switch SVM example to half-moon dataset (#421)

Author: st--

Diff for: examples/support-vector-machine/script.jl

@@ -1,5 +1,8 @@
 # # Support Vector Machine
 #
+# In this notebook we show how you can use KernelFunctions.jl to generate
+# kernel matrices for classification with a support vector machine, as
+# implemented by LIBSVM.
 
 using Distributions
 using KernelFunctions
@@ -8,39 +11,45 @@ using LinearAlgebra
 using Plots
 using Random
 
-## Set plotting theme
-theme(:wong)
-
 ## Set seed
 Random.seed!(1234);
 
-# Number of samples:
-N = 100;
+# ## Generate half-moon dataset
+
+# Number of samples per class:
+nin = nout = 50;
 
-# Select randomly between two classes:
-y_train = rand([-1, 1], N);
+# We generate data based on SciKit-Learn's sklearn.datasets.make_moons function:
 
-# Random attributes for both classes:
-X = Matrix{Float64}(undef, 2, N)
-rand!(MvNormal(randn(2), I), view(X, :, y_train .== 1))
-rand!(MvNormal(randn(2), I), view(X, :, y_train .== -1));
-x_train = ColVecs(X);
+class1x = cos.(range(0, π; length=nout))
+class1y = sin.(range(0, π; length=nout))
+class2x = 1 .- cos.(range(0, π; length=nin))
+class2y = 1 .- sin.(range(0, π; length=nin)) .- 0.5
+X = hcat(vcat(class1x, class2x), vcat(class1y, class2y))
+X .+= 0.1randn(size(X))
+x_train = RowVecs(X)
+y_train = vcat(fill(-1, nout), fill(1, nin));
 
-# Create a 2D grid:
+# Create a 100×100 2D grid for evaluation:
 test_range = range(floor(Int, minimum(X)), ceil(Int, maximum(X)); length=100)
 x_test = ColVecs(mapreduce(collect, hcat, Iterators.product(test_range, test_range)));
 
+# ## SVM model
+#
 # Create kernel function:
-k = SqExponentialKernel() ∘ ScaleTransform(2.0)
+k = SqExponentialKernel() ∘ ScaleTransform(1.5)
 
 # [LIBSVM](https://github.com/JuliaML/LIBSVM.jl) can make use of a pre-computed kernel matrix.
 # KernelFunctions.jl can be used to produce that.
-# Precomputed matrix for training (corresponds to linear kernel)
+#
+# Precomputed matrix for training
 model = svmtrain(kernelmatrix(k, x_train), y_train; kernel=LIBSVM.Kernel.Precomputed)
 
 # Precomputed matrix for prediction
-y_pr, _ = svmpredict(model, kernelmatrix(k, x_train, x_test));
+y_pred, _ = svmpredict(model, kernelmatrix(k, x_train, x_test));
 
-# Compute prediction on a grid:
-contourf(test_range, test_range, y_pr)
-scatter!(X[1, :], X[2, :]; color=y_train, lab="data", widen=false)
+# Visualize prediction on a grid:
+plot(; lim=extrema(test_range), aspect_ratio=1)
+contourf!(test_range, test_range, y_pred; levels=1, color=cgrad(:redsblues), alpha=0.7)
+scatter!(X[y_train .== -1, 1], X[y_train .== -1, 2]; color=:red, label="class 1")
+scatter!(X[y_train .== +1, 1], X[y_train .== +1, 2]; color=:blue, label="class 2")