Package 'tourr'

Description

For each datapoint this function calculates the orthogonal distance from the anchored projection plane.

Usage

anchored_orthogonal_distance(plane, data, anchor = NULL)

Arguments

Value

distance vector

Description

This function takes a numeric vector of input, and returns a function which allows you to compute the value of the Andrew's curve at every point along its path from -pi to pi.

Usage

andrews(x)

Arguments

Value

a function with single argument, theta

Examples

a <- andrews(1:2)
a(0)
a(-pi)
grid <- seq(-pi, pi, length = 50)
a(grid)

plot(grid, andrews(1:2)(grid), type = "l")
plot(grid, andrews(runif(5))(grid), type = "l")

Description

Returns n equidistant bins between -pi and pi

Usage

angular_breaks(n)

Arguments

Description

This is the function that powers all of the tour animations. If you want to write your own tour animation method, the best place to start is by looking at the code for animation methods that have already implemented in the package.

Usage

animate(
  data,
  tour_path = grand_tour(),
  display = display_xy(),
  start = NULL,
  aps = 1,
  fps = 10,
  max_frames = Inf,
  rescale = FALSE,
  sphere = FALSE,
  ...
)

Arguments

Details

See render to render animations to disk.

Value

an (invisible) list of bases visited during this tour

Examples

f <- flea[, 1:6]
animate(f, grand_tour(), display_xy())
# or in short
animate(f)
animate(f, max_frames = 30)

animate(f, max_frames = 10, fps = 1, aps = 0.1)

Description

Calculates an index that looks for the best projection of observations that are outside a pre-determined p-D ellipse.

Usage

anomaly_index()

Description

Test if all entries are colors

Usage

areColors(x)

Arguments

Description

Center a numeric vector by subtracting off its mean.

Usage

center(x)

Arguments

Description

Calculates the central mass index. See Cook and Swayne (2007) Interactive and Dynamic Graphics for Data Analysis for equations.

Usage

cmass()

Description

Computes the distance correlation based index on 2D projections of the data. dcor2d_2 uses the faster implementation of the distance correlation for bivariate data, see energy::dcor2d.

Usage

dcor2d()

dcor2d_2()

Description

The dependence tour combines a set of independent 1d tours to produce a nd tour. For the special case of 2d, this is known as a correlation tour. This tour corresponds to the multivariate method known as generalised canonical correlation, and is used to investigate dependence between groups of variables.

Usage

dependence_tour(pos)

Arguments

Details

Usually, you will not call this function directly, but will pass it to a method that works with tour paths like animate, save_history or render.

Examples

animate_xy(flea[, 1:3], dependence_tour(c(1, 2, 2)))
animate_xy(flea[, 1:4], dependence_tour(c(1, 2, 1, 2)))
animate_pcp(flea[, 1:6], dependence_tour(c(1, 2, 3, 2, 1, 3)))

Description

Animate a nD tour path with Andrews' curves. For more details about Andrew's curves, see andrews

Usage

display_andrews(col = "black", palette = "Zissou 1", ...)

animate_andrews(data, tour_path = grand_tour(3), col = "black", ...)

Arguments

See Also

animate for options that apply to all animations

Examples

animate_andrews(flea[, 1:6])
animate_andrews(flea[, 1:6], grand_tour(d = 3))
animate_andrews(flea[, 1:6], grand_tour(d = 6))

# It's easy to experiment with different tour paths:
animate_andrews(flea[, 1:6], guided_tour(cmass()))

Description

Animate a 2D tour path with density contour(s) and a scatterplot.

Usage

display_density2d(
  center = TRUE,
  axes = "center",
  half_range = NULL,
  col = "black",
  pch = 20,
  cex = 1,
  contour_quartile = c(0.25, 0.5, 0.75),
  edges = NULL,
  palette = "Zissou 1",
  axislablong = FALSE,
  ...
)

animate_density2d(data, tour_path = grand_tour(), ...)

Arguments

Examples

animate_density2d(flea[, 1:6])
animate(flea[, 1:6], tour_path = grand_tour(), display = display_density2d())
animate(flea[, 1:6],
  tour_path = grand_tour(),
  display = display_density2d(axes = "bottomleft")
)
animate(flea[, 1:6],
  tour_path = grand_tour(),
  display = display_density2d(half_range = 0.5)
)
animate_density2d(flea[, 1:6], tour_path = little_tour())

animate_density2d(flea[, 1:3], tour_path = guided_tour(holes()), sphere = TRUE)
animate_density2d(flea[, 1:6], center = FALSE)

# The default axes are centered, like a biplot, but there are other options
animate_density2d(flea[, 1:6], axes = "bottomleft")
animate_density2d(flea[, 1:6], axes = "off")
animate_density2d(flea[, 1:6], dependence_tour(c(1, 2, 1, 2, 1, 2)),
  axes = "bottomleft"
)

animate_density2d(flea[, -7], col = flea$species)

# You can also draw lines
edges <- matrix(c(1:5, 2:6), ncol = 2)
animate(
  flea[, 1:6], grand_tour(),
  display_density2d(axes = "bottomleft", edges = edges)
)

Description

Suggestion to use gray background and colour saturation (instead of gray shading) by Graham Wills.

Usage

display_depth(center = TRUE, half_range = NULL, ...)

animate_depth(data, tour_path = grand_tour(3), ...)

Arguments

See Also

animate for options that apply to all animations

Examples

animate_depth(flea[, 1:6])

Description

Animate a 1d tour path with a density plot or histogram.

Usage

display_dist(
  method = "density",
  center = TRUE,
  half_range = NULL,
  col = "black",
  rug = FALSE,
  palette = "Zissou 1",
  density_max = 3,
  bw = 0.2,
  scale_density = FALSE,
  ...
)

animate_dist(data, tour_path = grand_tour(1), ...)

