% 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

% Specify the number of clusters
K = 2;

%% 1a) Get coordinate list from pointclouds
% Coords used in this script
Pts = getPoints();
figure;
scatter(Pts(:,1),Pts(:,2))
title('Two Spirals')

n = size(Pts, 1);

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

%% 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, S);

%% 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);

% \----------------------------/
%     Your implementation
% \----------------------------/

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

%% 1f) Run K-means on input data
% \----------------------------/
%     Your implementation
% \----------------------------/
[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,dummy_map)
title('TODO: Plot the spectral clusters')
subplot(1,2,2)
gplotmap(W,Pts,dummy_map)
title('TODO: Plot the K-means clusters')