Data Transformations

Histogram

AlgebraOfGraphics.histogram — Function
histogram(; bins=automatic, weights=automatic, normalization=:none)

Compute a histogram. bins can be an Int to create that number of equal-width bins over the range of values. Alternatively, it can be a sorted iterable of bin edges. The histogram can be normalized by setting normalization. Possible values are:

  • :pdf: Normalize by sum of weights and bin sizes. Resulting histogram has norm 1 and represents a PDF.
  • :density: Normalize by bin sizes only. Resulting histogram represents count density of input and does not have norm 1.
  • :probability: Normalize by sum of weights only. Resulting histogram represents the fraction of probability mass for each bin and does not have norm 1.
  • :none: Do not normalize.

Weighted data is supported via the keyword weights.

Note

Normalizations are computed withing groups. For example, in the case of normalization=:pdf, sum of weights within each group will be equal to 1.

using AlgebraOfGraphics, CairoMakie
set_aog_theme!()

df = (x=randn(1000), y=randn(1000), z=rand(["a", "b", "c"], 1000))
specs = data(df) * mapping(:x, layout=:z) * histogram(bins=range(-2, 2, length=15))
draw(specs)
specs = data(df) * mapping(:x, dodge=:z, color=:z) * histogram(bins=range(-2, 2, length=15))
draw(specs)
specs = data(df) * mapping(:x, stack=:z, color=:z) * histogram(bins=range(-2, 2, length=15))
draw(specs)
data(df) * mapping(:x, :y, layout=:z) * histogram(bins=15) |> draw

Density

AlgebraOfGraphics.density — Function
density(; datalimits, npoints, kernel, bandwidth)

Fit a kernel density estimation of data. Here, datalimits specifies the range for which the density should be calculated, npoints is the number of points used by Makie to draw the line and kernel and bandwidth are forwarded to KernelDensity.kde.

df = (x=randn(5000), y=randn(5000), z=rand(["a", "b", "c", "d"], 5000))
datalimits = ((-2.5, 2.5),)
xz = data(df) * mapping(:x, layout=:z) * AlgebraOfGraphics.density(; datalimits)
axis = (; ylabel="")
draw(xz; axis)
data(df) * mapping(:x, :y, layout=:z) * AlgebraOfGraphics.density(npoints=50) |> draw
specs = data(df) * mapping(:x, :y, layout=:z) *
    AlgebraOfGraphics.density(npoints=50) * visual(Surface)

draw(specs, axis=(type=Axis3, zticks=0:0.1:0.2, limits=(nothing, nothing, (0, 0.2))))

Frequency

df = (x=rand(["a", "b", "c"], 100), y=rand(["a", "b", "c"], 100), z=rand(["a", "b", "c"], 100))
specs = data(df) * mapping(:x, layout=:z) * frequency()
draw(specs)
specs = data(df) * mapping(:x, layout=:z, color=:y, stack=:y) * frequency()
draw(specs)
specs = data(df) * mapping(:x, :y, layout=:z) * frequency()
draw(specs)

Expectation

df = (x=rand(["a", "b", "c"], 100), y=rand(["a", "b", "c"], 100), z=rand(100), c=rand(["a", "b", "c"], 100))
specs = data(df) * mapping(:x, :z, layout=:c) * expectation()
draw(specs)
specs = data(df) * mapping(:x, :z, layout=:c, color=:y, dodge=:y) * expectation()
draw(specs)
specs = data(df) * mapping(:x, :y, :z, layout=:c) * expectation()
draw(specs)

Linear

AlgebraOfGraphics.linear — Function
linear(; interval)

Compute a linear fit of y ~ 1 + x. An optional named mapping weights determines the weights. Use interval to specify what type of interval the shaded band should represent. Valid values of interval are :confidence delimiting the uncertainty of the predicted relationship, and :prediction delimiting estimated bounds for new data points.

x = 1:0.05:10
a = rand(1:7, length(x))
y = 1.2 .* x .+ a .+ 0.5 .* randn.()
df = (; x, y, a)
specs = data(df) * mapping(:x, :y, color=:a => nonnumeric) * (linear() + visual(Scatter))
draw(specs)

Smoothing

AlgebraOfGraphics.smooth — Function
smooth(span=0.75, degree=2)

Fit a loess model. span is the degree of smoothing, typically in [0,1]. Smaller values result in smaller local context in fitting. degree is the polynomial degree used in the loess model.

x = 1:0.05:10
a = rand(1:7, length(x))
y = sin.(x) .+ a .+ 0.1 .* randn.()
df = (; x, y, a)
specs = data(df) * mapping(:x, :y, color=:a => nonnumeric) * (smooth() + visual(Scatter))
draw(specs)

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