PairViz is an R package which provides orderings of objects for visualisation purposes. This vignette demonstrates the use of PairViz constructing parallel coordinate plots, which place emphasis on different data patterns.

First, we select six of the variables in `mtcars`

, and
make a parallel coordinate plot. We will use the variant on a PCP
provided by PairViz, which is the function `pcp`

.

```
suppressPackageStartupMessages(library(PairViz))
<- mtcars[,c(1,3:7)]
data pcp(data,horizontal=TRUE,lwd=2, col="grey50",
main = "Standard PCP")
```

The standard PCP will plot the variables in order of appearance in
the data frame. It is obvious from this plot for instance that
`mpg`

and `disp`

are negatively correlated. By
following the line segments you might be able to see that
`mpg`

and `hp`

are also negatively correlated, but
but associations with other variables are difficult to ascertain.

We could use one of the eulerian functions of PairViz to produce
orderings of variables where all pairs of variables are adjacent. In the
next display, we use `hpaths`

, which gives three hamiltonians
where each pair of variables is adjacent at least once.

```
<- hpaths(1:ncol(data),matrix=FALSE)
o par(cex.axis=.7)
pcp(data,order=o,horizontal=TRUE,lwd=2, col="grey50",
main = "Hamiltonian decomposition")
```

From this we see that `mpg`

is also strongly negatively
correlated with `wt`

, `hp`

and `drat`

,
and that there is not a strong association between `mpg`

and
`drat`

.

To make the patterns in the PCP a bit clearer, we will construct an eulerian where high correlation variables appear early on in the sequence.

The code below makes a `dist`

with the correlation between
variables.

`<- as.dist(cor(data)) corw `

As the function `eulerian`

constructs a path visiting
lower weight edges first (and we want to visit high correlation
variables first), we form the path as

```
<- eulerian(-corw)
o
o#> [1] 5 2 3 5 6 1 4 6 2 4 3 6 3 1 2 4 5 1
```

Forming the PCP based on this order we get

```
par(cex.axis=.7)
pcp(data,order=o,horizontal=TRUE,lwd=2, col="grey50",
main = "Weighted eulerian")
```

The first three panels on the left hand side have many parallel line segments indicative of positively correlated variables. On the right hand side of the PCP, the panels have many high-low line segments which means variables are negatively correlated.

PairViz has an augmented version of a PCP which shows summary measures for each pair of variables, to assist in interpretation.

The code below constructs the summary measures, one column for positive correlations, the second for negative correlations.

```
<- dist2edge(corw)
corw <- cbind(corw*(corw>0), corw*(corw<0))
edgew par(cex.axis=.7)
guided_pcp(data,edgew, path=o,pcp.col="grey50" ,lwd=2,
main="Weighted eulerian with correlation guide",
bar.col = c("lightpink1","lightcyan1"),
bar.ylim=c(-1,1),bar.axes=TRUE)
```

The above plot shows clearly that correlation generally decreases from left to right.

If you prefer, omit the guides, but instead colour the panels according to the sign of the correlation.

```
<- path_weights(corw,o)
pathw <- ifelse(pathw>0, "lightpink1", "lightcyan")
corcols par(cex.axis=.7)
pcp(data,order=o,col="grey50" ,lwd=2,
main="Weighted eulerian with correlation guide",
panel.colors = corcols)
```

The guided_pcp function also has a panel.colors argument, so it is possible to keep the guides and also colour the panels.

We access the data, remove NAs, transform two highly skewed variables, give variables shortnames, and set up a colour vector for plots.

```
if (!requireNamespace("alr4", quietly = TRUE)){
install.packages("alr4")
}
suppressPackageStartupMessages(library(alr4))
data(sleep1)
<- na.omit(sleep1)
data # these vars changed to factors in alr4, change from alr3
$D <- as.numeric(data$D)
data$P <- as.numeric(data$P)
data$SE <- as.numeric(data$SE)
data
# logging the brain and body weights
4:5] <- log(data[,4:5])
data[,
# short variable names
colnames(data) <- c("SW","PS" ,"TS" ,"Bd", "Br","L","GP","P" ,"SE" , "D" )
# colours for cases, split Life values into 3 equal sized groups
<- scales::alpha(c("red","navy","lightblue3" ),.6)
cols1 <- cols1[cut(rank(data$L),3,labels=FALSE)] cols
```

