mp4: done MATLAB

mp4/3elt_hist.tex

@@ -0,0 +1,48 @@
+% This file was created by matlab2tikz.
+%
+\definecolor{mycolor1}{rgb}{0.00000,0.44700,0.74100}%
+%
+\begin{tikzpicture}
+
+\begin{axis}[%
+width=2.603in,
+height=4.754in,
+at={(1.011in,0.642in)},
+scale only axis,
+xmin=0.3,
+xmax=4.7,
+ymin=0,
+ymax=1800,
+axis background/.style={fill=white}
+]
+\addplot[ybar interval, fill=mycolor1, fill opacity=0.6, draw=black, area legend] table[row sep=crcr] {%
+x	y\\
+0.5	1088\\
+1.5	965\\
+2.5	869\\
+3.5	1798\\
+4.5	1798\\
+};
+\end{axis}
+
+\begin{axis}[%
+width=2.603in,
+height=4.754in,
+at={(4.436in,0.642in)},
+scale only axis,
+xmin=0.3,
+xmax=4.7,
+ymin=0,
+ymax=3500,
+axis background/.style={fill=white}
+]
+\addplot[ybar interval, fill=mycolor1, fill opacity=0.6, draw=black, area legend] table[row sep=crcr] {%
+x	y\\
+0.5	31\\
+1.5	1560\\
+2.5	3098\\
+3.5	31\\
+4.5	31\\
+};
+\end{axis}
+\end{tikzpicture}%

mp4/Project_4_Maggioni_Claudio.tex

@@ -1,13 +1,22 @@
 \documentclass[unicode,11pt,a4paper,oneside,numbers=endperiod,openany]{scrartcl}
 
+\usepackage{graphicx}
+\usepackage{subcaption}
+\usepackage{amsmath}
 \input{assignment.sty}
-
-
-
+\usepackage{pgfplots}
+\pgfplotsset{compat=newest}
+\usetikzlibrary{plotmarks}
+\usetikzlibrary{arrows.meta}
+\usepgfplotslibrary{patchplots}
+\usepackage{grffile}
+\usepackage{amsmath}
+\usepackage{subcaption}
+\usepgfplotslibrary{external}
+\tikzexternalize
 
 \begin{document}
 
-
 \setassignment
 \setduedate{Wednesday, 18 November 2020, 11:55 PM}
 
@@ -26,5 +35,24 @@
 
 \end{enumerate}
 
+\begin{figure}
+	\centering\input{airfoil1_clu.tex}
+	\caption{Graphs for \textit{Airfoil1}}
+\end{figure}
+\begin{figure}
+	\centering\input{barth_clu.tex}
+	\caption{Graphs for \textit{Barth}}
+\end{figure}
+\begin{figure}
+	\centering\input{grid2_clu.tex}
+	\caption{Graphs for \textit{Grid2}}
+\end{figure}
+\begin{figure}
+	\centering\input{3elt_clu.tex}
+	\caption{Graphs for \textit{3elt}}
+\end{figure}
+
+\begin{figure}
+\end{figure}
 
 \end{document}

mp4/Project_4_Maggioni_Claudio/src/ClusterGraphs.m

@@ -2,64 +2,74 @@
 % USI, ICS, Lugano
 % Numerical Computing 
 
-clear all;close all;
+clear variables;
+close all;
 warning OFF;
 
 addpath ../datasets
 addpath ../datasets/Meshes
 
-load airfoil1.mat
-% load barth.mat
-% load grid2.mat
-% load 3elt.mat
+MATS = {'airfoil1', 'barth', 'grid2', '3elt'};
 
-% Specify the number of clusters
-K = 4;
-% Read graph
-W   = Problem.A;
-Pts = Problem.aux.coord;
-n   = size(Pts,1);
-% dummy var
-dummy_map = ones(n,1);
+for i = 1:length(MATS)
+    load(strcat(MATS{i}, '.mat'));
 
-figure;
-spy(W)
-title('Adjacency matrix')
-%% 2a) Create the Laplacian matrix and plot the graph using the 2nd and 3rd eigenvectors
-% \----------------------------/
-%     Your implementation
-% \----------------------------/
+    % Specify the number of clusters
+    K = 4;
+    % Read graph
+    W   = Problem.A;
+    Pts = Problem.aux.coord;
+    n   = size(Pts,1);
+    % dummy var
+    dummy_map = ones(n,1);
 
-% Eigen-decomposition
-% \----------------------------/
-%     Your implementation
-% \----------------------------/
+    figure;
+    spy(W)
+    xlabel(strcat(MATS{i}, ': adjacency matrix'))
+    %matlab2tikz('showInfo', false, strcat('../../', MATS{i}, '_adj.tex'))
     
-% Plot and compare
-figure;
-subplot(1,2,1);
-gplot(W,Pts)
-xlabel('Nodal coordinates')
-subplot(1,2,2);
-gplot(W,Pts)
-xlabel('TODO: Plot using Eigenvector coordinates')
+    %% 2a) Create the Laplacian matrix and plot the graph using the 2nd and 3rd eigenvectors
+    [L,~] = CreateLapl(W);
+    [V,~] = eigs(L, 4, 'smallestabs');
 
