Julia Iris PCA

using Plots;
using Base;
using LinearAlgebra;
using Statistics;
using DataFrames;
using CSV;
using StatsPlots;

filename = "/home/nchashch/BORG/SEM6/ITASOU/dataset/iris.data";
df = CSV.read(filename, header=false)
df = dropmissing(df);
header = [:sepal_length, :sepal_width, :petal_length, :petal_width, :species];
names!(df, header);
features = header[1:4];
X = convert(Matrix, df[:, features]);
X_s = (X .- mean(X, dims=1)) ./ std(X, dims=1);
n, _ = size(X_s)
Gram = transpose(X_s) * X_s / (n - 1);
lambda = eigvals(Gram);
vecs = eigvecs(Gram);
println(lambda);
PCA = X_s * vecs
pca = DataFrame(PCA)
pca[:species] = df[:species]

function pca()

println(first(pca, 5));

plt1 = @df pca scatter(:x4, :x3, group=:species,
                title = "Iris Dataset PCA",
                xlabel = "Frist principal component", ylabel = "Second principal component",
                m=(0.7, [:cross :hex :star7], 5),
                bg=RGB(.2,.2,.2),
                );

plt2 = @df df scatter(:sepal_length, :sepal_width, group=:species,
               title = "Iris Dataset",
               xlabel = "Sepal length", ylabel = "Sepal width",
               m=(0.7, [:cross :hex :star7], 5),
               bg=RGB(.2,.2,.2),
               );

plot(plt1, plt2)