8-iris-logistics-reg

Author

math4mad

简介
  1. ref: probml page84 figure 2.13
  2. dataset:iris
  3. plots:使用 GLMakie:contourf 方法

1. load package

Code 
    include("../utils.jl")
    import MLJ:fit!,fitted_params
    using GLMakie,MLJ,CSV,DataFrames

2 process data

2.1 import iris datset

Code 
iris = load_iris();

#selectrows(iris, 1:3)  |> pretty

iris = DataFrames.DataFrame(iris);
first(iris,5)|>display
y, X = unpack(iris, ==(:target); rng=123);

X=select!(X,3:4)

byCat = iris.target
categ = unique(byCat)
colors1 = [:orange,:lightgreen,:purple];
5×5 DataFrame
Row sepal_length sepal_width petal_length petal_width target
Float64 Float64 Float64 Float64 Cat…
1 5.1 3.5 1.4 0.2 setosa
2 4.9 3.0 1.4 0.2 setosa
3 4.7 3.2 1.3 0.2 setosa
4 4.6 3.1 1.5 0.2 setosa
5 5.0 3.6 1.4 0.2 setosa

2.2 make desc boundary data

生成决策边界实际是利用训练模型对区间内的每个点都做出预测,利用两个属性的最大值和最小值 生成 grid 数据,这是 test数据

Code 
# grid data
   n1 = n2 = 200
   tx = LinRange(0, 8, 200)
   ty = LinRange(-1, 4, 200)
   X_test = mapreduce(collect, hcat, Iterators.product(tx, ty))
   X_test = MLJ.table(X_test')
Tables.MatrixTable{LinearAlgebra.Adjoint{Float64, Matrix{Float64}}} with 40000 rows, 2 columns, and schema:
 :x1  Float64
 :x2  Float64

3. Logisitcs model

3.1 training model

Code 
     LogisticClassifier = @load LogisticClassifier pkg=MLJLinearModels
      
     model = machine(LogisticClassifier(), X,y )
     fit!(model)
import MLJLinearModels ✔
[ Info: For silent loading, specify `verbosity=0`. 
[ Info: Training machine(LogisticClassifier(lambda = 2.220446049250313e-16, …), …).
┌ Info: Solver: MLJLinearModels.LBFGS{Optim.Options{Float64, Nothing}, NamedTuple{(), Tuple{}}}
│   optim_options: Optim.Options{Float64, Nothing}
└   lbfgs_options: NamedTuple{(), Tuple{}} NamedTuple()
trained Machine; caches model-specific representations of data
  model: LogisticClassifier(lambda = 2.220446049250313e-16, …)
  args: 
    1:  Source @794 ⏎ Table{AbstractVector{Continuous}}
    2:  Source @579 ⏎ AbstractVector{Multiclass{3}}

3.2 predict

Code 
ŷ = MLJ.predict(model, X_test)

res=mode.(ŷ)|>d->reshape(d,200,200)
function trans(i)
     
    if i=="setosa"
       res=1
    elseif  i=="versicolor"
       res=2
       
    else
       res=3
    end
end
ypred=[trans(res[i,j]) for i in 1:200, j in 1:200]
200×200 Matrix{Int64}:
 1  1  1  1  1  1  1  1  1  1  1  1  1  …  2  2  2  2  2  2  2  2  2  2  2  2
 1  1  1  1  1  1  1  1  1  1  1  1  1     2  2  2  2  2  2  2  2  2  2  2  2
 1  1  1  1  1  1  1  1  1  1  1  1  1     2  2  2  2  2  2  2  2  2  2  2  2
 1  1  1  1  1  1  1  1  1  1  1  1  1     2  2  2  2  2  2  2  2  2  2  2  2
 1  1  1  1  1  1  1  1  1  1  1  1  1     2  2  2  2  2  2  2  2  2  2  2  2
 1  1  1  1  1  1  1  1  1  1  1  1  1  …  2  2  2  2  2  2  2  2  2  2  2  2
 1  1  1  1  1  1  1  1  1  1  1  1  1     2  2  2  2  2  2  2  2  2  2  2  2
 1  1  1  1  1  1  1  1  1  1  1  1  1     2  2  2  2  2  2  2  2  2  2  2  2
 1  1  1  1  1  1  1  1  1  1  1  1  1     2  2  2  2  2  2  2  2  2  2  2  2
 1  1  1  1  1  1  1  1  1  1  1  1  1     2  2  2  2  2  2  2  2  2  2  2  2
 1  1  1  1  1  1  1  1  1  1  1  1  1  …  2  2  2  2  2  2  2  2  2  2  2  2
 1  1  1  1  1  1  1  1  1  1  1  1  1     2  2  2  2  2  2  2  2  2  2  2  2
 1  1  1  1  1  1  1  1  1  1  1  1  1     2  2  2  2  2  2  2  2  2  2  2  2
 ⋮              ⋮              ⋮        ⋱        ⋮              ⋮           
 2  2  2  2  2  2  2  2  2  2  2  2  2     3  3  3  3  3  3  3  3  3  3  3  3
 2  2  2  2  2  2  2  2  2  2  2  2  2     3  3  3  3  3  3  3  3  3  3  3  3
 2  2  2  2  2  2  2  2  2  2  2  2  2  …  3  3  3  3  3  3  3  3  3  3  3  3
 2  2  2  2  2  2  2  2  2  2  2  2  2     3  3  3  3  3  3  3  3  3  3  3  3
 2  2  2  2  2  2  2  2  2  2  2  2  2     3  3  3  3  3  3  3  3  3  3  3  3
 2  2  2  2  2  2  2  2  2  2  2  2  2     3  3  3  3  3  3  3  3  3  3  3  3
 2  2  2  2  2  2  2  2  2  2  2  2  2     3  3  3  3  3  3  3  3  3  3  3  3
 2  2  2  2  2  2  2  2  2  2  2  2  2  …  3  3  3  3  3  3  3  3  3  3  3  3
 2  2  2  2  2  2  2  2  2  2  2  2  2     3  3  3  3  3  3  3  3  3  3  3  3
 2  2  2  2  2  2  2  2  2  2  2  2  2     3  3  3  3  3  3  3  3  3  3  3  3
 2  2  2  2  2  2  2  2  2  2  2  2  2     3  3  3  3  3  3  3  3  3  3  3  3
 2  2  2  2  2  2  2  2  2  2  2  2  2     3  3  3  3  3  3  3  3  3  3  3  3

4 plot res

Code 
   function  add_legend(axs)
      Legend(fig[1,2], axs,"Label";width=100,height=200)
   end

   function desision_boundary(ax)
      axs=[]
      for (k, c) in enumerate(categ)
         indc = findall(x -> x == c, byCat)
         #@show indc
         x=scatter!(iris[:,3][indc],iris[:,4][indc];color=colors1[k],markersize=14)
         push!(axs,x)
      end
      return axs
   end

   fig = Figure(resolution=(800,600))
   ax=Axis(fig[1,1],xlabel="Petal length",ylabel="Petal width",title=L"Iris Logistics classfication")
   contourf!(ax,tx, ty, ypred, levels=length(categ))
   axs=desision_boundary(ax)
   Legend(fig[1,2],[axs...],categ)
   fig