Gets the maximum contributor variables from svd()

Description

This function is inspired by Jeff Leeks Data Analysis course where he suggests that one way to use the svd is to look at the most influential rows for first columns in the V matrix.

Usage

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getSvdMostInfluential(mtrx, quantile, similarity_threshold,
  plot_selection = TRUE, plot_threshold = 0.05, varnames = NULL)

Arguments

mtrx

A matrix or data frame with the variables. Note: if it contains missing variables make sure to impute prior to this function as the svd can't handle missing values.

quantile

The SVD D-matrix gives an estimate for the amount that is explained. This parameter is used for selecting the columns that have that quantile of explanation.

similarity_threshold

A quantile for how close other variables have to be in value to maximum contributor of that particular column. If you only want the maximum value then set this value to 1.

plot_selection

As this is all about variable exploring it is often interesting to see how the variables were distributed among the vectors

plot_threshold

The threshold of the plotted bars, measured as percent explained by the D-matrix. By default it is set to 0.05.

varnames

A vector with alternative names to the colnames

Details

This function expands on that idea and adds the option of choosing more than just the most contributing variable for each row. For instance two variables may have a major impact on a certain component where the second variable has 95 important in that particular component it makes sense to include it in the selection.

It is of course useful when you have many continuous variables and you want to determine a subgroup to look at, i.e. finding the needle in the haystack.

Value

Returns a list with vector with the column numbers that were picked in the "most_influential" variable and the svd caluclation in the "svd"

Examples

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org_par <- par(ask=TRUE)
set.seed(12345); 

# Simulate data with a pattern
dataMatrix <- matrix(rnorm(15*160),ncol=15)
colnames(dataMatrix) <- 
  c(paste("Pos.3:", 1:3, sep=" #"), 
    paste("Neg.Decr:", 4:6, sep=" #"), 
    paste("No pattern:", 7:8, sep=" #"),
    paste("Pos.Incr:", 9:11, sep=" #"),
    paste("No pattern:", 12:15, sep=" #"))
for(i in 1:nrow(dataMatrix)){
  # flip a coin
  coinFlip1 <- rbinom(1,size=1,prob=0.5)
  coinFlip2 <- rbinom(1,size=1,prob=0.5)
  coinFlip3 <- rbinom(1,size=1,prob=0.5)
  
  # if coin is heads add a common pattern to that row
  if(coinFlip1){
    cols <- grep("Pos.3", colnames(dataMatrix))
    dataMatrix[i, cols] <- dataMatrix[i, cols] + 3
  }
  
  if(coinFlip2){
    cols <- grep("Neg.Decr", colnames(dataMatrix))
    dataMatrix[i, cols] <- dataMatrix[i, cols] - seq(from=5, to=15, length.out=length(cols))
  }
  
  if(coinFlip3){
    cols <- grep("Pos.Incr", colnames(dataMatrix))
    dataMatrix[i,cols] <- dataMatrix[i,cols] + seq(from=3, to=15, length.out=length(cols))
  }
}

# Illustrate data
heatmap(dataMatrix, Colv=NA, Rowv=NA, margins=c(7,2), labRow="")

svd_out <- svd(scale(dataMatrix))

library(lattice)
b_clr <- c("steelblue", "darkred")
key <- simpleKey(rectangles = TRUE, space = "top", points=FALSE,
  text=c("Positive", "Negative"))
key$rectangles$col <- b_clr

b1 <- barchart(as.table(svd_out$v[,1]),
  main="First column",
  horizontal=FALSE, col=ifelse(svd_out$v[,1] > 0, 
      b_clr[1], b_clr[2]),
  ylab="Impact value", 
  scales=list(x=list(rot=55, labels=colnames(dataMatrix), cex=1.1)),
  key = key)

b2 <- barchart(as.table(svd_out$v[,2]),
  main="Second column",
  horizontal=FALSE, col=ifelse(svd_out$v[,2] > 0, 
      b_clr[1], b_clr[2]),
  ylab="Impact value", 
  scales=list(x=list(rot=55, labels=colnames(dataMatrix), cex=1.1)),
  key = key)

b3 <- barchart(as.table(svd_out$v[,3]),
  main="Third column",
  horizontal=FALSE, col=ifelse(svd_out$v[,3] > 0, 
      b_clr[1], b_clr[2]),
  ylab="Impact value", 
  scales=list(x=list(rot=55, labels=colnames(dataMatrix), cex=1.1)),
  key = key)

b4 <- barchart(as.table(svd_out$v[,4]),
  main="Fourth column",
  horizontal=FALSE, col=ifelse(svd_out$v[,4] > 0, 
      b_clr[1], b_clr[2]),
  ylab="Impact value", 
  scales=list(x=list(rot=55, labels=colnames(dataMatrix), cex=1.1)),
  key = key)

# Note that the fourth has the no pattern columns as the
# chosen pattern, probably partly because of the previous
# patterns already had been identified
print(b1, position=c(0,0.5,.5,1), more=TRUE)
print(b2, position=c(0.5,0.5,1,1), more=TRUE)
print(b3, position=c(0,0,.5,.5), more=TRUE)
print(b4, position=c(0.5,0,1,.5))

# Let's look at how well the SVD identifies
# the most influential columns
getSvdMostInfluential(dataMatrix, 
                      quantile=.8, 
                      similarity_threshold = .9,
                      plot_threshold = .05,
                      plot_selection = TRUE)
par(org_par)

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