul, (x[nn, ] - median(as.numeric(x[nn, 
                      ], ...)))/(max(.abs(as.numeric(x[nn, ], 
                      ...) - median(as.numeric(x[nn, ], ...)))))), 
                    n6 = rbind(resul, (x[nn, ])/sd(as.numeric(x[nn, 
                      ], ...))), n6a = rbind(resul, (x[nn, ])/mad(as.numeric(x[nn, 
                      ], ...))), n7 = rbind(resul, (x[nn, ])/(max(as.numeric(x[nn, 
                      ], ...)) - min(as.numeric(x[nn, ], ...)))), 
                    n8 = rbind(resul, (x[nn, ])/(max(as.numeric(x[nn, 
                      ], ...)))), n9 = rbind(resul, (x[nn, ])/(mean(as.numeric(x[nn, 
                      ], ...)))), n9a = rbind(resul, (x[nn, ])/(median(as.numeric(x[nn, 
                      ], ...)))), n10 = rbind(resul, (x[nn, ])/(sum(as.numeric(x[nn, 
                      ], ...)))), n11 = rbind(resul, (x[nn, ])/(sum(as.numeric(x[nn, 
                      ])^2, ...)^0.5)), n12 = rbind(resul, (x[nn, 
                      ] - mean(as.numeric(x[nn, ], ...)))/(sum((as.numeric(x[nn, 
                      ], ...) - mean(as.numeric(x[nn, ], ...)))^2, 
                      ...)^0.5)), n12a = rbind(resul, (x[nn, 
                      ] - median(as.numeric(x[nn, ], ...)))/(sum((as.numeric(x[nn, 
                      ]) - median(as.numeric(x[nn, ], ...)))^2, 
                      ...)^0.5)), n13 = rbind(resul, (x[nn, ] - 
                      ((max(as.numeric(x[nn, ], ...)) + min(as.numeric(x[nn, 
                        ], ...)))/2))/((max(as.numeric(x[nn, 
                      ], ...)) - min(as.numeric(x[nn, ], ...)))/2)))
                  p <- switch(type, n0 = c(0, 1), n1 = c(mean(x[nn, 
                    ], ...), (sd(x[nn, ], ...))), n2 = c(median(x[nn, 
                    ], ...), (mad(x[nn, ], ...))), n3 = c((mean(x[nn, 
                    ], ...)), (max(x[nn, ], ...) - min(x[nn, 
                    ], ...))), n3a = c(median(x[nn, ], ...), 
                    (max(x[nn, ], ...) - min(x[nn, ], ...))), 
                    n4 = c((min(x[nn, ], ...)), (max(x[nn, ], 
                      ...) - min(x[nn, ], ...))), n5 = c((mean(x[nn, 
                      ], ...)), (max(.abs(mean(x[nn, ], ...))))), 
                    n5a = c((x[nn, ] - median(x[nn, ], ...)), 
                      (max(.abs(median(x[nn, ], ...))))), n6 = c(0, 
                      sd(x[nn, ], ...)), n6a = c((0), mad(x[nn, 
                      ], ...)), n7 = c(0, max(x[nn, ], ...) - 
                      min(x[nn, ], ...)), n8 = c(0, max(x[nn, 
                      ], ...)), n9 = c(0, mean(x[nn, ], ...)), 
                    n9a = c(0, median(x[nn, ], ...)), n10 = c(0, 
                      sum(x[nn, ], ...)), n11 = c(0, (sum(x[nn, 
                      ]^2, ...)^0.5)), n12 = c((mean(x[nn, ], 
                      ...)), (sum((mean(x[nn, ], ...))^2, ...)^0.5)), 
                    n12a = c(median(x[nn, ], ...), (sum((x[nn, 
                      ] - median(x[nn, ], ...))^2, ...)^0.5)), 
                    n13 = c(((max(x[nn, ], ...) + min(x[nn, ], 
                      ...))/2), ((max(x[nn, ], ...) - min(x[nn, 
                      ], ...))/2)))
                  params <- cbind(params, p)
                }
                else {
                  resul <- rbind(resul, x[nn, ])
                  params <- cbind(params, c(NA, NA))
                  warning("Data not numeric, normalization not applicable")
                }
            }
        }
        resul <- data.frame(resul)
        center <- params[1, ]
        scale <- params[2, ]
        names(resul) <- names(x)
        row.names(resul) <- row.names(x)
        if (bycolumn) {
            if (!is.null(dimnames(x)[[2]])) {
                names(center) <- dimnames(x)[[2]]
                names(scale) <- dimnames(x)[[2]]
            }
            else {
                names(center) <- 1:ncol(x)
                names(scale) <- 1:ncol(x)
            }
        }
        else {
            if (!is.null(dimnames(x)[[1]])) {