Arguments

See Also

animate for options that apply to all animations

Examples

animate_dist(flea[, 1:6])

# Change inputs, to color by group, fix y axis, change bin width
# and scale bar height or density at each projection
animate_dist(flea[, 1:6], col=flea$species, density_max=5)
animate_dist(flea[, 1:6], col=flea$species, density_max=5, bw=0.1)
animate_dist(flea[, 1:6], col=flea$species, scale_density=TRUE)

# When the distribution is not centred, it tends to wander around in a
# distracting manner
animate_dist(flea[, 1:6], center = FALSE)

# Alternatively, you can display the distribution with a histogram
animate_dist(flea[, 1:6], method = "hist")

Description

Animate a nD tour path with Chernoff's faces. Can display up to 18 dimensions.

Usage

display_faces(...)

animate_faces(data, tour_path = grand_tour(3), ...)

Arguments

Details

This function requires the TeachingDemos package to draw the Chernoff faces. See faces2 for more details.

See Also

animate for options that apply to all animations

Examples

# The drawing code is fairly slow, so this animation works best with a
# limited number of cases
flea_s <- rescale(flea[,1:6])
animate_faces(flea_s[19:24, 1:6])

animate_faces(flea_s[19:24, 1:6], grand_tour(5))

Description

This function is designed to allow comparisons across multiple groups, especially for examining things like two (or more) different models on the same data. The primary display is a scatterplot, with lines or contours overlaid.

Usage

display_groupxy(
  centr = TRUE,
  axes = "center",
  half_range = NULL,
  col = "black",
  pch = 20,
  cex = 1,
  edges = NULL,
  edges.col = "black",
  edges.width = 1,
  group_by = NULL,
  plot_xgp = TRUE,
  palette = "Zissou 1",
  shapeset = c(15:17, 23:25),
  axislablong = FALSE,
  ...
)

animate_groupxy(data, tour_path = grand_tour(), ...)

Arguments

Examples

animate_groupxy(flea[, 1:6], col = flea$species,
  pch = flea$species, group_by = flea$species)
animate_groupxy(flea[, 1:6], col = flea$species,
  pch = flea$species, group_by = flea$species,
  plot_xgp = FALSE)
# Edges example
x <- data.frame(x1=runif(10, -1, 1), x2=runif(10, -1, 1), x3=runif(10, -1, 1))
x$cl <- factor(c(rep("A", 3), rep("B", 3), rep("C", 4)))
x.edges <- cbind(from=c(1,2, 4,5, 7,8,9), to=c(2,3, 5,6, 8,9,10))
x.edges.col <- factor(c(rep("A", 2), rep("B", 2), rep("C", 3)))
animate_groupxy(x[,1:3], col=x$cl, group_by=x$cl, edges=x.edges, edges.col=x.edges.col)

Description

Animate a 1D tour path for data where individuals are ranked by a multivariate index. Allows one to examine the sensitivity of the ranking on the linear combination. Variables should be scaled to be between 0-1. This is only designed to work with a local tour, or a radial tour.

Usage

display_idx(
  center = FALSE,
  half_range = NULL,
  abb_vars = TRUE,
  col = "red",
  cex = 3,
  panel_height_ratio = c(3, 2),
  label_x_pos = 0.7,
  label = NULL,
  label_cex = 1,
  label_col = "grey80",
  add_ref_line = TRUE,
  axis_bar_col = "#000000",
  axis_bar_lwd = 3,
  axis_label_cex_upper = 1,
  axis_label_cex_lower = 1,
  axis_bar_label_cex = 1,
  axis_bar_label_col = "#000000",
  axis_var_cex = 1,
  axis_var_col = "#000000",
  palette = "Zissou 1",
  ...
)

animate_idx(data, tour_path = grand_tour(1), ...)

Arguments

Examples

data(places)
places_01 <- apply(places[1:10,1:9], 2, function(x) (x-min(x))/(max(x)-min(x)))
b <- matrix(rep(1/sqrt(9), 9), ncol=1)
places_init <- cbind(places_01, idx = as.vector(as.matrix(places_01) %*% b))
places_sorted <- places_init[order(places_init[,10]), 1:9]
animate_idx(places_sorted, tour_path = local_tour(b, angle=pi/8),
            label=as.character(places$stnum[1:9]),
            label_x_pos = 0)

Description

Animate a 1d tour path with an image plot. This animation requires a different input data structure, a 3d array. The first two dimensions are locations on a grid, and the 3rd dimension gives the observations to be mixed with the tour.

Usage

display_image(xs, ys, ...)

animate_image(data, tour_path = grand_tour(1), ...)

Arguments

See Also

animate for options that apply to all animations

Examples

str(ozone)
animate_image(ozone)

Description

Animate a 2D tour path on data that has been transformed into principal components, and also show the original variable axes.

Usage

display_pca(
  center = TRUE,
  axes = "center",
  half_range = NULL,
  col = "black",
  pch = 20,
  cex = 1,
  pc_coefs = NULL,
  edges = NULL,
  edges.col = "black",
  palette = "Zissou 1",
  axislablong = FALSE,
  ...
)

animate_pca(data, tour_path = grand_tour(), rescale = FALSE, ...)

Arguments

Examples

flea_std <- apply(flea[,1:6], 2, function(x) (x-mean(x))/sd(x))
flea_pca <- prcomp(flea_std, center = FALSE, )
flea_coefs <- flea_pca$rotation[, 1:3]
flea_scores <- flea_pca$x[, 1:3]
animate_pca(flea_scores, pc_coefs = flea_coefs)

Description

Animate a nD tour path with a parallel coordinates plot.

Usage

display_pcp(...)

animate_pcp(data, tour_path = grand_tour(3), ...)

Arguments

Details

The lines show the observations, and the points, the values of the projection matrix.

See Also

animate for options that apply to all animations

Examples

animate_pcp(flea[, 1:6], grand_tour(3))
animate_pcp(flea[, 1:6], grand_tour(5))

Description

Animate a 2D tour path with a sage scatterplot that uses a radial transformation on the projected points to re-allocate the volume projected across the 2D plane.

Usage

display_sage(
  axes = "center",
  half_range = NULL,
  col = "black",
  pch = 20,
  gam = 1,
  R = NULL,
  palette = "Zissou 1",
  axislablong = FALSE,
  ...
)

animate_sage(data, tour_path = grand_tour(), ...)

