Visualization

Jeff Goldsmith, Fabian Scheipl

2024-02-23

The tidyfun package is designed to facilitate functional data analysis in R, with particular emphasis on compatibility with the tidyverse. In this vignette, we illustrate data visualization using tidyfun.

We’ll draw on tidyfun::chf_df and tidyfun::dti_df, as well as the fda::CanadianWeather data.

Plotting with ggplot

ggplot is a powerful framework for visualization. In this section, we’ll assume some basic familiarity with the package; if you’re new to ggplot, this primer may be helpful.

tidyfun includes pasta-themed geoms and plots for functional data:

• geom_spaghetti for lines
• geom_meatballs for (lines &) points
• gglasagna for heatmaps, with an order-argument for arranging lasagna layers / heat map rows.
• geom_capellini for little sparklines / glyphs on maps etc.
• geom_errorband – a functional data version of geom_ribbon

geom_spaghetti and geom_meatballs

One of the most fundamental plots for functional data is the spaghetti plot, which is implemented in tidyfun + ggplot through geom_spaghetti:

chf_df |>
  filter(id == 1) |>
  ggplot(aes(y = activity)) +
  geom_spaghetti()

A variant on the spaghetti plot is the meatballs plot, which shows both the “noodles” (i.e. functional observations visualized as curves) and the “meatballs” (i.e. observed data values visualized as points).

chf_df |>
  filter(id == 1, day == "Mon") |>
  ggplot(aes(y = activity)) +
  geom_meatballs()

Using with other ggplot features

The new geoms in tidyfun “play nicely” with standard ggplot aesthetics and options.

You can, for example, define the color aesthetic for plots of tf variables using other observations:

chf_df |>
  filter(id %in% 1:5) |>
  ggplot(aes(y = activity, color = gender)) +
  geom_spaghetti(alpha = 0.2)

You can also use facetting:

chf_df |>
  filter(day %in% c("Mon", "Sun")) |>
  ggplot(aes(y = activity, color = gender)) +
  geom_spaghetti(alpha = 0.1) +
  facet_grid(~day)

Another example, using the DTI data, is below.

dti_df |>
  ggplot() +
  geom_spaghetti(aes(y = cca, col = case, alpha = 0.2 + 0.4 * (case == "control"))) +
  facet_wrap(~sex) +
  scale_alpha(guide = "none", range = c(0.2, 0.4))

Together with tidyfun’s tools for functional data wrangling and summary statistics, the integration with ggplot2 can produce useful exploratory analyses, like the plot below showing group-wise smoothed and unsmoothed mean activity profiles:

chf_df |>
  group_by(gender, day) |>
  summarize(mean_act = mean(activity)) |>
  mutate(smooth_mean = tfb(mean_act, verbose = FALSE)) |>
  filter(day %in% c("Mon", "Sun")) |>
  ggplot(aes(y = smooth_mean, color = gender)) +
  geom_spaghetti(linewidth = 1.25, alpha = 1) +
  geom_meatballs(aes(y = mean_act), alpha = 0.1) +
  facet_grid(~day)
## `summarise()` has grouped output by 'gender'. You can override using the
## `.groups` argument.
## Percentage of input data variability preserved in basis representation (per
## functional observation, approximate): Min. 1st Qu.  Median Mean 3rd Qu.  Max.
## 100 100 100 100 100 100
## Percentage of input data variability preserved in basis representation (per
## functional observation, approximate): Min. 1st Qu.  Median Mean 3rd Qu.  Max.
## 100 100 100 100 100 100
## Percentage of input data variability preserved in basis representation (per
## functional observation, approximate): Min. 1st Qu.  Median Mean 3rd Qu.  Max.
## 100 100 100 100 100 100
## Percentage of input data variability preserved in basis representation (per
## functional observation, approximate): Min. 1st Qu.  Median Mean 3rd Qu.  Max.
## 100 100 100 100 100 100

… or the plot below showing group-wise mean functions +/- twice their pointwise standard errors:

chf_df |>
  group_by(gender, day) |>
  summarize(
    mean_act = mean(activity),
    sd_act = sd(activity)
  ) |>
  group_by(gender, day) |>
  mutate(
    upper_act = mean_act + 2 * sd_act,
    lower_act = mean_act - 2 * sd_act
  ) |>
  filter(day %in% c("Mon", "Sun")) |>
  ggplot(aes(y = mean_act, color = gender, fill = gender)) +
  geom_spaghetti(alpha = 1) +
  geom_errorband(aes(ymax = upper_act, ymin = lower_act), alpha = 0.3) +
  facet_grid(day ~ gender)
## `summarise()` has grouped output by 'gender'. You can override using the
## `.groups` argument.

gglasagna

Lasagna plots are “a saucy alternative to spaghetti plots”. They are a variant on a heatmaps which show functional observations in rows and use color to illustrate values taken at different arguments.

In tidyfun, lasagna plots are implemented through gglasagna. A first example, using the CHF data, is below.

chf_df |>
  filter(day %in% c("Mon", "Sun")) |>
  gglasagna(activity)

A somewhat more involved example, demonstrating the order argument and taking advantage of facets, is next.

dti_df |>
  gglasagna(
    tf = cca,
    order = tf_integrate(cca, definite = TRUE),
    arg = seq(0, 1, length.out = 101)
  ) +
  theme(axis.text.y = element_text(size = 6)) +
  facet_wrap(~case, ncol = 2, scales = "free")

geom_capellini

To illustrate geom_capellini, we’ll start with some data prep for the iconic Canadian Weather data:

canada <- data.frame(
  place = fda::CanadianWeather$place,
  region = fda::CanadianWeather$region,
  lat = fda::CanadianWeather$coordinates[, 1],
  lon = -fda::CanadianWeather$coordinates[, 2]
)

canada$temp <- tfd(t(fda::CanadianWeather$dailyAv[, , 1]), arg = 1:365)
canada$precipl10 <- tfd(t(fda::CanadianWeather$dailyAv[, , 3]), arg = 1:365) |>
  tf_smooth()
## using f = 0.15 as smoother span for lowess

canada_map <-
  data.frame(maps::map("world", "Canada", plot = FALSE)[c("x", "y")])

Now we can plot a map of Canada with annual temperature averages in red, precipitation in blue:

ggplot(canada, aes(x = lon, y = lat)) +
  geom_capellini(aes(tf = precipl10),
    width = 4, height = 5, colour = "blue",
    line.linetype = 1
  ) +
  geom_capellini(aes(tf = temp),
    width = 4, height = 5, colour = "red",
    line.linetype = 1
  ) +
  geom_path(data = canada_map, aes(x = x, y = y), alpha = 0.1) +
  coord_quickmap()

Plotting with base R

tidyfun includes several extensions of base R graphics, which operate on tf vectors. For example, one can use plot to create either spaghetti or lasagna plots, and lines to add lines to an existing plot:

cca <- dti_df$cca |>
  tfd(arg = seq(0, 1, length.out = 93), interpolate = TRUE)

layout(t(1:2))

plot(cca, type = "spaghetti")
lines(c(median(cca), mean = mean(cca)), col = c(2, 4))

plot(cca, type = "lasagna", col = viridis(50))

These plot methods use all the same graphics options and can be edited like other base graphics:

cca_five <- cca[1:5]

cca_five |> plot(xlim = c(-0.15, 1), col = pal_5, lwd = 2)

text(
  x = -0.1, y = cca_five[, 0.07], labels = names(cca_five), col = pal_5, cex = 1.5
)

median(cca_five) |> lines(col = pal_5[3], lwd = 4)