Calculate scagnostics for the data. `sc`

is a matrix whose
rows are values for 9 scagnostics,

```
library(scagnostics)
#> Loading required package: rJava
library(RColorBrewer)
<- scagnostics(data)
sc <- rownames(sc)
scags
scags#> [1] "Outlying" "Skewed" "Clumpy" "Sparse" "Striated" "Convex"
#> [7] "Skinny" "Stringy" "Monotonic"
```

As we will make plots involving different scagnostics, we will assign colours to scagnostics, for consistency across plots.

```
<- rev(brewer.pal(9, "Pastel1"))
scag_cols names(scag_cols) <- scags
```

Define a utility function which returns a subset of scagnostics, retaining the class attribute.

```
<- function(sc,names){
select_scagnostics <- sc[names,]
sc1 class(sc1) <- class(sc)
return(sc1)
}
```

Consider the outlying scagnostic. Suppose we want to construct a PCP, each variable appearing once, where pairs of variables with a high outlier score appear adjacently in the sequence.

```
<- select_scagnostics(sc,"Outlying")
scOut <- edge2dist(scOut) # dOut is a dist
dOut <- as.matrix(dOut)
dOut rownames(dOut) <- colnames(dOut)<- names(data)
```

`dOut`

is a symmetric matrix where each entry gives the
outlying score for the scatterplot labelled by the row and column names.
Note that the function `edge2dist`

relies on the fact that
objects of class scagnostics are in order (1,2), (1,3), (2,3),(1,4)
etc

To find the variable ordering with the highest (or nearly highest) total outlier score use one of

```
<- order_best(-dOut, maxexact=10)
o <-order_best(-dOut)
o <-order_tsp(-dOut) o
```

The first call to `order_best`

above finds the best
ordering by a brute force evaluation of all 10! factorial permutations,
and so this is a bit slow. Without the `maxexact=10`

input,
order_best evaluates only a sample of permulations for sequences of
length above 9. order_tsp uses a TSP solver from package TSP. We will
use the result of the first call to order_best, which gives

`<-c( 2 , 4 , 1, 5 , 6, 7 , 3 , 8, 9, 10) o `

The guided PCP based on this ordering is

```
par(tcl = -.2, cex.axis=.8,mgp=c(3,.3,0))
guided_pcp(data,scOut, path=o,pcp.col=cols,lwd=1.4,
main= "Best Hamiltonian for outliers",bar.col = scag_cols["Outlying"],legend=FALSE,bar.axes=TRUE,bar.ylim=c(0,max(scOut)))
```

Notice that panels involving discrete-valued variables P,SE and D score zero on the outlying index. The L-GP pair of variables has the highest outlier score and two outliers are evident. The outlier cases are the two species (Human and Asian Elephant) with the highest life expectancy (L). Asian Elephant also has the highest value of gestation time (GP)

```
<- order(data$L, decreasing=T)[1:2]
outliers rownames(data)[outliers]
#> [1] "Human" "Asian_elephant"
```

For future use we will construct a colour vector marking these two outliers.

```
<- rep("grey50", nrow(data))
colOut 1]] <- "red" # Human
colOut[outliers[2]] <- "blue" colOut[outliers[
```

Suppose next we want to pick the ordering of PCP axes where high scores on the two measures Striated and Sparse are obtained.

`<- t(select_scagnostics(sc,c("Striated", "Sparse"))) scSS `

As we did with the calculation for Outliers, we can turn
`scSS`

into a distance matrix and then use one of
`order_best`

or `order_tsp`

to produces the best
ordering.

```
<- edge2dist(scSS[,1]) + edge2dist(scSS[,2])
dSS # You might think edge2dist(scSS[,1]+ scSS[,2]) would work, but as scSS[,1]+ scSS[,2] is
# not of class scagnostics, edge2dist will not fill the dist in the correct order
<- as.matrix(dSS)
dSS rownames(dSS) <- colnames(dSS)<- names(data)
order_best(-dSS,maxexact=10)
```

A shortcut calculation is

```
find_path(-scSS, order_best,maxexact=10) # for the best path
# or
find_path(-scSS, order_best) # for a nearly "best" path
```

The best path gives

`<- c(4, 10 , 2 , 9 , 1, 7 , 8, 6 , 5 ,3) o `

The guided PCP based on this ordering is

```
par(tcl = -.2, cex.axis=.8,mgp=c(3,.3,0))
guided_pcp(data,scSS, path=o,pcp.col=cols,lwd=1.4,
main= "Best Hamiltonian for Striated + Sparse",
bar.col = scag_cols[c("Striated", "Sparse")],
legend=FALSE,bar.axes=TRUE,bar.ylim=c(0,.6))
```