# Chapter 1 Introduction

Circular layout is very useful to represent complicated information. First, it elegantly represents information with long axes or a large amount of categories; second, it intuitively shows data with multiple tracks focusing on the same object; third, it easily demonstrates relations between elements. It provides an efficient way to arrange information on the circle and it is beautiful.

Circos is a pioneer tool widely used for circular layout representations implemented in Perl. It greatly enhances the visualization of scientific results (especially in Genomics field). Thus, plots with circular layout are normally named as “circos plot”. Here the circlize package aims to implement Circos in R. One important advantage for the implementation in R is that R is an ideal environment which provides seamless connection between data analysis and data visualization. circlize is not a front-end wrapper to generate configuration files for Circos, while completely coded in R style by using R’s elegant statistical and graphic engine. We aim to keep the flexibility and configurability of Circos, but also make the package more straightforward to use and enhance it to support more types of graphics.

In this book, chapters in Part I give detailed overviews of the general circlize functionalities. Part II introduces functions specifically designed for visualizing genomic datasets. Part III gives comprehensive guilds on visualizing relationships by Chord diagram.

## 1.1 Principle of design

A circular layout is composed of sectors and tracks. For data in different categories, they are allocated into different sectors and for multiple measurements of the same category, they are represented as stacked tracks from outside of the circle to the inside. The intersection of a sector and a track is called a cell (or a grid, a panel), which is the basic unit in a circular layout. It is an imaginary plotting region for data points in a certain category.

Since most of the figures are composed of simple graphics, such as points, lines, polygon, circlize implements low-level graphic functions for adding graphics in the circular plotting regions, so that more complicated graphics can be easily generated by different combinations of low-level graphic functions. This principle ensures the generality that types of high-level graphics are not restricted by the software itself and high-level packages focusing on specific interests can be built on it.

Currently there are following low-level graphic functions that can be used for adding graphics. The usage is very similar to the functions without circos. prefix from the base graphic engine, except there are some enhancement specifically designed for circular visualization.

• circos.points(): adds points in a cell.
• circos.lines(): adds lines in a cell.
• circos.segments(): adds segments in a cell.
• circos.rect(): adds rectangles in a cell.
• circos.polygon(): adds polygons in a cell.
• circos.text(): adds text in a cell.
• circos.axis() ands circos.yaxis(): add axis in a cell.

Following functions arrange the circular layout.

• circos.initialize(): allocates sectors on the circle.
• circos.track(): creates plotting regions for cells in one single track.
• circos.update(): updates an existed cell.
• circos.par(): graphic parameters.
• circos.info(): prints general parameters of current circular plot.
• circos.clear(): resets graphic parameters and internal variables.

Thus, theoretically, you are able to draw most kinds of circular figures by the above functionalities. Figure 1.1 lists several complex circular plots made by circlize. After going through this book, you will definitely be able to implement yours.

## 1.2 A quick glance

Before we go too deep into the details, I first demonstrate a simple example with using basic functionalities in circlize package to help you to get a basic idea of how the package works.

First let’s generate some random data. There needs a character vector to represent categories, a numeric vector of x values and a vectoe of y values.

set.seed(999)
n = 1000
df = data.frame(factors = sample(letters[1:8], n, replace = TRUE),
x = rnorm(n), y = runif(n))

First we initialize the circular layout. The circle is split into sectors based on the data range on x-axes in each category. In following code, df$x is split by df$factors and the width of sectors are automatically calculated based on data ranges in each category. Be default, sectors are positioned started from $$\theta = 0$$ (in the polar coordinate system) and go along the circle clock-wisely. You may not see anything after running following code because no track has been added yet.

library(circlize)
circos.par("track.height" = 0.1)
circos.initialize(factors = df$factors, x = df$x)

We set a global parameter track.height to 0.1 by the option function circis.par() so that all tracks which will be added have a default height of 0.1. The circle used by circlize always has a radius of 1, so a height of 0.1 means 10% of the circle radius.

Note that the allocation of sectors only needs values on x direction (or on the circular direction), the values on y direction (radical direction) will be used in the step of creating tracks.

After the circular layout is initialized, graphics can be added to the plot in a track-by-track manner. Before drawing anything, we need to know that all tracks should be first created by circos.trackPlotRegion() or, for short, circos.track(), then the low-level functions can be added afterwards. Just think in the base R graphic engine, you need first call plot() then you can use functions such as points() and lines() to add graphics. Since x ranges for cells in the track have already been defined in the initialization step, here we only need to specify the y ranges for each cell. The y ranges can be specified by y argument as a numeric vector (so that y ranges will be automatically extracted and calculated in each cell) or ylim argument as a vector of length two. In principle, y ranges should be same for all cells in a same track. (See Figure 1.2)

circos.track(factors = df$factors, y = df$y,
panel.fun = function(x, y) {
circos.text(CELL_META$xcenter, CELL_META$cell.ylim[2] + uy(5, "mm"),
CELL_META$sector.index) circos.axis(labels.cex = 0.6) }) col = rep(c("#FF0000", "#00FF00"), 4) circos.trackPoints(df$factors, df$x, df$y, col = col, pch = 16, cex = 0.5)
circos.text(-1, 0.5, "text", sector.index = "a", track.index = 1)

Axes for the circular plot are normally drawn on the most outside of the circle. Here we add axes in the first track by putting circos.axis() inside the self-defined function panel.fun (see the code above). circos.track() creates plotting region in a cell-by-cell manner and the panel.fun is actually executed immediately after the plotting region for a certain cell is created. Thus, panel.fun actually means adding graphics in the “current cell” (Usage of panel.fun is further discussed in Section 2.7). Without specifying any arguments, circos.axis() draws x-axes on the top of each cell (or the outside of each cell).