Arguments

Examples

# Generate uniform samples in a 10d sphere using the geozoo package
sphere10 <- geozoo::sphere.solid.random(10)$points
# Columns need to be named before launching the tour
colnames(sphere10) <- paste0("x", 1:10)
# Standard grand tour display, points cluster near center
animate_xy(sphere10)
# Sage display, points are uniformly distributed across the disk
animate_sage(sphere10)

Description

Animate a nD tour path with a scatterplot matrix.

Usage

display_scatmat(...)

animate_scatmat(data, tour_path = grand_tour(3), ...)

Arguments

Details

The lines show the observations, and the points, the values of the projection matrix.

See Also

animate for options that apply to all animations

Examples

animate_scatmat(flea[, 1:6], grand_tour(2))
animate_scatmat(flea[, 1:6], grand_tour(6))

Description

Animate a 2D tour path with a sliced scatterplot.

Usage

display_slice(
  center = TRUE,
  axes = "center",
  half_range = NULL,
  col = "black",
  pch_slice = 20,
  pch_other = 46,
  cex_slice = 2,
  cex_other = 1,
  v_rel = NULL,
  anchor = NULL,
  anchor_nav = "off",
  edges = NULL,
  edges.col = "black",
  palette = "Zissou 1",
  axislablong = FALSE,
  ...
)

animate_slice(data, tour_path = grand_tour(), rescale = FALSE, ...)

Arguments

Examples

# Generate samples on a 3d and 5d hollow sphere using the geozoo package
sphere3 <- geozoo::sphere.hollow(3)$points
sphere5 <- geozoo::sphere.hollow(5)$points

# Columns need to be named before launching the tour
colnames(sphere3) <- c("x1", "x2", "x3")
colnames(sphere5) <- c("x1", "x2", "x3", "x4", "x5")

# Animate with the slice display using the default parameters
animate_slice(sphere3)
animate_slice(sphere5)

# Animate with off-center anchoring
anchor3 <- matrix(rep(0.7, 3), ncol=3)
anchor5 <- matrix(rep(0.3, 5), ncol=5)
animate_slice(sphere3, anchor = anchor3)
# Animate with thicker slice to capture more points in each view
animate_slice(sphere5, anchor = anchor5, v_rel = 0.02)

Description

Animate a nD tour path with star glyphs.

Usage

display_stars(...)

animate_stars(data, tour_path = grand_tour(3), ...)

Arguments

Details

Currently, scaling doesn't seem to be computed absolutely correctly, as centres move around as well as outside points.

See Also

animate for options that apply to all animations

Examples

animate_stars(flea[1:10, 1:6])
animate_stars(flea[1:10, 1:6], grand_tour(5))
animate_stars(flea[, 1:6], grand_tour(5))
animate_stars(flea[1:10, 1:6], grand_tour(5),
  col.stars = rep("grey50", 10), radius = FALSE
)

Description

Uses red-blue anaglyphs to display a 3d tour path. You'll need some red- blue glasses to get much out of this displays!

Usage

display_stereo(blue, red, cex = 1, ...)

animate_stereo(
  data,
  tour_path = grand_tour(3),
  blue = rgb(0, 0.91, 0.89),
  red = rgb(0.98, 0.052, 0),
  ...
)

Arguments

Examples

animate_stereo(flea[, 1:6])

Description

Animate a 2D tour path with a point trails

Usage

display_trails(
  center = TRUE,
  axes = "center",
  half_range = NULL,
  col = "black",
  pch = 20,
  cex = 1,
  past = 3,
  axislablong = FALSE,
  ...
)

animate_trails(data, tour_path = grand_tour(), ...)

Arguments

Examples

animate_trails(flea[,1:6], col=flea$species)

Description

Animate a 2D tour path with a scatterplot.

Usage

display_xy(
  center = TRUE,
  axes = "center",
  half_range = NULL,
  col = "black",
  pch = 20,
  cex = 1,
  edges = NULL,
  edges.col = "black",
  edges.width = 1,
  obs_labels = NULL,
  ellipse = NULL,
  ellc = NULL,
  ellmu = NULL,
  ellmarks = TRUE,
  palette = "Zissou 1",
  shapeset = c(15:17, 23:25),
  axislablong = FALSE,
  ...
)

animate_xy(data, tour_path = grand_tour(), ...)

Arguments

Examples

animate_xy(flea[, 1:6])
animate(flea[, 1:6], tour_path = grand_tour(), display = display_xy())
animate(flea[, 1:6],
  tour_path = grand_tour(),
  display = display_xy(),
  scale = TRUE
)
animate(flea[, 1:6],
  tour_path = grand_tour(),
  display = display_xy(half_range = 0.5)
)
animate_xy(flea[, 1:6], tour_path = little_tour())
animate_xy(flea[, 1:3], tour_path = guided_tour(holes()), sphere = TRUE)
animate_xy(flea[, 1:6], center = FALSE)

# The default axes are centered, like a biplot, but there are other options
animate_xy(flea[, 1:6], axes = "bottomleft")
animate_xy(flea[, 1:6], axes = "off")
animate_xy(flea[, 1:6], dependence_tour(c(1, 2, 1, 2, 1, 2)),
  axes = "bottomleft"
)

animate_xy(flea[, -7], col = flea$species)
animate_xy(flea[, -7], col = flea$species,
             pch = flea$species)

animate_xy(flea[, -7], col = flea$species,
  obs_labels=as.character(1:nrow(flea)), axes="off")

# You can also draw lines
edges <- matrix(c(1:5, 2:6), ncol = 2)
animate(
  flea[, 1:6], grand_tour(),
  display_xy(axes = "bottomleft", edges = edges)
)
# An ellipse can be drawn on the data using a specified var-cov
animate_xy(flea[, 1:6], axes = "off", ellipse=cov(flea[,1:6]))

Description

Draw tour axes on the projected data with base graphics

Usage

draw_tour_axes(
  proj,
  labels,
  limits = 1,
  position = "center",
  axis.col = "grey50",
  axis.lwd = 1,
  axis.text.col = "grey50",
  longlabels,
  ...
)

Arguments

Examples

data(flea)
flea_std <- apply(flea[,1:6], 2, function(x) (x-mean(x))/sd(x))
prj <- basis_random(ncol(flea[,1:6]), 2)
flea_prj <- as.data.frame(as.matrix(flea_std) %*% prj)
par(pty = "s", mar = rep(0.1, 4))
plot(flea_prj$V1, flea_prj$V2,
     xlim = c(-3, 3), ylim = c(-3, 3),
     xlab="P1", ylab="P2")
draw_tour_axes(prj, colnames(flea)[1:6], limits=3)

plot(flea_prj$V1, flea_prj$V2,
     xlim = c(-3, 3), ylim = c(-3, 3),
     xlab="P1", ylab="P2")
draw_tour_axes(prj, colnames(flea)[1:6], limits=3, position="bottomleft")
draw_tour_axes(prj, colnames(flea)[1:6], axislablong=TRUE)

Description

Estimate cutoff eps for section pursuit.