                names(center) <- dimnames(x)[[1]]
                names(scale) <- dimnames(x)[[1]]
            }
            else {
                names(center) <- 1:nrow(x)
                names(scale) <- 1:nrow(x)
            }
        }
    }
    else if (is.matrix(x)) {
        if (is.numeric(resul <- x)) {
            params <- NULL
            resul <- NULL
            if (bycolumn) {
                for (i in 1:ncol(x)) {
                  resul <- switch(type, n0 = cbind(resul, (x[, 
                    i])), n1 = cbind(resul, (x[, i] - mean(x[, 
                    i], ...))/(sd(x[, i], ...))), n2 = cbind(resul, 
                    (x[, i] - median(x[, i], ...))/(mad(x[, i], 
                      ...))), n3 = cbind(resul, (x[, i] - mean(x[, 
                    i], ...))/(max(x[, i], ...) - min(x[, i], 
                    ...))), n3a = cbind(resul, (x[, i] - median(x[, 
                    i], ...))/(max(x[, i], ...) - min(x[, i], 
                    ...))), n4 = cbind(resul, (x[, i] - min(x[, 
                    i], ...))/(max(x[, i], ...) - min(x[, i], 
                    ...))), n5 = cbind(resul, (x[, i] - mean(x[, 
                    i], ...))/(max(.abs(x[, i] - mean(x[, i], 
                    ...))))), n5a = cbind(resul, (x[, i] - median(x[, 
                    i], ...))/(max(.abs(x[, i] - median(x[, i], 
                    ...))))), n6 = cbind(resul, (x[, i])/sd(x[, 
                    i], ...)), n6a = cbind(resul, (x[, i])/mad(x[, 
                    i], ...)), n7 = cbind(resul, (x[, i])/(max(x[, 
                    i], ...) - min(x[, i], ...))), n8 = cbind(resul, 
                    (x[, i])/(max(x[, i], ...))), n9 = cbind(resul, 
                    (x[, i])/(mean(x[, i], ...))), n9a = cbind(resul, 
                    (x[, i])/(median(x[, i], ...))), n10 = cbind(resul, 
                    (x[, i])/(sum(x[, i], ...))), n11 = cbind(resul, 
                    (x[, i])/(sum(x[, i]^2, ...)^0.5)), n12 = cbind(resul, 
                    (x[, i] - mean(x[, i], ...))/(sum((x[, i] - 
                      mean(x[, i], ...))^2, ...)^0.5)), n12a = cbind(resul, 
                    (x[, i] - median(x[, i], ...))/(sum((x[, 
                      i] - median(x[, i], ...))^2, ...)^0.5)), 
                    n13 = cbind(resul, (x[, i] - ((max(x[, i], 
                      ...) + min(x[, i], ...))/2))/((max(x[, 
                      i], ...) - min(x[, i], ...))/2)))
                  p <- switch(type, n0 = c(0, 1), n1 = c((mean(x[, 
                    i], ...)), (sd(x[, i], ...))), n2 = c(median(x[, 
                    i], ...), (mad(x[, i], ...))), n3 = c((mean(x[, 
                    i], ...)), (max(x[, i], ...) - min(x[, i], 
                    ...))), n3a = c(median(x[, i], ...), (max(x[, 
                    i], ...) - min(x[, i], ...))), n4 = c((min(x[, 
                    i], ...)), (max(x[, i], ...) - min(x[, i], 
                    ...))), n5 = c((mean(x[, i], ...)), (max(.abs(mean(x[, 
                    i], ...))))), n5a = c((x[, i] - median(x[, 
                    i], ...)), (max(.abs(median(x[, i], ...))))), 
                    n6 = c(0, sd(x[, i], ...)), n6a = c((0), 
                      mad(x[, i], ...)), n7 = c(0, max(x[, i], 
                      ...) - min(x[, i], ...)), n8 = c(0, max(x[, 
                      i], ...)), n9 = c(0, mean(x[, i], ...)), 
                    n9a = c(0, median(x[, i], ...)), n10 = c(0, 
                      sum(x[, i], ...)), n11 = c(0, (sum(x[, 
                      i]^2, ...)^0.5)), n12 = c((mean(x[, i], 
                      ...)), (sum((mean(x[, i], ...))^2, ...)^0.5)), 
                    n12a = c(median(x[, i], ...), (sum((x[, i] - 
                      median(x[, i], ...))^2, ...)^0.5)), n13 = c(((max(x[, 
                      i], ...) + min(x[, i], ...))/2), ((max(x[, 
                      i], ...) - min(x[, i], ...))/2)))
                  params <- cbind(params, p)
                }
            }
            else {
