University of Iowa College of Liberal Arts and Sciences

The same idea as a slope graph, but usually with more variables.

Some references:

Some R implementations:

Function Package
parallelplot lattice
ggparcoord GGally
ipcp iplots
ggobi rggobi
parcoords parcoords (on GitHub; uses D3)

Australian Crabs in Parallel Coordinates

Using the crabs data from MASS:

library(GGally)
data(crabs, package = "MASS")
ggparcoord(crabs)

Focus only on the measurements:

ggparcoord(crabs, columns = 4:8)

Color by sex:

ggparcoord(crabs, columns = 4:8, groupColumn = "sex")

Color by sp:

ggparcoord(crabs, columns = 4:8, groupColumn = "sp")

After scaling by CL:

cr <- mutate(crabs,
             FLCL = FL / CL, RWCL = RW / CL, CWCL = CW / CL, BDCL = BD / CL)
ggparcoord(cr, columns = 9:12, groupColumn = "sp")

Reorder the variables:

ggparcoord(cr, columns = c(10, 9, 11, 12), groupColumn = "sp")

Reorder again:

ggparcoord(cr, columns = c(10, 9, 12, 11), groupColumn = "sp")

Reverse the CWCL variable:

ggparcoord(mutate(cr, CWCL = -CWCL),
           columns = c(10, 9, 12, 11), groupColumn = "sp")

Olive Oils in Parallel Coordinates

data(olive, package = "tourr")
olive$Region <- factor(olive$region,
                       labels = c("North", "South", "Sardinia"))
ggparcoord(olive, groupColumn = "Region", columns = 3 : 8)

South is separated out by high values of eicosenoic

Look at the other regions:

ons <- filter(olive, Region != "South")
ons <- droplevels(ons)
ggparcoord(ons, groupColumn = "Region", columns = 3:10)

linoleic seems to allow some separation of North and Sardinia

Rearrange to place linoleic next to arachidic:

ggparcoord(ons, groupColumn = "Region", columns = c(3:7, 9, 8, 10))

This shows the joint discriminator found with scatter plots.

Interactive Approaches

Interactive version in iplots:

library(iplots)
ipcp(cr)
ipcp(cr[-(3:8)])
ipcp(cr[c(1, 2, 10, 9, 12, 11)])

Interactive version in rggobi:

library(rggobi)
ggobi(cr)

Interactive version using the D3 library via the parcoords package:

parcoords::parcoords(cr[c(1, 2, 9:12)], , rownames = FALSE,
                     reorder = TRUE, brushMode = "1D",
                     color = list(
                         colorScale = htmlwidgets::JS("d3.scale.category10()"),
                         colorBy = "sp"))

Some Calibration Examples

x <- rnorm(100)
d1 <- data.frame(x1 = x, x2 = rnorm(x), x3 = x)
d2 <- mutate(d1, x3 = -x)
ggparcoord(d1)

library(lattice)
parallelplot(d1)

parallelplot(d1, horizontal.axis = FALSE)

Mostly parallel lines indicate positive association:

ggparcoord(d1[c(1, 3, 2)])

Near intersection in a point indicates negative association:

ggparcoord(d2)

ggparcoord(d2[c(1, 3, 2)])

A quadratic relationship:

ggparcoord(mutate(d2, x3 = x1 ^ 2)[c(1, 3, 2)])

Diamonds Data

Using a sample of 5000 observations (about 10%) and parallelplot from lattice:

library(ggplot2)
ds <- diamonds[sample(nrow(diamonds), 5000), ]
parallelplot(~ds, group = cut, data = ds, horizontal.axis = FALSE,
             auto.key = TRUE)

parallelplot(~ds, group = cut, data = ds, horizontal.axis = FALSE,
             auto.key = TRUE,
             panel = function(...) {
                 panel.parallel(...)
                 levs <- levels(ds$cut)
                 panel.text(2, seq(0, 1, len = length(levs)), levs)
             })

Rearrange variables:

ds1 <- select(ds, cut, carat, price, x, y, z)
parallelplot(~ds1, group = cut, data = ds1, horizontal.axis = FALSE,
             auto.key = TRUE,
             panel = function(...) {
                 panel.parallel(...)
                 levs <- levels(ds$cut)
                 panel.text(2, seq(0, 1, len = length(levs)), levs)
             })

Conditioning on cut:

dsnc <- select(ds, -cut)
parallelplot(~ dsnc | cut, data = ds, horizontal.axis = FALSE,
             scales = list(x = list(rot = 45)))

parallelplot(~dsnc | cut, data = ds, col = "black")

parallelplot(~dsnc | cut, data = ds, col = "black", alpha = 0.05)

Rearrange variables:

ds1nc <- select(ds1, -cut)
parallelplot(~ ds1nc | cut, data = ds1, col = "black", alpha = 0.05)

Variations using ggparcoords and a smaller sample:

ds <- diamonds[sample(nrow(diamonds), 500), ]
ggparcoord(ds, scale = "uniminmax", groupColumn = "cut")

ggparcoord(ds, scale = "uniminmax", groupColumn = "cut", columns = c(1, 3:10))

ds1 <- mutate(ds, ncut = as.numeric(cut))
ggparcoord(ds1, scale = "uniminmax", groupColumn = "cut", columns = c(1, 3:11))

Using separate facets for the cut levels:

ggparcoord(ds, scale = "uniminmax", columns = c(1, 3:10)) +
    facet_wrap(~ ds$cut) + coord_flip()

Adding box plots and violin plots:

ggparcoord(ds, scale = "uniminmax", columns = c(1, 3:10),
           alphaLines = 0.1, boxplot = TRUE) +
    facet_wrap(~ ds$cut) + coord_flip()

ggparcoord(ds, scale = "uniminmax", columns = c(1, 3:10), alphaLines = 0.1) +
    geom_boxplot(aes_string(group = "variable"), width = 0.3,
                 outlier.color = NA) +
    facet_wrap(~ds$cut) + coord_flip()
## Warning: `aes_string()` was deprecated in ggplot2 3.0.0.
## ℹ Please use tidy evaluation idioms with `aes()`.
## ℹ See also `vignette("ggplot2-in-packages")` for more information.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.

ggparcoord(ds, scale = "uniminmax", columns = c(1, 3:10), alphaLines = 0.1) +
    geom_violin(aes_string(group = "variable"), width = 0.5) +
    facet_wrap(~ds$cut) + coord_flip()

Useful Adjustments and Additions

Useful adjustments:

An interactive implementation should ideally support all of these.

Another useful feature is to be able to record the adjustments made.

This work is licensed under the CC BY-NC 3.0 Creative Commons License.