Usage

estimate_eps(N, p, res, K, K_theta, r_breaks)

Arguments

Description

This data is from a paper by A. A. Lubischew, "On the Use of Discriminant Functions in Taxonomy", Biometrics, Dec 1962, pp.455-477. Data is standardized, and original units are in flea_raw.

Usage

flea

Format

A 74 x 7 numeric array

Details

• tars1, width of the first joint of the first tarsus in microns (the sum of measurements for both tarsi)

• tars2, the same for the second joint

• head, the maximal width of the head between the external edges of the eyes in 0.01 mm

• ade1, the maximal width of the aedeagus in the fore-part in microns

• ade2, the front angle of the aedeagus ( 1 unit = 7.5 degrees)

• ade3, the aedeagus width from the side in microns

• species, which species is being examined - concinna, heptapotamica, heikertingeri

Examples

head(flea)
animate_xy(flea[, -7])
animate_xy(flea[, -7], col = flea[, 7])

Description

The frozen guided tour

Usage

frozen_guided_tour(frozen, index_f, d = 2, max.tries = 25)

Arguments

See Also

cmass, holes and lda_pp for examples of index functions. The function should take a numeric matrix and return a single number, preferrably between 0 and 1.

Examples

frozen <- matrix(NA, nrow = 4, ncol = 2)
frozen[3, ] <- .5
animate_xy(flea[, 1:4], frozen_guided_tour(frozen, holes()))

Description

A frozen tour fixes some of the values of the orthonormal projection matrix and allows the others to vary freely according to any of the other tour methods. This frozen tour is a frozen grand tour. See frozen_guided_tour for a frozen guided tour.

Usage

frozen_tour(d = 2, frozen)

Arguments

Details

Usually, you will not call this function directly, but will pass it to a method that works with tour paths like animate, save_history or render.

Examples

frozen <- matrix(NA, nrow = 4, ncol = 2)
frozen[3, ] <- .5
animate_xy(flea[, 1:4], frozen_tour(2, frozen))

frozen <- matrix(NA, nrow = 4, ncol = 2)
frozen[1, 1] <- 0.5
animate_xy(flea[, 1:4], frozen_tour(2, frozen))

# Doesn't work - a bug?
frozen <- matrix(NA, nrow = 4, ncol = 2)
frozen[1:2, 1] <- 1 / 4
animate_xy(flea[, 1:4], frozen_tour(2, frozen))

## Not run: 
# This freezes one entire direction which causes a problem,
# and is caught by error handling.
# If you want to do this it would be best with a dependence
# tour, with one variable set one axis, eg 3rd variable to
# x axis would be indicated from the code below
frozen <- matrix(NA, nrow = 4, ncol = 2)
frozen[3, ] <- c(0, 1)
animate_xy(flea[, 1:4], frozen_tour(2, frozen))

## End(Not run)

# Two frozen variables in five.
frozen <- matrix(NA, nrow = 5, ncol = 2)
frozen[3, ] <- .5
frozen[4, ] <- c(-.2, .2)
animate_xy(flea[, 1:5], frozen_tour(2, frozen))

Description

This method generates target bases by randomly sampling on the space of all d-dimensional planes in p-space.

Usage

grand_tour(d = 2, ...)

Arguments

Details

Usually, you will not call this function directly, but will pass it to a method that works with tour paths like animate, save_history or render.

Examples

# All animation methods use the grand tour path by default
animate_dist(flea[, 1:6])
animate_xy(flea[, 1:6])
animate_pcp(flea[, 1:6])
animate_pcp(flea[, 1:6], grand_tour(4))

# The grand tour is a function:
tour2d <- grand_tour(2)
is.function(tour2d)

# with two parameters, the previous projection and the data set
args(tour2d)
# if the previous projection is null, it will generate a starting
# basis, otherwise the argument is ignored
tour2d(NULL, mtcars)
# the data argument is just used to determine the correct dimensionality
# of the output matrix
tour2d(NULL, mtcars[, 1:2])

Description

The guided anomaly tour is a variation of the guided tour that is using an ellipse to determine anomalies on which to select target planes.

Usage

guided_anomaly_tour(
  index_f,
  d = 2,
  alpha = 0.5,
  cooling = 0.99,
  max.tries = 25,
  max.i = Inf,
  ellipse,
  ellc = NULL,
  ellmu = NULL,
  search_f = search_geodesic,
  ...
)

Arguments

Details

Usually, you will not call this function directly, but will pass it to a method that works with tour paths like animate_xy, save_history or render.

See Also

slice_index for an example of an index functions. search_geodesic, search_better, search_better_random for different search strategies

Examples

animate_xy(flea[, 1:6], guided_anomaly_tour(anomaly_index(),
  ellipse=cov(flea[,1:6])), ellipse=cov(flea[,1:6]), axes="off")

Description

The guided section tour is a variation of the guided tour that is using a section pursuit index for the selection of target planes.

Usage

guided_section_tour(
  index_f,
  d = 2,
  alpha = 0.5,
  cooling = 0.99,
  max.tries = 25,
  max.i = Inf,
  v_rel = NULL,
  anchor = NULL,
  search_f = search_geodesic,
  ...
)

Arguments

Details

Usually, you will not call this function directly, but will pass it to a method that works with tour paths like animate_slice, save_history or render.