                for (i in 1:nrow(x)) {
                  resul <- switch(type, n0 = rbind(resul, (x[i, 
                    ])), n1 = rbind(resul, (x[i, ] - mean(x[i, 
                    ], ...))/(sd(x[i, ], ...))), n2 = rbind(resul, 
                    (x[i, ] - median(x[i, ], ...))/(mad(x[i, 
                      ], ...))), n3 = rbind(resul, (x[i, ] - 
                    mean(x[i, ], ...))/(max(x[i, ], ...) - min(x[i, 
                    ], ...))), n3a = rbind(resul, (x[i, ] - median(x[i, 
                    ], ...))/(max(x[i, ], ...) - min(x[i, ], 
                    ...))), n4 = rbind(resul, (x[i, ] - min(x[i, 
                    ], ...))/(max(x[i, ], ...) - min(x[i, ], 
                    ...))), n5 = rbind(resul, (x[i, ] - mean(x[i, 
                    ], ...))/(max(.abs(x[i, ] - mean(x[i, ], 
                    ...))))), n5a = rbind(resul, (x[i, ] - median(x[i, 
                    ], ...))/(max(.abs(x[i, ] - median(x[i, ], 
                    ...))))), n6 = rbind(resul, (x[i, ])/sd(x[i, 
                    ], ...)), n6a = rbind(resul, (x[i, ])/mad(x[i, 
                    ], ...)), n7 = rbind(resul, (x[i, ])/(max(x[i, 
                    ], ...) - min(x[i, ], ...))), n8 = rbind(resul, 
                    (x[i, ])/(max(x[i, ], ...))), n9 = rbind(resul, 
                    (x[i, ])/(mean(x[i, ], ...))), n9a = rbind(resul, 
                    (x[i, ])/(median(x[i, ], ...))), n10 = rbind(resul, 
                    (x[i, ])/(sum(x[i, ], ...))), n11 = rbind(resul, 
                    (x[i, ])/(sum(x[i, ]^2, ...)^0.5)), n12 = rbind(resul, 
                    (x[i, ] - mean(x[i, ], ...))/(sum((x[i, ] - 
                      mean(x[i, ], ...))^2, ...)^0.5)), n12a = rbind(resul, 
                    (x[i, ] - median(x[i, ], ...))/(sum((x[i, 
                      ] - median(x[i, ], ...))^2, ...)^0.5)), 
                    n13 = rbind(resul, (x[i, ] - ((max(x[i, ], 
                      ...) + min(x[i, ], ...))/2))/((max(x[i, 
                      ], ...) - min(x[i, ], ...))/2)))
                  p <- switch(type, n0 = c(0, 1), n1 = c(mean(x[i], 
                    ...), sd(x[i, ], ...)), n2 = c(median(x[i, 
                    ], ...), (mad(x[i, ], ...))), n3 = c((mean(x[i, 
                    ], ...)), (max(x[i, ], ...) - min(x[i, ], 
                    ...))), n3a = c(median(x[i, ], ...), (max(x[i, 
                    ], ...) - min(x[i, ], ...))), n4 = c((min(x[i, 
                    ], ...)), (max(x[i, ], ...) - min(x[i, ], 
                    ...))), n5 = c((mean(x[i, ], ...)), (max(.abs(mean(x[i, 
                    ], ...))))), n5a = c((x[i, ] - median(x[i, 
                    ], ...)), (max(.abs(median(x[i, ], ...))))), 
                    n6 = c(0, sd(x[i, ], ...)), n6a = c((0), 
                      mad(x[i, ], ...)), n7 = c(0, max(x[i, ], 
                      ...) - min(x[i, ], ...)), n8 = c(0, max(x[i, 
                      ], ...)), n9 = c(0, mean(x[i, ], ...)), 
                    n9a = c(0, median(x[i, ], ...)), n10 = c(0, 
                      sum(x[i, ], ...)), n11 = c(0, (sum(x[i, 
                      ]^2, ...)^0.5)), n12 = c((mean(x[i, ], 
                      ...)), (sum((mean(x[i, ], ...))^2, ...)^0.5)), 
                    n12a = c(median(x[i, ], ...), (sum((x[i, 
                      ] - median(x[i, ], ...))^2, ...)^0.5)), 
                    n13 = c(((max(x[i, ], ...) + min(x[i, ], 
                      ...))/2), ((max(x[i, ], ...) - min(x[i, 
                      ], ...))/2)))
                  params <- cbind(params, p)
                }
            }
            center <- params[1, ]
            scale <- params[2, ]
            if (bycolumn) {
                if (!is.null(dimnames(x)[[2]])) {
                  names(center) <- dimnames(x)[[2]]
                  names(scale) <- dimnames(x)[[2]]
                }
                else {
                  names(center) <- 1:ncol(x)
                  names(scale) <- 1:ncol(x)
                }
