% Cluster 2D pointclouds with spectral clustering and compare with k-means
% USI, ICS, Lugano
% Numerical Computing 

clear variables;
close all;
warning OFF;

addpath ../datasets
addpath ../datasets/Meshes

%% 1a) Get coordinate list from pointclouds
% Coords used in this script
[Pts_spirals,Pts_clusterin,Pts_corn,Pts_halfk,Pts_fullmoon,Pts_out] = getPoints();

TITLES = ["Two Spirals", "Cluster in cluster", "Corners", "Half crescent", "Full crescent", "Outlier"];
RUNS = {Pts_spirals, Pts_clusterin, Pts_corn, Pts_halfk, Pts_fullmoon, Pts_out};
KS = {2, 2, 4, 2, 2, 4};

for i = 1:6
    % Specify the number of clusters
    Pts = RUNS{i};
    K = KS{i};
    disp(TITLES(i));
    
    figure;
    scatter(Pts(:,1),Pts(:,2))
    title(TITLES(i))

    n = size(Pts, 1);
    
    % Create Gaussian similarity function
    [S] = similarityfunc(Pts(:,1:2), 2 * log(n));

    %% 1b) Find the minimal spanning tree of the full graph. Use the information
    %      to determine a valid value for epsilon        
    H = minSpanTree(S);
    epsilon = max(H(H > 0), [], 'all');

    %% 1c) Create the epsilon similarity graph
    [G] = epsilonSimGraph(epsilon,Pts);

    %% 1d) Create the adjacency matrix for the epsilon case
    W = S .* G;
    figure;
    gplotg(W,Pts(:,1:2))
    title('Adjacency matrix')

    %% 1e) Create the Laplacian matrix and implement spectral clustering
    [L,Diag] = CreateLapl(W);
    [V,~] = eigs(L, K, 'SA');

    % Cluster rows of eigenvector matrix of L corresponding to K smallest
    % eigennalues. Use kmeans for that.
    [D_spec,x_spec]     = kmeans_mod(V,K,n);

    %% 1f) Run K-means on input data
    [D_kmeans,x_kmeans] = kmeans_mod(Pts,K,n);

    %% 1g) Visualize spectral and k-means clustering results
    figure;
    subplot(1,2,1)
    gplotmap(W,Pts,x_spec)
    title(strcat(TITLES(i), ': Spectral clusters'))
    subplot(1,2,2)
    gplotmap(W,Pts,x_kmeans)
    title(strcat(TITLES(i), ': K-means clusters'))
    matlab2tikz('showInfo', false, strcat('../../', TITLES{i}, '.tex'));
    
end