See Also

slice_index for an example of an index functions. search_geodesic, search_better, search_better_random for different search strategies

Examples

# Generate samples on a 3d hollow sphere using the geozoo package
set.seed(12345)
sphere3 <- geozoo::sphere.hollow(3)$points
# Columns need to be named before launching the tour
colnames(sphere3) <- c("x1", "x2", "x3")
# Off-center anchoring
anchor3 <- matrix(rep(0.75, 3), ncol=3)
# Index setup
r_breaks <- linear_breaks(5, 0, 1)
a_breaks <- angular_breaks(10)
eps <- estimate_eps(nrow(sphere3), ncol(sphere3), 0.1 / 1, 5 * 10, 10, r_breaks)
idx <- slice_index(r_breaks, a_breaks, eps, bintype = "polar", power = 1, reweight = TRUE, p = 3)
# Running the guided section tour select sections showing a big hole in the center
animate_slice(sphere3, guided_section_tour(idx, v_rel = 0.1, anchor = anchor3, max.tries = 5),
  v_rel = 0.1, anchor = anchor3
)

Description

Instead of choosing new projections at random like the grand tour, the guided tour always tries to find a projection that is more interesting than the current projection.

Usage

guided_tour(
  index_f,
  d = 2,
  cooling = 0.99,
  max.tries = 25,
  max.i = Inf,
  search_f = search_geodesic,
  n_jellies = 30,
  n_sample = 100,
  alpha = 0.5,
  ...
)

Arguments

Details

Currently the index functions only work in 2d.

Usually, you will not call this function directly, but will pass it to a method that works with tour paths like animate, save_history or render.

See Also

cmass, holes and lda_pp for examples of index functions. The function should take a numeric matrix and return a single number, preferably between 0 and 1. search_geodesic, search_better, search_better_random for different search strategies

Examples

flea_std <- apply(flea[,1:6], 2, function(x) (x-mean(x))/sd(x))
animate_xy(flea_std, guided_tour(holes()), sphere = TRUE)

animate_xy(flea_std, guided_tour(holes(), search_f = search_better_random), sphere = TRUE)
animate_dist(flea_std, guided_tour(holes(), 1), sphere = TRUE)
animate_xy(flea_std, guided_tour(lda_pp(flea$species)), sphere = TRUE, col = flea$species)

# save_history is particularly useful in conjunction with the
# guided tour as it allows us to look at the tour path in many different
# ways
f <- flea_std[, 1:3]
tries <- replicate(5, save_history(f, guided_tour(holes())), simplify = FALSE)

Description

Calculates the holes index. See Cook and Swayne (2007) Interactive and Dynamic Graphics for Data Analysis for equations.

Usage

holes()

Description

This function takes a set of bases and produces a tour by geodesically interpolating between each basis

Usage

interpolate(basis_set, angle = 0.05, cycle = FALSE)

Arguments

Examples

t1 <- save_history(flea[, 1:6], grand_tour(1), max = 3)
dim(t1)
dim(interpolate(t1, 0.01))
dim(interpolate(t1, 0.05))
dim(interpolate(t1, 0.1))
t2 <- save_history(flea[, 1:6], grand_tour(2), max = 2)
dim(interpolate(t2, 0.05))

Description

This data came from an investigation of an experimental laser at Bellcore. It was a tunable laser, in the sense that both its wavelength and power output were controllable.

Format

A 64 x 4 numeric array

Details

Rotation helped the experimental physicists to characterize the laser, which turned out not to be a very good one, due to its unstable operating region.

This data initially came to the statistics research group when Janette Cooper asked Paul Tukey to help her analyze the data she had collected to describe the laser.

• ifront, current applied to the front of the laser

• iback, current applied to the back of the laser

• power, output power

• lambda, output wavelength

Examples

head(laser)
animate_xy(laser[, -4])

Description

Calculate the LDA projection pursuit index. See Cook and Swayne (2007) Interactive and Dynamic Graphics for Data Analysis for equations.

Usage

lda_pp(cl)

Arguments

Description

Returns n equidistant bins between a and b

Usage

linear_breaks(n, a, b)

Arguments

Description

The little tour is a planned tour that travels between all axis parallel projections. (John McDonald named this type of tour.)

Usage

little_tour(d = 2)

Arguments

Details

Usually, you will not call this function directly, but will pass it to a method that works with tour paths like animate, save_history or render.

Examples

animate_xy(flea[, 1:6], little_tour())
animate_pcp(flea[, 1:6], little_tour(3))
animate_scatmat(flea[, 1:6], little_tour(3))
animate_pcp(flea[, 1:6], little_tour(4))

Description

The local tour alternates between the starting position and a nearby random projection.

Usage

local_tour(start, angle = pi/4)

Arguments

Details

Usually, you will not call this function directly, but will pass it to a method that works with tour paths like animate, save_history or render.

Examples

animate_xy(flea[, 1:3], local_tour(basis_init(3, 2)))
animate_xy(flea[, 1:3], local_tour(basis_init(3, 2), 0.2))
animate_xy(flea[, 1:3], local_tour(basis_random(3, 2), 0.2))

Description

Computes the Mahalanobis distance using a provided variance-covariance matrix of observations from 0.

Usage

mahal_dist(x, vc)

Arguments

Description

The manual slice tour takes the current projection, with display_slice, and changes the slice center.

Usage

manual_slice(
  data,
  proj,
  var = 1,
  nsteps = 20,
  v_rel = 0.01,
  rescale = FALSE,
  sphere = FALSE,
  col = "black",
  half_range = NULL,
  anchor_nav = "topright",
  palette = "Zissou 1",
  ...
)

Arguments

Examples

# Note that you might need to use the quartz()
# on OSX to see the animation
sphere5 <- data.frame(geozoo::sphere.hollow(5)$points)
proj <- basis_random(5, 2)
manual_slice(sphere5, proj, var=3, nsteps=10, rescale=TRUE, half_range=1.5)

Description

Map vector of factors to color

Usage

mapColors(x, palette)

Arguments

Description

Map vector of factors to pch

Usage

mapShapes(x, shapeset)

Arguments

Description

Compute the maximum and total information coefficient indexes, see minerva::mine.