            }
            else {
                if (!is.null(dimnames(x)[[1]])) {
                  names(center) <- dimnames(x)[[1]]
                  names(scale) <- dimnames(x)[[1]]
                }
                else {
                  names(center) <- 1:nrow(x)
                  names(scale) <- 1:nrow(x)
                }
            }
        }
        else {
            warning("Data not numeric, normalization not applicable")
            center <- NA
            scale <- NA
        }
        dimnames(resul) <- dimnames(x)
    }
    else if (is.list(x)) {
        resul <- list(length(x))
        center <- list(length(x))
        scale <- list(length(x))
        xx <- as.numeric(x)
        center <- switch(type, n0 = 0, n1 = mean(xx, ...), n2 = (median(xx, 
            ...)), n3 = (mean(xx, ...)), n3a = (median(xx, ...)), 
            n4 = (min(xx, ...)), n5 = (mean(xx, ...)), n5a = (median(xx, 
                ...)), n6 = 0, n6a = 0, n7 = 0, n8 = 0, n9 = 0, 
            n9a = 0, n10 = 0, n11 = 0, n12 = (mean(xx, ...)), 
            n12a = (median(xx, ...)), n13 = (((max(xx, ...) + 
                min(xx, ...))/2)))
        scale <- switch(type, n0 = 1, n1 = sd(xx), n2 = mad(xx, 
            ...), n3 = (max(xx, ...) - min(xx, ...)), n3a = (max(xx, 
            ...) - min(xx, ...)), n4 = (max(xx, ...) - min(xx, 
            ...)), n5 = (max(.abs((xx) - mean(xx, ...)))), n5a = (max(.abs((xx) - 
            median(xx, ...)))), n6 = sd(xx), n6a = mad(xx, ...), 
            n7 = (max(xx, ...) - min(xx, ...)), n8 = (max(xx, 
                ...)), n9 = (mean(xx, ...)), n9a = (median(xx, 
                ...)), n10 = (sum(xx, ...)), n11 = (sum(xx^2, 
                ...)^0.5), n12 = (sum((xx - mean(xx, ...))^2, 
                ...)^0.5), n12a = (sum((xx - median(xx, ...))^2, 
                ...)^0.5), n13 = ((max(xx, ...) - min(xx, ...))/2))
        for (i in 1:length(x)) if (is.numeric(resul[[i]] <- x[[i]])) {
            resul[[i]] <- switch(type, n0 = x[[i]], n1 = (x[[i]] - 
                mean(xx, ...))/sd(xx), n2 = (x[[i]] - median(xx, 
                ...))/mad(xx, ...), n3 = (x[[i]] - mean(xx, ...))/(max(xx, 
                ...) - min(xx, ...)), n3a = (x[[i]] - median(xx, 
                ...))/(max(xx, ...) - min(xx, ...)), n4 = (x[[i]] - 
                min(xx, ...))/(max(xx, ...) - min(xx, ...)), 
                n5 = (x[[i]] - mean(xx, ...))/(max(.abs((xx) - 
                  mean(xx, ...)))), n5a = (x[[i]] - median(xx, 
                  ...))/(max(.abs((xx) - median(xx, ...)))), 
                n6 = x[[i]]/sd(xx), n6a = x[[i]]/mad(xx, ...), 
                n7 = x[[i]]/(max(xx, ...) - min(xx, ...)), n8 = x[[i]]/(max(xx, 
                  ...)), n9 = x[[i]]/(mean(xx, ...)), n9a = x[[i]]/(median(xx, 
                  ...)), n10 = x[[i]]/(sum(xx, ...)), n11 = x[[i]]/(sum(xx^2, 
                  ...)^0.5), n12 = (x[[i]] - mean(xx, ...))/(sum((xx - 
                  mean(xx, ...))^2, ...)^0.5), n12a = (x[[i]] - 
                  median(xx, ...))/(sum((xx - median(xx, ...))^2, 
                  ...)^0.5), n13 = (x[[i]] - ((max(xx, ...) + 
                  min(xx, ...))/2))/((max(xx, ...) - min(xx, 
                  ...))/2))
        }
        else {
            warning("Data not numeric, normalization not applicable")
        }
    }
    else if (!is.numeric(resul <- x)) {
        warning("Data not numeric, normalization not applicable")
        center <- NA
        scale <- NA
    }
    else stop("unknown input type")
    if (is.numeric(t <- x)) {
        if (sum(as.numeric(x) <= 0) > 0) {
            if (type == "n6" || type == "n6a" || type == "n7" || 
                type == "n8" || type == "n9" || type == "n9a" || 
                type == "n10" || type == "n11") {
                warning("Data for this kind of normalization should be positive")
            }
        }
    }
    attr(resul, "normalized:shift") <- center
    attr(resul, "normalized:scale") <- scale
    resul
}