Generating Synthetic Data

MLJ has a set of functions - make_blobs, make_circles, make_moons and make_regression (closely resembling functions in scikit-learn of the same name) - for generating synthetic data sets. These are useful for testing machine learning models (e.g., testing user-defined composite models; see Composing Models)

Generating Gaussian blobs

MLJBase.make_blobs — Function

X, y = make_blobs(n=100, p=2; kwargs...)

Generate Gaussian blobs for clustering and classification problems.

Return value

By default, a table X with p columns (features) and n rows (observations), together with a corresponding vector of n Multiclass target observations y, indicating blob membership.

Keyword arguments

shuffle=true: whether to shuffle the resulting points,
centers=3: either a number of centers or a c x p matrix with c pre-determined centers,
cluster_std=1.0: the standard deviation(s) of each blob,
center_box=(-10. => 10.): the limits of the p-dimensional cube within which the cluster centers are drawn if they are not provided,
eltype=Float64: machine type of points (any subtype of AbstractFloat).
rng=nothing: any AbstractRNG object, or integer to seed a MersenneTwister (for reproducibility).
as_table=true: whether to return the points as a table (true) or a matrix (false). If false the target y has integer element type.

Example

X, y = make_blobs(100, 3; centers=2, cluster_std=[1.0, 3.0])

using MLJ, DataFrames
X, y = make_blobs(100, 3; centers=2, cluster_std=[1.0, 3.0])
dfBlobs = DataFrame(X)
dfBlobs.y = y
first(dfBlobs, 3)

3 rows × 4 columns

	x1	x2	x3	y
	Float64	Float64	Float64	Cat…
1	5.23505	-2.42104	8.55979	1
2	5.47173	-4.14289	8.06756	1
3	3.67883	4.64465	-2.97643	2

using VegaLite
dfBlobs |> @vlplot(:point, x=:x1, y=:x2, color = :"y:n")

svg

dfBlobs |> @vlplot(:point, x=:x1, y=:x3, color = :"y:n")

svg

Generating concentric circles

MLJBase.make_circles — Function

X, y = make_circles(n=100; kwargs...)

Generate n labeled points close to two concentric circles for classification and clustering models.

Return value

By default, a table X with 2 columns and n rows (observations), together with a corresponding vector of n Multiclass target observations y. The target is either 0 or 1, corresponding to membership to the smaller or larger circle, respectively.

Keyword arguments

shuffle=true: whether to shuffle the resulting points,
noise=0: standard deviation of the Gaussian noise added to the data,
factor=0.8: ratio of the smaller radius over the larger one,

eltype=Float64: machine type of points (any subtype of AbstractFloat).
rng=nothing: any AbstractRNG object, or integer to seed a MersenneTwister (for reproducibility).
as_table=true: whether to return the points as a table (true) or a matrix (false). If false the target y has integer element type.

Example

X, y = make_circles(100; noise=0.5, factor=0.3)

using MLJ, DataFrames
X, y = make_circles(100; noise=0.05, factor=0.3)
dfCircles = DataFrame(X)
dfCircles.y = y
first(dfCircles, 3)

3 rows × 3 columns

	x1	x2	y
	Float64	Float64	Cat…
1	-0.82483	0.582929	1
2	0.332802	0.0725552	0
3	-0.00207019	-0.952648	1

using VegaLite
dfCircles |> @vlplot(:circle, x=:x1, y=:x2, color = :"y:n")

svg

Sampling from two interleaved half-circles

MLJBase.make_moons — Function

    make_moons(n::Int=100; kwargs...)

Generates labeled two-dimensional points lying close to two interleaved semi-circles, for use with classification and clustering models.

Return value

Keyword arguments

shuffle=true: whether to shuffle the resulting points,
noise=0.1: standard deviation of the Gaussian noise added to the data,
xshift=1.0: horizontal translation of the second center with respect to the first one.
yshift=0.3: vertical translation of the second center with respect to the first one.
eltype=Float64: machine type of points (any subtype of AbstractFloat).
rng=nothing: any AbstractRNG object, or integer to seed a MersenneTwister (for reproducibility).
as_table=true: whether to return the points as a table (true) or a matrix (false). If false the target y has integer element type.

Example

X, y = make_moons(100; noise=0.5)

using MLJ, DataFrames
X, y = make_moons(100; noise=0.05)
dfHalfCircles = DataFrame(X)
dfHalfCircles.y = y
first(dfHalfCircles, 3)

3 rows × 3 columns

	x1	x2	y
	Float64	Float64	Cat…
1	-0.508034	0.838574	0
2	1.13543	-0.690555	1
3	0.801578	0.585921	0

using VegaLite
dfHalfCircles |> @vlplot(:circle, x=:x1, y=:x2, color = :"y:n")

svg

Regression data generated from noisy linear models

MLJBase.make_regression — Function

make_regression(n, p; kwargs...)

Generate Gaussian input features and a linear response with Gaussian noise, for use with regression models.

Return value

By default, a table X with p columns and n rows (observations), together with a corresponding vector of n Continuous target observations y.

Keywords

`intercept=true: whether to generate data from a model with intercept,
sparse=0: portion of the generating weight vector that is sparse,
noise=0.1: standard deviation of the Gaussian noise added to the response,
outliers=0: portion of the response vector to make as outliers by adding a random quantity with high variance. (Only applied if binary is false)
binary=false: whether the target should be binarized (via a sigmoid).
eltype=Float64: machine type of points (any subtype of AbstractFloat).
rng=nothing: any AbstractRNG object, or integer to seed a MersenneTwister (for reproducibility).
as_table=true: whether to return the points as a table (true) or a matrix (false).

Example

X, y = make_regression(100, 5; noise=0.5, sparse=0.2, outliers=0.1)

using MLJ, DataFrames
X, y = make_regression(100, 5; noise=0.5, sparse=0.2, outliers=0.1)
dfRegression = DataFrame(X)
dfRegression.y = y
first(dfRegression, 3)

3 rows × 6 columns

	x1	x2	x3	x4	x5	y
	Float64	Float64	Float64	Float64	Float64	Float64
1	-1.74901	-2.31892	-1.36151	-1.35412	2.82726	0.0903681
2	-0.253894	-0.824376	1.02774	-1.4742	-0.542286	-0.125437
3	-2.11399	0.905413	0.980601	-0.513972	-0.672957	-0.314759