Usage

MIC()

TIC()

Description

Compares the similarity between the projected distribution and a normal distribution.

• norm_bin: compares the count in 100 histogram bins

• norm_kol: compares the cdf based on the Kolmogorov–Smirnov test (KS test)

Usage

norm_bin(nr)

norm_kol(nr)

Arguments

Examples

# manually compute the norm_kol index
# create the index function
set.seed(123)
index <- norm_kol(nrow(flea[, 1:3]))
# create the projection
proj <- matrix(c(1, 0, 0), nrow = 3)
# pre-process the example data
flea_s <- sphere_data(flea[, 1:3])
# produce the index value
index(flea_s %*% proj)

Description

This data is from a paper by Forina, Armanino, Lanteri, Tiscornia (1983) Classification of Olive Oils from their Fatty Acid Composition, in Martens and Russwurm (ed) Food Research and Data Anlysis. We thank Prof. Michele Forina, University of Genova, Italy for making this dataset available.

Format

A 572 x 10 numeric array

Details

• region Three super-classes of Italy: North, South and the island of Sardinia

• area Nine collection areas: three from North, four from South and 2 from Sardinia

• palmitic, palmitoleic, stearic, oleic, linoleic, linolenic, arachidic, eicosenoic fatty acids percent x 100

Examples

head(olive)
animate_xy(olive[, c(7, 9, 10)])
animate_xy(olive[, c(7, 9, 10)], col = olive[, 1])

Description

This data set is a subset of the data from the 2006 ASA Data expo challenge. The data are monthly ozone averages on a very coarse 24 by 24 grid covering Central America, from Jan 1995 to Dec 2000. The data is stored in a 3d area with the first two dimensions representing latitude and longitude, and the third representing time.

Format

A 24 x 24 x 72 numeric array

Examples

example(display_image)

Description

This computes the projected values of each observation at each step, and allows you to recreate static views of the animated plots.

Usage

path_curves(history, data = attr(history, "data"))

Arguments

Examples

path1d <- save_history(flea[, 1:6], grand_tour(1), 3)
path2d <- save_history(flea[, 1:6], grand_tour(2), 3)

if (require("ggplot2")) {
  plot(path_curves(path1d))
  plot(path_curves(interpolate(path1d)))

  plot(path_curves(path2d))
  plot(path_curves(interpolate(path2d)))

  # Instead of relying on the built in plot method, you might want to
  # generate your own.  Here are few examples of alternative displays:

  df <- path_curves(path2d)
  ggplot(data = df, aes(x = step, y = value, group = obs:var, colour = var)) +
    geom_line() +
    facet_wrap(~obs)

  library(tidyr)
  ggplot(
    data = pivot_wider(df,
      id_cols = c(obs, step),
      names_from = var, names_prefix = "Var",
      values_from = value
    ),
    aes(x = Var1, y = Var2)
  ) +
    geom_point() +
    facet_wrap(~step) +
    coord_equal()
}

Description

Compute distance matrix from bases.

Usage

path_dist(history)

Arguments

Examples

# This code is to be used as an example but you should increase
# the max from 2 to 50, say, to check tour coverage.
flea_std <- apply(flea[,1:6], 2, function(x) (x-mean(x))/sd(x))
grand <- interpolate(save_history(flea_std, max = 2), 0.2)
# The grand tour  -----------------------------
# Look at the tour path in a tour, how well does it cover a sphere
# Using MDS to summarise the high-d space of projections
# Last basis is a duplicate, needs removing
d <- path_dist(grand[,,-dim(grand)[[3]]])
ord <- as.data.frame(MASS::isoMDS(d)$points)
require(ggplot2)
ggplot(data = ord, aes(x=V1, y=V2)) +
  geom_path() +
  coord_equal() +
  labs(x = NULL, y = NULL)

# Compare five guided tours  -----------------------------
holes1d <- guided_tour(holes(), 1)
tour_reps <- replicate(5, save_history(flea_std, holes1d, max = 2),
  simplify = FALSE
)
tour_reps2 <- lapply(tour_reps, interpolate, 0.2)

bases <- unlist(lapply(tour_reps2, as.list), recursive = FALSE)
class(bases) <- "history_list"
index_values <- paths_index(tour_reps2, holes())
index_values$step <- index_values$step.1
d <- path_dist(bases)
ord <- as.data.frame(cmdscale(d, 2))

info <- cbind(ord, index_values)
ggplot(data = info, aes(x = step, y = value, group = try)) +
  geom_line()
##ggplot(data = info, aes(x = V1, y = V2, group = try)) +
##  geom_path() +
##  geom_point(aes(size = value)) +
##  coord_equal()
##last_plot() + facet_wrap(~try)

Description

Compute index values for a tour history.

Usage

path_index(history, index_f, data = attr(history, "data"))

Arguments

See Also

save_history for options to save history

Examples

fl_holes <- save_history(flea[, 1:6], guided_tour(holes()), sphere = TRUE)
path_index(fl_holes, holes())
## path_index(fl_holes, cmass())

plot(path_index(fl_holes, holes()), type = "l")
## plot(path_index(fl_holes, cmass()), type = "l")


# Use interpolate to show all intermediate bases as well
hi <- path_index(interpolate(fl_holes), holes())
hi
plot(hi)

Description

Calculate the PDA projection pursuit index. See Lee and Cook (2009) A Projection Pursuit Index for Large p, Small n Data

Usage

pda_pp(cl, lambda = 0.2)

Arguments

Description

The "places data" were distributed to interested ASA members a few years ago so that they could apply contemporary data analytic methods to describe these data and then present results in a poster session at the ASA annual conference. Latitude and longitude have been added by Paul Tukey.

Format

A 329 x 14 numeric array

Details

____________________________________________________________________

The first dataset is taken from the Places Rated Almanac, by Richard Boyer and David Savageau, copyrighted and published by Rand McNally. This book order (SBN) number is 0-528-88008-X, and it retails for $14.95 . The data are reproduced on disk by kind permission of the publisher, and with the request that the copyright notice of Rand McNally, and the names of the authors appear in any paper or presentation using these data.