-%% 2b) Cluster each graph in K = 4 clusters with the spectral and the 
-%      k-means method, and compare yourresults visually for each case.
+    % Plot and compare
+    figure;
+    subplot(2,2,1);
+    gplot(W,Pts)
+    title(strcat(MATS{i}, ': nodal coordinates'))
+    subplot(2,2,2);
+    gplot(W,V(:, 2:3))
+    title(strcat(MATS{i}, ': eigenvector coordinates'))
 
-% \----------------------------/
-%     Your implementation
-% \----------------------------/
+    %% 2b) Cluster each graph in K = 4 clusters with the spectral and the 
+    %      k-means method, and compare yourresults visually for each case.
 
+    [D_spec,x_spec]     = kmeans_mod(V, K, n);
+    [D_kmeans,x_kmeans] = kmeans_mod(Pts, K, n);
 
-% Compare and visualize
-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')
+    % Compare and visualize
+    subplot(2,2,3);
+    gplotmap(W,Pts,x_spec)
+    title(strcat(MATS{i}, ': spectral clusters'))
+    subplot(2,2,4);
+    gplotmap(W,Pts,x_kmeans)
+    title(strcat(MATS{i}, ': k-means clusters'))
+    matlab2tikz('showInfo', false, strcat('../../', MATS{i}, '_clu.tex'))
 
-%% 2c) Calculate the number of nodes per cluster
-[Spec_nodes,Kmeans_nodes] = USI_ClusterMetrics(K,dummy_map,dummy_map);
+    cx = sum(x_spec == 1:4);
+    ck = sum(x_kmeans == 1:4);
+    fprintf('%10s spectral: %4d %4d %4d %4d k-means: %4d %4d %4d %4d\n', ...
+        MATS{i}, cx(1), cx(2), cx(3), cx(4), ck(1), ck(2), ck(3), ck(4));  
+    
+    figure;
+    subplot(1,2,1);
+    title(strcat(MATS{i}, ': spectral histogram'));
+    histogram(x_spec, [0:4] + 0.5);
+    subplot(1,2,2);
+    title(strcat(MATS{i}, ': k-means histogram'));
+    histogram(x_kmeans, [0:4] + 0.5);
+    matlab2tikz('showInfo', false, strcat('../../', MATS{i}, '_hist.tex'));
+    
+    %% 2c) Calculate the number of nodes per cluster
+    [Spec_nodes,Kmeans_nodes] = ClusterMetrics(K,dummy_map,dummy_map);
+end

mp4/Project_4_Maggioni_Claudio/src/ClusterPoints.m

@@ -9,56 +9,61 @@ 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')
+[Pts_spirals,Pts_clusterin,Pts_corn,Pts_halfk,Pts_fullmoon,Pts_out] = getPoints();
 
-n = size(Pts, 1);
+TITLES = ["Two Spirals", "Cluster in", "Corn", "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};
 
-% Create Gaussian similarity function
-[S] = similarityfunc(Pts(:,1:2));
+for i = 1:6
+    % Specify the number of clusters
+    Pts = RUNS{i};
+    K = KS{i};
+    disp(TITLES(i));
     
-%% 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');
+    figure;
+    scatter(Pts(:,1),Pts(:,2))
+    title(TITLES(i))
 
-%% 1c) Create the epsilon similarity graph
-[G] = epsilonSimGraph(epsilon,Pts, S);
+    n = size(Pts, 1);
     
-%% 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);
+    % Create Gaussian similarity function
+    [S] = similarityfunc(Pts(:,1:2), 10 * log(n));
 
-% \----------------------------/
-%     Your implementation
-% \----------------------------/
+    %% 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');
 
-% 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);
+    %% 1c) Create the epsilon similarity graph
+    [G] = epsilonSimGraph(epsilon,Pts);
 
-%% 1f) Run K-means on input data
-% \----------------------------/
-%     Your implementation
-% \----------------------------/
-[D_kmeans,x_kmeans] = kmeans_mod(Pts,K,n);
+    %% 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'))
+end
     
-%% 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')

mp4/Project_4_Maggioni_Claudio/src/epsilonSimGraph.m

@@ -1,4 +1,4 @@
-function [G] = epsilonSimGraph(epsilon, Pts, S)
+function [G] = epsilonSimGraph(epsilon, Pts)
 % Construct an epsilon similarity graph
 % Input
 % epsilon: size of neighborhood (calculate from Prim's Algorithm) 
@@ -14,6 +14,15 @@ fprintf('----------------------------\n');
 fprintf('epsilon similarity graph\n');
 fprintf('----------------------------\n');
 
