Draw and display a Venn diagram

Description

This function uses a variety of input data to draw and display a Venn diagram with up to 7 sets.

Usage

venn(x, snames = "", counts = NULL, ilabels = FALSE, ellipse = FALSE,
     zcolor = "bw", opacity = 0.3, size = 15, cexil = 0.6, cexsn = 0.85,
     borders = TRUE, ...)

Arguments

Details

The argument x can be either:
- a single number (of sets), between 1 and 7
- a metacommand (character) to draw custom intersection zones
- a list, containing values for the different sets: each component is a set, and only up to 7 components are processed.
- a dataset of boolean values.

A "zone" is a union of set intersections. There are exactly 2^k intersections in a Venn diagram, where k is the number of sets. To highlight an entire set, we need a union of all possible intersections which form that set.

For example, in a 3 sets diagram, the (overall) first set is composed by four intersections:
100 for what is in the first set but outside sets 2 and outside set 3
101 for the intersection between sets 1 and 3, outside set 2
110 for the intersection between sets 1 and 2, outside set 3
111 for the intersection between all three sets.

A meta-language can be used to define these intersections, using the values of 1 for what is inside the set, 0 for what is outside the set, and - when its either inside or outside of the set.

The command "1--" is translated as "display only the first, entire set" is equivalent with the union of the four intersections "100 + 101 + 110 + 111".

The parameter setnames should have the same length as the number of sets specified by the parameter x.

When the parameter x is used as a metacommand, the number of sets is calculated as the number of characters in each intersection of the metacommand. One such character command is "100 + 101 + 110 + 111" or "1--", and all intersections have exactly three characters.

It is also possible to use a regular, disjunctive normal form, like "A", which is equivalent with "Abc + AbC + ABc + ABC". When x is an expression written in DNF, if a valid R statement then quoting is not even necessary.

The argument snames establishes names for the different sets, or in its absence it is taken from LETTERS. When x is a list or a dataframe, snames is taken from their names. The length of the snames indicates the total number of sets.

A numerical vector can be supplied with the argument counts, when the argument x is a single number of sets. The counts should match the increasing order of the binary representation for the set intersections. When the argument x is a list, the counts are taken from the number of common values for each intersection, and when x is a data frame, (comprised of exclusively boolean values 0 and 1) the counts are taken from the number of similar rows. If a particular intersection does not have any common values (or no rows), the count "0" is left blank and not displayed in the diagram.

The argument ellipse differentiates between two types of diagrams for 4 and 5 sets. The idea is to allow for as much space as possible for each intersection (also as equal as possible) and that is impossible if preserving the shape of an ellipse. The default is to create large space for the intersections, but users who prefer an ellipse might want to set this argument to TRUE.

Colors to fill the desired zones (or entire sets) can be supplied via the argument zcolor (the default is "bw" black and white, which means no colors at all). Users can either chose the predefined color style, using zcolor = "style", or supply a vector of custom colors for each zone. If only one custom color is supplied, it will be recycled for all zones.

When using zcolor = "style", any other additional arguments for the borders are ignored.

A different set of predefined colors is used, when argument x is a QCA type object (a truth table, either from a class tt or from a class qca). If custom colors are provided via zcolor, it should have a length of 3 colors: the first for the absence of the outcome (0), the second for the presence of the outcome (1), and the third for the contradictions (C). Remainders have no color, by default.

The argument cexil works only if the intersection labels (ilabels) or intersection counts are activated, and it sets the size of the labels via a cex argument. In the absence of a specific value from the user, it's default is set to 0.6 for all Venn diagrams with up to five sets, and it automatically decreases to 0.5 for six sets and 0.45 for seven sets.

Via ..., users can specify additional parameters, mainly for the outer borders of the sets, as specified by par. All of them are feeded to the function lines() which is responsible with the borders.

For up to 3 sets, the shapes can be circular. For more than 3 sets, the shape cannot be circular: for 4 and 5 sets they can be ellipses, while for more than 5 sets the shapes cannot be continous (they might be monotone, but not continous). The 7 sets diagram is called "Adelaide" (Ruskey, 2005).

The most challenging diagram is the one with 6 sets, where for many years it was thought a Venn diagram didn't even exist. All diagrams are symetric, except for the one with 6 sets, where some of the sets have different shapes. The diagram in this package is an adaptation from Mamakani, K., Myrvold W. and F. Ruskey (2011).

The argument border can be used only for custom intersections and/or unions, it has no effect when x is a list, or a data frame, or a truth table object.

References

Ruskey, F. and M. Weston. 2005. Venn diagrams. Electronic Journal of Combinatorics, Dynamic Survey DS5.

Mamakani, K., Myrvold W. and F. Ruskey. 2011. Generating all Simple Convexly-drawable Polar Symmetric 6-Venn Diagrams. International Workshop on Combinatorial Algorithms, Victoria. LNCS, 7056, 275-286.

Examples

# A simple Venn diagram with 3 sets
venn(3)

# with a vector of counts: 1 for "000", 2 for "001" etc.
venn(3, counts = 1:8)

# display the first whole set
venn("1--")

# an equivalent command, from all intersections
venn("100, 110, 101, 111")

# adding the labels for the intersections
venn("1--", ilabels = TRUE)

# using different parameters for the borders
venn(4, lty = 5, col = "navyblue")

# using ellipses
venn(4, lty = 5, col = "navyblue", ellipse = TRUE)

# a 5 sets Venn diagram
venn(5)

# a 5 sets Venn diagram using ellipses
venn(5, ellipse = TRUE)

# a 5 sets Venn diagram with intersection labels
venn(5, ilabels = TRUE)

# and a predefined color style
venn(5, ilabels = TRUE, zcolor = "style")

# a union of two sets
venn("1---- + ----1")

# with different colors
venn("1---- , ----1", zcolor = "red, blue")

# same colors for the borders
venn("1---- , ----1", zcolor = "red, blue", col = "red, blue")

# 6 sets diagram
venn(6)

# 7 sets "Adelaide"
venn(7)


# artistic version
venn(c("1000000", "0100000", "0010000", "0001000",
       "0000100", "0000010", "0000001", "1111111"))

# without all borders
venn(c("1000000", "0100000", "0010000", "0001000",
       "0000100", "0000010", "0000001", "1111111"),
     borders = FALSE)


# when x is a list
set.seed(12345)
x <- list(First = 1:20, Second = 10:30, Third = sample(25:50, 15))
venn(x)

# when x is a dataframe
set.seed(12345)
x <- as.data.frame(matrix(sample(0:1, 150, replace=TRUE), ncol=5))
venn(x)


# using sum of products notation
venn("A + Bc", snames = "A,B,C,D")

# the union of two sets, example from above
venn("A + E", snames = "A,B,C,D,E", zcol = "red, blue")



# produce Venn diagrams for QCA objects

library(QCA)

data(CVF)
obj <- truthTable(CVF, "PROTEST", incl.cut = 0.85)

venn(obj)


# to set opacity based on inclusion scores
# (less inclusion, more transparent)

venn(obj, opacity = obj$tt$incl)


# custom labels for intersections

pCVF <- minimize(obj, include = "?")
venn(pCVF$solution[[1]], zcol = "#ffdd77, #bb2020, #1188cc")
cases <- paste(c("HungariansRom", "CatholicsNIreland", "AlbaniansFYROM",
                 "RussiansEstonia"), collapse = "\n")
coords <- unlist(getCentroid(getZones(pCVF$solution[[1]][2])))
text(coords[1], coords[2], labels = cases, cex = 0.85)