The nine rating criteria used by Places Rated Almanac are: Climate and Terrain Housing Health Care and Environment Crime Transportation Education The Arts Recreation Economics

For all but two of the above criteria, the higher the score, the better. For Housing and Crime, the lower the score the better.

The scores are computed using the following component statistics for each criterion (see the Places Rated Almanac for details):

Climate and Terrain: very hot and very cold months, seasonal temperature variation, heating- and cooling-degree days, freezing days, zero-degree days, ninety-degree days.

Housing: utility bills, property taxes, mortgage payments.

Health Care and Environment: per capita physicians, teaching hospitals, medical schools, cardiac rehabilitation centers, comprehensive cancer treatment centers, hospices, insurance/hospitalization costs index, flouridation of drinking water, air pollution.

Crime: violent crime rate, property crime rate.

Transportation: daily commute, public transportation, Interstate highways, air service, passenger rail service.

Education: pupil/teacher ratio in the public K-12 system, effort index in K-12, accademic options in higher education.

The Arts: museums, fine arts and public radio stations, public television stations, universities offering a degree or degrees in the arts, symphony orchestras, theatres, opera companies, dance companies, public libraries.

Recreation: good restaurants, public golf courses, certified lanes for tenpin bowling, movie theatres, zoos, aquariums, family theme parks, sanctioned automobile race tracks, pari-mutuel betting attractions, major- and minor- league professional sports teams, NCAA Division I football and basketball teams, miles of ocean or Great Lakes coastline, inland water, national forests, national parks, or national wildlife refuges, Consolidated Metropolitan Statistical Area access.

Economics: average household income adjusted for taxes and living costs, income growth, job growth.

Examples

head(places)
animate_xy(places[, 1:9])

Description

The planned tour takes you from one basis to the next in a set order. Once you have visited all the planned bases, you either stop or start from the beginning once more (if cycle = TRUE).

Usage

planned_tour(basis_set, cycle = FALSE)

planned2_tour(basis_set)

Arguments

Details

Usually, you will not call this function directly, but will pass it to a method that works with tour paths like animate, save_history or render.

See Also

The little_tour, a special type of planned tour which cycles between all axis parallel projections.

Examples

twod <- save_history(flea[, 1:3], max = 5)
str(twod)
animate_xy(flea[, 1:3], planned_tour(twod))
animate_xy(flea[, 1:3], planned_tour(twod, TRUE))

oned <- save_history(flea[, 1:6], grand_tour(1), max = 3)
animate_dist(flea[, 1:6], planned_tour(oned))

Description

Computes the Frobenius norm between two bases, in radians. This is equals to the Euclidean norm of the vector of principal angles between the two subspaces.

Usage

proj_dist(x, y)

Arguments

Description

The radial tour rotates a chosen variable axis out of the current projection.

Usage

radial_tour(start, mvar = 1, ...)

Arguments

Details

Usually, you will not call this function directly, but will pass it to a method that works with tour paths like animate, save_history or render.

Examples

animate_xy(flea[, 1:6], radial_tour(basis_random(6, 2), mvar = 4), rescale=TRUE)
animate_xy(flea[, 1:6], radial_tour(basis_random(6, 2), mvar = c(3,4)), rescale=TRUE)
animate_dist(flea[, 1:6], radial_tour(basis_random(6, 1), mvar = 4), rescale=TRUE)
animate_scatmat(flea[, 1:6], radial_tour(basis_random(6, 3), mvar = 4), rescale=TRUE)

Description

Columns:

Format

A 112 x 11 numeric array

Details

e11 e13 e15 e18 e21 p0 p7 p14 a class1 class2

• e11, an ebryonic timepoint from the original data with the number corresponding to the day

• e13, an ebryonic timepoint from the original data with the number corresponding to the day

• e15, an ebryonic timepoint from the original data with the number corresponding to the day

• e18, an ebryonic timepoint from the original data with the number corresponding to the day

• e21, an ebryonic timepoint from the original data with the number corresponding to the day

• p0, a postnatal timpoint from the original data with the number corresponding to the day

• p7, a postnatal timpoint from the original data with the number corresponding to the day

• p14, a postnatal timpoint from the original data with the number corresponding to the day

• a, a postnatal timpoint from the original data. It is equivalent to p90.

• class1, is the high-level class: its range is 1:4

• class2, breaks down the high-level classes, so its range is 1:14

Rows: Each case is a gene (or gene family?) And each cell is the gene expression level for that gene at time t, averaging a few measured values and normalizing using the maximum expression value for that gene.

Reference (available on the web at pnas.org): Large-scale temporal gene expression mapping of central nervous system development by X. Wen, S. Fuhrman, G. S. Michaels, D. B. Carr, S. Smith, J. L. Barker, R. Somogyi in the Proceedings of the National Academy of Science, Vol 95, pp. 334-339, January 1998

References

https://www.pnas.org

Examples

head(ratcns)
animate_xy(ratcns[, 1:8], col = ratcns[, 10])

Description

Render frames of animation to disk

Usage

render(
  data,
  tour_path,
  display,
  dev,
  ...,
  apf = 1/10,
  frames = 50,
  rescale = FALSE,
  sphere = FALSE,
  start = NULL
)

Arguments

Examples

tmp_path <- tempdir()
render(flea[, 1:6], grand_tour(), display_xy(), "pdf",
  frames = 3,
  file.path(tmp_path, "test.pdf")
)
render(flea[, 1:6], grand_tour(), display_xy(), "png",
  frames = 3,
  file.path(tmp_path, "test-%03d.png")
)

Description

This function takes a set of frames as produced by save_history(), and creates the projected data and axes in for format needed to create the animation using plotly. It will be useful for showing a tour where mouseover can be used to identify points. Note that for now this only works for 2D projections.