-G = S <= epsilon;
-
+n = size(Pts, 1);
+G = zeros(n, n);
+for i = 1:n
+    for j = 1:n
+        dist = norm((Pts(i, :) - Pts(j, :)), 2);
+        if dist < epsilon
+            G(i, j) = 1;
+            G(j, i) = 1;
+        end
+    end
+end
 end

mp4/Project_4_Maggioni_Claudio/src/kmeans_mod.m

@@ -16,7 +16,7 @@ D = c;
 x = zeros(size(Y,1),1);
 D_old = inf*ones(size(D));
 count = 1;
-while norm(D - D_old) > 0.00001 & count < 500
+while norm(D - D_old) > 0.00001 && count < 500
     D_old = D;
     % Assign points to clusters
     for i = 1:n

mp4/airfoil1_hist.tex

@@ -0,0 +1,48 @@
+% This file was created by matlab2tikz.
+%
+\definecolor{mycolor1}{rgb}{0.00000,0.44700,0.74100}%
+%
+\begin{tikzpicture}
+
+\begin{axis}[%
+width=2.603in,
+height=4.754in,
+at={(1.011in,0.642in)},
+scale only axis,
+xmin=0.3,
+xmax=4.7,
+ymin=0,
+ymax=1200,
+axis background/.style={fill=white}
+]
+\addplot[ybar interval, fill=mycolor1, fill opacity=0.6, draw=black, area legend] table[row sep=crcr] {%
+x	y\\
+0.5	971\\
+1.5	1050\\
+2.5	1150\\
+3.5	1082\\
+4.5	1082\\
+};
+\end{axis}
+
+\begin{axis}[%
+width=2.603in,
+height=4.754in,
+at={(4.436in,0.642in)},
+scale only axis,
+xmin=0.3,
+xmax=4.7,
+ymin=0,
+ymax=2000,
+axis background/.style={fill=white}
+]
+\addplot[ybar interval, fill=mycolor1, fill opacity=0.6, draw=black, area legend] table[row sep=crcr] {%
+x	y\\
+0.5	344\\
+1.5	739\\
+2.5	1869\\
+3.5	1301\\
+4.5	1301\\
+};
+\end{axis}
+\end{tikzpicture}%

mp4/barth_hist.tex

@@ -0,0 +1,48 @@
+% This file was created by matlab2tikz.
+%
+\definecolor{mycolor1}{rgb}{0.00000,0.44700,0.74100}%
+%
+\begin{tikzpicture}
+
+\begin{axis}[%
+width=2.603in,
+height=4.754in,
+at={(1.011in,0.642in)},
+scale only axis,
+xmin=0.3,
+xmax=4.7,
+ymin=0,
+ymax=2500,
+axis background/.style={fill=white}
+]
+\addplot[ybar interval, fill=mycolor1, fill opacity=0.6, draw=black, area legend] table[row sep=crcr] {%
+x	y\\
+0.5	1588\\
+1.5	1490\\
+2.5	2206\\
+3.5	1407\\
+4.5	1407\\
+};
+\end{axis}
+
+\begin{axis}[%
+width=2.603in,
+height=4.754in,
+at={(4.436in,0.642in)},
+scale only axis,
+xmin=0.3,
+xmax=4.7,
+ymin=0,
+ymax=4000,
+axis background/.style={fill=white}
+]
+\addplot[ybar interval, fill=mycolor1, fill opacity=0.6, draw=black, area legend] table[row sep=crcr] {%
+x	y\\
+0.5	71\\
+1.5	3617\\
+2.5	71\\
+3.5	2932\\
+4.5	2932\\
+};
+\end{axis}
+\end{tikzpicture}%

mp4/grid2_hist.tex

@@ -0,0 +1,48 @@
+% This file was created by matlab2tikz.
+%
+\definecolor{mycolor1}{rgb}{0.00000,0.44700,0.74100}%
+%
+\begin{tikzpicture}
+
+\begin{axis}[%
+width=2.603in,
+height=4.754in,
+at={(1.011in,0.642in)},
+scale only axis,
+xmin=0.3,
+xmax=4.7,
+ymin=0,
+ymax=1400,
+axis background/.style={fill=white}
+]
+\addplot[ybar interval, fill=mycolor1, fill opacity=0.6, draw=black, area legend] table[row sep=crcr] {%
+x	y\\
+0.5	785\\
+1.5	1305\\
+2.5	827\\
+3.5	379\\
+4.5	379\\
+};
+\end{axis}
+
+\begin{axis}[%
+width=2.603in,
+height=4.754in,
+at={(4.436in,0.642in)},
+scale only axis,
+xmin=0.3,
+xmax=4.7,
+ymin=0,
+ymax=1400,
+axis background/.style={fill=white}
+]
+\addplot[ybar interval, fill=mycolor1, fill opacity=0.6, draw=black, area legend] table[row sep=crcr] {%
+x	y\\
+0.5	1271\\
+1.5	1183\\
+2.5	604\\
+3.5	238\\
+4.5	238\\
+};
+\end{axis}
+\end{tikzpicture}%