Parallel Coordinates

Parallel Coordinates Plot (PCP) is a plot type used to visualize EEG activity for some channels. It can fully represent condition and channel dimensions using lines. It can also partially represent time and trials.

Each vertical axis represents a voltage level for a channel. Each line represents a trial, each colour represents a condition.

Setup

Package loading

using Unfold
using UnfoldMakie
using DataFrames
using CairoMakie

Data generation

include("../../../example_data.jl")
r1, positions = example_data();
r2 = deepcopy(r1)
r2.coefname .= "B" # create a second category
r2.estimate .+= rand(length(r2.estimate)) * 0.1
results_plot = vcat(r1, r2);

Plot PCPs

plot_parallelcoordinates(
    subset(results_plot, :channel => x -> x .<= 5);
    mapping = (; color = :coefname),
    ax_labels = ["FP1", "F3", "F7", "FC3", "C3"],
)

Additional features

Normalization

On the first image, there is no normalization and the extremes of all axes are the same and equal to the max and min values across all chanells. On the second image, there is a minmax normalization, so each axis has its own extremes based on the min and max of the data.

Typically, parallel plots are normalized per axis. Whether this makes sense for estimating channel x, we do not know.

f = Figure()
plot_parallelcoordinates(
    f[1, 1],
    subset(results_plot, :channel => x -> x .< 10);
    mapping = (; color = :coefname),
    axis = (; title = "normalize = nothing"),
)
plot_parallelcoordinates(
    f[2, 1],
    subset(results_plot, :channel => x -> x .< 10);
    mapping = (; color = :coefname),
    normalize = :minmax,
    axis = (; title = "normalize = :minmax"),
)
f

Color schemes

Use only categorical with high contrast between adjacent colors. More: change colormap.

f = Figure()
plot_parallelcoordinates(
    f[1, 1],
    subset(results_plot, :channel => x -> x .<= 5);
    mapping = (; color = :coefname),
    visual = (; colormap = :tab10),
    axis = (; title = "colormap = tab10"),
)
plot_parallelcoordinates(
    f[2, 1],
    subset(results_plot, :channel => x -> x .<= 5);
    mapping = (; color = :coefname),
    visual = (; colormap = :Accent_3),
    axis = (; title = "colormap = Accent_3"),
)
f

Labels

Use ax_labels to specify labels for the axes.

plot_parallelcoordinates(
    subset(results_plot, :channel => x -> x .< 5);
    visual = (; color = :darkblue),
    ax_labels = ["Fz", "Cz", "O1", "O2"],
)

Tick labels

Specify tick labels on axis. There are four different options for the tick labels.

f = Figure(size = (400, 800))
plot_parallelcoordinates(
    f[1, 1],
    subset(results_plot, :channel => x -> x .< 5, :time => x -> x .< 0);
    ax_labels = ["Fz", "Cz", "O1", "O2"],
    ax_ticklabels = :all,
    normalize = :minmax,
    axis = (; title = "ax_ticklabels = :all"),
) # show all ticks on all axes
plot_parallelcoordinates(
    f[2, 1],
    subset(results_plot, :channel => x -> x .< 5, :time => x -> x .< 0);
    ax_labels = ["Fz", "Cz", "O1", "O2"],
    ax_ticklabels = :left,
    normalize = :minmax,
    axis = (; title = "ax_ticklabels = :left"),
) # show all ticks on the left axis, but only extremities on others
plot_parallelcoordinates(
    f[3, 1],
    subset(results_plot, :channel => x -> x .< 5, :time => x -> x .< 0);
    ax_labels = ["Fz", "Cz", "O1", "O2"],
    ax_ticklabels = :outmost,
    normalize = :minmax,
    axis = (; title = "ax_ticklabels = :outmost"),
) # show ticks on extremities of all axes

plot_parallelcoordinates(
    f[4, 1],
    subset(results_plot, :channel => x -> x .< 5, :time => x -> x .< 0);
    ax_labels = ["Fz", "Cz", "O1", "O2"],
    ax_ticklabels = :none,
    normalize = :minmax,
    axis = (; title = "ax_ticklabels = :none"),
) #  disable all ticks
f

Bending the parallel plot

Bending the linescan be helpful to make them more visible.

f = Figure()
plot_parallelcoordinates(
    f[1, 1],
    subset(results_plot, :channel => x -> x .< 10),
    axis = (; title = "bend = false"),
)
plot_parallelcoordinates(
    f[2, 1],
    subset(results_plot, :channel => x -> x .< 10),
    bend = true,
    axis = (; title = "bend = true"),
)
f

Transparancy

uf_5chan = example_data("UnfoldLinearModelMultiChannel")

f = Figure()
plot_parallelcoordinates(
    f[1, 1],
    uf_5chan;
    mapping = (; color = :coefname),
    visual = (; alpha = 0.1),
    axis = (; title = "alpha = 0.1"),
)
plot_parallelcoordinates(
    f[2, 1],
    uf_5chan,
    mapping = (; color = :coefname),
    visual = (; alpha = 0.9),
    axis = (; title = "alpha = 0.9"),
)
f

Configurations of Parallel coordinates plot

plot_parallelcoordinates(data::Union{DataFrame, AbstractMatrix}; kwargs...)
plot_parallelcoordinates!(f::Union{GridPosition, GridLayout, Figure}, data::Union{DataFrame, AbstractMatrix}; kwargs)

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