Usage

render_anim(
  data,
  vars = NULL,
  frames,
  edges = NULL,
  axis_labels = NULL,
  obs_labels = NULL,
  limits = 1,
  position = "center"
)

Arguments

Value

list containing indexed projected data, edges, circle and segments for axes

Examples

data(flea)
flea_std <- apply(flea[,1:6], 2, function(x) (x-mean(x))/sd(x))
t1 <- save_history(flea_std, max=2)
t1i <- tourr::interpolate(t1, 0.1)
p <- render_anim(data=flea_std, frames=t1i)
if (require(ggplot2)) {
  pg <- ggplot() +
    geom_path(data=p$circle, aes(x=c1, y=c2, frame=frame)) +
    geom_segment(data=p$axes, aes(x=x1, y=y1, xend=x2, yend=y2, frame=frame)) +
    geom_text(data=p$axes, aes(x=x2, y=y2, frame=frame, label=axis_labels)) +
    geom_point(data=p$frames, aes(x=P1, y=P2, frame=frame, label=obs_labels)) +
    coord_equal() +
    theme_bw() +
    theme(axis.text=element_blank(),
        axis.title=element_blank(),
        axis.ticks=element_blank(),
        panel.grid=element_blank())
  if (interactive()) {
    require(plotly)
    ggplotly(pg, width=500, height=500) |>
      animation_button(label="Go") |>
      animation_slider(len=0.8, x=0.5, xanchor="center") |>
      animation_opts(easing="linear", transition=0, redraw=FALSE)
  }
}

Description

Render frames of animation to a gif file

Usage

render_gif(
  data,
  tour_path,
  display,
  gif_file = "animation.gif",
  ...,
  apf = 1/10,
  frames = 50,
  rescale = FALSE,
  sphere = FALSE,
  start = NULL,
  loop = TRUE
)

Arguments

Examples

## Not run: 
# gifski needs to be installed to render a gif
if (requireNamespace("gifski", quietly = TRUE)) {
  gif_file <- file.path(tempdir(), "test.gif")
  render_gif(flea[, 1:6], grand_tour(), display_xy(), gif_file)
  utils::browseURL(gif_file)
  unlink(gif_file)
}

## End(Not run)

Description

This function takes a projection matrix as produced by save_history(), and draws it on the projected data like a biplot. This will product the data objects needed in order for the user to plot with base or ggplot2. Note that for now this only works for 2D projections.

Usage

render_proj(
  data,
  prj,
  axis_labels = NULL,
  obs_labels = NULL,
  limits = 1,
  position = "center"
)

Arguments

Value

list containing projected data, circle and segments for axes

Examples

data(flea)
flea_std <- apply(flea[,1:6], 2, function(x) (x-mean(x))/sd(x))
prj <- basis_random(ncol(flea[,1:6]), 2)
p <- render_proj(flea_std, prj)
if (require("ggplot2")) {
  ggplot() +
    geom_path(data=p$circle, aes(x=c1, y=c2)) +
    geom_segment(data=p$axes, aes(x=x1, y=y1, xend=x2, yend=y2)) +
    geom_text(data=p$axes, aes(x=x2, y=y2, label=rownames(p$axes))) +
    geom_point(data=p$data_prj, aes(x=P1, y=P2)) +
    xlim(-1,1) + ylim(-1, 1) +
    theme_bw() +
    theme(aspect.ratio=1,
       axis.text=element_blank(),
       axis.title=element_blank(),
       axis.ticks=element_blank(),
       panel.grid=element_blank())
}

Description

Standardise each column to have range [0, 1]

Usage

rescale(df)

Arguments

Description

Save a tour path so it can later be displayed in many different ways.

Usage

save_history(
  data,
  tour_path = grand_tour(),
  max_bases = 100,
  start = NULL,
  rescale = FALSE,
  sphere = FALSE,
  step_size = Inf,
  ...
)

Arguments

Examples

# You can use a saved history to replay tours with different visualisations

t1 <- save_history(flea[, 1:6], max = 3)
animate_xy(flea[, 1:6], planned_tour(t1))
## andrews_history(t1)
## andrews_history(interpolate(t1))

## t1 <- save_history(flea[, 1:6], grand_tour(4), max = 3)
## animate_pcp(flea[, 1:6], planned_tour(t1))
## animate_scatmat(flea[, 1:6], planned_tour(t1))

## t1 <- save_history(flea[, 1:6], grand_tour(1), max = 3)
## animate_dist(flea[, 1:6], planned_tour(t1))

testdata <- matrix(rnorm(100 * 3), ncol = 3)
testdata[1:50, 1] <- testdata[1:50, 1] + 10
testdata <- sphere_data(testdata)
t2 <- save_history(testdata, guided_tour(holes(), max.tries = 10),
  max = 5
)
animate_xy(testdata, planned_tour(t2))

# Or you can use saved histories to visualise the path that the tour took.
plot(path_index(interpolate(t2), holes()))

Description

Search for a better projection near the current projection.

Usage

search_better(
  current,
  alpha = 0.5,
  index,
  tries,
  max.tries = Inf,
  ...,
  method = "linear",
  cur_index = NA
)

Arguments

Examples

animate_xy(flea[, 1:6], guided_tour(holes(), search_f = search_better))

Description

Given an initial $t0$, the cooling scheme updates temperature at

$T = t0 /\log(i + 1)$

The candidate basis is sampled via

$B_j = (1 - \alpha) * B_i + \alpha * B$

where alpha defines the neighbourhood, $B_i$ is the current basis, B is a randomly generated basis The acceptance probability is calculated as

$prob = \exp{-abs(I(B_i) - I(B_j))/ T}$

For more information, see https://projecteuclid.org/download/pdf_1/euclid.ss/1177011077

Usage

search_better_random(
  current,
  alpha = 0.5,
  index,
  tries,
  max.tries = Inf,
  method = "linear",
  cur_index = NA,
  t0 = 0.01,
  ...
)

Arguments

Examples

animate_xy(flea[, 1:6], guided_tour(holes(), search_f = search_better_random))

Description

This is a novel method for finding more interesting projections for the guided tour. It works by first taking a small step in n random directions, and then picking the direction that looks most promising (based on the height of the index function), which is effectively a gradient search. Then it performs a linear search along the geodesic in that direction, traveling up to half way around the sphere.

Usage

search_geodesic(
  current,
  alpha = 1,
  index,
  tries,
  max.tries = 5,
  ...,
  n = 5,
  delta = 0.01,
  cur_index = NA
)

Arguments