improve writing

Author: st--

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
@@ -16,21 +19,23 @@ Random.seed!(1234);
 # Number of samples per class:
 nin = nout = 50;
 
-# Generate data
-## based on SciKit-Learn's sklearn.datasets.make_moons function
+# We generate data based on SciKit-Learn's sklearn.datasets.make_moons function:
+
 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);
+x_train = RowVecs(X)
 y_train = vcat(fill(-1, nout), fill(1, nin));
 
 # 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(1.5)
 
@@ -43,12 +48,8 @@ model = svmtrain(kernelmatrix(k, x_train), y_train; kernel=LIBSVM.Kernel.Precomp
 # Precomputed matrix for prediction
 y_pred, _ = svmpredict(model, kernelmatrix(k, x_train, x_test));
 
-# Compute prediction on a grid:
-plot(; lim=extrema(test_range))
+# 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", widen=false
-)
-scatter!(
-    X[y_train .== +1, 1], X[y_train .== +1, 2]; color=:blue, label="class 2", widen=false
-)
+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")