ggsprings

ggsprings is designed to implement an extension of geom_path which draws paths as springs instead of straight lines. Aside from possible artistic use, the main impetus for this is to draw points connected by springs, with properties of length, diameter and tension. The initial code for this comes from ggplot2: Elegant Graphics for Data Analysis (3e), Ch. 21

A leading example is to illustrate how least squares regression is “solved” by connecting data points to a rod, where the springs are constrained to be vertical. The mathematics behind this are well-described in this Math Stackexchange post, where the least squares estimates of intercept and slope are shown to be the equilibrium position that minimized the sum of forces and torques exerted by springs.

If the springs are allowed to be free, the physical solution is the major PCA axis.

How to do this is described in the ggplot2 book, https://ggplot2-book.org/ext-springs. The current version here was copied/pasted from the book.

A blog post by Joshua Loftus, Least squares by springs illustrates this, citing code from Thomas Lin Pederson. Code to reproduce the first example is contained in examples/springs.R and examples/gapminder-ex.R.

Illustrations

These images show the intent of ggsprings package.

Least squares regression

A plot of lifeExp vs. gdpPercap from the gapminder data, with gdpPercap on a log10 scale, using the code in the examples/ folder. Springs are connected between the observed value y = lifeExp and the fitted value on the regression line, yend = yhat, computed with predict() for the linear model. tension was set to 5 + (lifeExp - yhat)^2). Code for this is in examples/gapminder-ex.R

spring_plot <- simple_plot +
  geom_spring(aes(x = gdpPercap,
                  xend = gdpPercap,
                  y = lifeExp,
                  yend = yhat,
                  diameter = diameter,
                  tension = tension), color = "darkgray") +
  stat_smooth(method = "lm", se = FALSE) +
  geom_point(size = 2)

spring_plot

Principal components analysis

In PCA, the first principal component maximizes the variance of the linear combination, or equivalently, minimizes the sum of squares of perpendicular distances of the points to the line.

Animated version

This StatsExchange post show an animation of the process of fitting PCA by springs.

It doesn’t actually draw springs, but it gets the animation right. You can see that the forces of the springs initially produce large changes in the fitted line, these cause the line to swing back and forth across it’s final position, and shortly the forces begin to balance out.

This animation is written in Matlib, using the code in pca_animmation.m.

Installation

You can install the current version of ggsprings from this repo,

remotes::install.github("friendly/ggsprings")

TODO

• Finish documenting the package. I don’t quite know how to document a ggproto or to use @inheritParams for ggplot2 extensions. Add some more examples illustrating spring aesthetics and features.

• Use the package to re-create the gapminder example.

• Try to use gganimate for an animated example.

• Make a hex logo

• Write a vignette explaining the connection betweem least squares and springs better.

Example

Some basic examples top show what is working:

library(ggsprings)
library(ggplot2)
library(tibble)
#library(dplyr)

set.seed(421)
df <- tibble(
  x = runif(5, max = 10),
  y = runif(5, max = 10),
  xend = runif(5, max = 10),
  yend = runif(5, max = 10),
  class = sample(letters[1:2], 5, replace = TRUE)
)

ggplot(df) +
  geom_spring(aes(x = x, y = y,
                  xend = xend, yend = yend,
                  color = class),
              linewidth = 2) 

# Using tension and diameter as aesthetics


df <- tibble(
  x = runif(5, max = 10),
  y = runif(5, max = 10),
  xend = runif(5, max = 10),
  yend = runif(5, max = 10),
  class = sample(letters[1:2], 5, replace = TRUE),
  tension = runif(5),
  diameter = runif(5, 0.5, 1.5)
)

ggplot(df, aes(x, y, xend = xend, yend = yend)) +
  geom_spring(aes(tension = tension,
                  diameter = diameter,
                  color = class),
              linewidth = 1.2) 

Related

• An interactive demo by Trey Goesh allows you to visualize the effect of moving points, changing spring parameters, etc.