Also, we add sector name outside the first track by using circos.text(). CELL_META provides “meta information” for the current cell. There are several parameters which can be retrieved by CELL_META. All its usage is explained in Section 2.7. In above code, the sector names are drawn outside the cells and you may see warning messages saying data points exceeding the plotting regions. That is total fine and no worry about it. You can also add sector names by creating an empty track without borders as the first track and add sector names in it (like what circos.initializeWithIdeogram() and chordDiagram() do, after you go through following chapters).

When specifying the position of text on the y direction, an offset of uy(5, "mm") is added to the y position of the text. In circos.text(), x and y values are measured in the data coordinate (the coordinate in cell), and uy() function (or ux() which is measured on x direction) converts absolute units to corresponding values in data coordinate. Section 2.8.2 provides more information of converting units in different coordinates.

After the track is created, points are added to the first track by circos.trackPoints(). circos.trackPoints() simply adds points in all cells simultaneously. As further explained in Section 3.1, it can be replaced by putting circos.text() in panel.fun, however, circos.trackPoints() would be more convenient if only the points are needed to put in the cells. It is quite straightforward to understand that this function needs a categorical variable (df$factors), values on x direction and y direction (df$x and df$y). Low-level functions such as circos.text() can also be used outside panel.fun as shown in above code. If so, sector.index and track.index need to be specified explicitly because the “current” sector and “current” track may not be what you want. If the graphics are directly added to the track which are most recently created, track.index can be ommitted because this track is just marked as the “current” track. OK, now we add histograms to the second track. Here circos.trackHist() is a high- level function which means it creates a new track (as you can imagin hist() is also a high-level function). bin.size is explicitly set so that the bin size for histograms in all cells are the same and can be compared to each other. (See Figure 1.3) bgcol = rep(c("#EFEFEF", "#CCCCCC"), 4) circos.trackHist(df$factors, df$x, bin.size = 0.2, bg.col = bgcol, col = NA) In the third track and in panel.fun, we randomly picked 10 data points in each cell, sort them and connect them with lines. In following code, when factors, x and y arguments are set in circos.track(), x values and y values are split by df$factors and corresponding subset of x and y values are sent to panel.fun through panel.fun’s x and y arguments. Thus, x an y in panel.fun are exactly the values in the “current” cell. (See Figure 1.4)

circos.track(factors = df$factors, x = df$x, y = df$y, panel.fun = function(x, y) { ind = sample(length(x), 10) x2 = x[ind] y2 = y[ind] od = order(x2) circos.lines(x2[od], y2[od]) }) Now we go back to the second track and update the cell in sector “d”. This is done by circos.updatePlotRegion() or the short version circos.update(). The function erases graphics which have been added. circos.update() can not modify the xlim and ylim of the cell as well as other settings related to the position of the cell. circos.update() needs to explicitly specify the sector index and track index unless the “current” cell is what you want to update. After the calling of circos.update(), the “current” cell is redirected to the cell you just specified and you can use low-level graphic functions to add graphics directly into it. (See Figure 1.5) circos.update(sector.index = "d", track.index = 2, bg.col = "#FF8080", bg.border = "black") circos.points(x = -2:2, y = rep(0.5, 5), col = "white") circos.text(CELL_META$xcenter, CELL_META$ycenter, "updated", col = "white") Next we continue to create new tracks. Although we have gone back to the second track, when creating a new track, the new track is still created after the track which is most inside. In this new track, we add heatmaps by circos.rect(). Note here we haven’t set the input data, while simply set ylim argument because heatmaps just fill the whole cell from the most left to right and from bottom to top. Also the exact value of ylim is not important and x, y in panel.fun() are not used (actually they are both NULL). (See Figure 1.6) circos.track(ylim = c(0, 1), panel.fun = function(x, y) { xlim = CELL_META$xlim
ylim = CELL_META\$ylim
breaks = seq(xlim[1], xlim[2], by = 0.1)
n_breaks = length(breaks)
circos.rect(breaks[-n_breaks], rep(ylim[1], n_breaks - 1),
breaks[-1], rep(ylim[2], n_breaks - 1),
col = rand_color(n_breaks), border = NA)
})

In the most inside of the circle, links or ribbons are added. There can be links from single point to point, point to interval or interval to interval. Section 3.9 gives detailed usage of links. (See Figure 1.7)

circos.link("a", 0, "b", 0, h = 0.4)
circos.link("c", c(-0.5, 0.5), "d", c(-0.5,0.5), col = "red",
border = "blue", h = 0.2)
circos.link("e", 0, "g", c(-1,1), col = "green", border = "black", lwd = 2, lty = 2)

Finally we need to reset the graphic parameters and internal variables, so that it will not mess up your next plot.

circos.clear()