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+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}% \ No newline at end of file diff --git a/mp4/Project_4_Maggioni_Claudio.pdf b/mp4/Project_4_Maggioni_Claudio.pdf new file mode 100644 index 0000000..8f93c41 Binary files /dev/null and b/mp4/Project_4_Maggioni_Claudio.pdf differ diff --git a/mp4/Project_4_Maggioni_Claudio.tex b/mp4/Project_4_Maggioni_Claudio.tex index b07e936..c28c362 100644 --- a/mp4/Project_4_Maggioni_Claudio.tex +++ b/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} diff --git a/mp4/Project_4_Maggioni_Claudio/similarityfunc.m b/mp4/Project_4_Maggioni_Claudio/similarityfunc.m new file mode 100644 index 0000000..e69de29 diff --git a/mp4/Project_4_Maggioni_Claudio/src/ClusterGraphs.m b/mp4/Project_4_Maggioni_Claudio/src/ClusterGraphs.m index f854021..2c86918 100644 --- a/mp4/Project_4_Maggioni_Claudio/src/ClusterGraphs.m +++ b/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')) + + %% 2a) Create the Laplacian matrix and plot the graph using the 2nd and 3rd eigenvectors + [L,~] = CreateLapl(W); + [V,~] = eigs(L, 4, 'smallestabs'); -% 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') + % 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')) -%% 2b) Cluster each graph in K = 4 clusters with the spectral and the -% k-means method, and compare yourresults visually for each case. + %% 2b) Cluster each graph in K = 4 clusters with the spectral and the + % k-means method, and compare yourresults visually for each case. -% \----------------------------/ -% Your implementation -% \----------------------------/ + [D_spec,x_spec] = kmeans_mod(V, K, n); + [D_kmeans,x_kmeans] = kmeans_mod(Pts, K, n); + % 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')) -% 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') - -%% 2c) Calculate the number of nodes per cluster -[Spec_nodes,Kmeans_nodes] = USI_ClusterMetrics(K,dummy_map,dummy_map); \ No newline at end of file + 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 \ No newline at end of file diff --git a/mp4/Project_4_Maggioni_Claudio/src/ClusterPoints.m b/mp4/Project_4_Maggioni_Claudio/src/ClusterPoints.m index 7154f3f..535e0c6 100644 --- a/mp4/Project_4_Maggioni_Claudio/src/ClusterPoints.m +++ b/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)); + + figure; + scatter(Pts(:,1),Pts(:,2)) + title(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'); + n = size(Pts, 1); + + % Create Gaussian similarity function + [S] = similarityfunc(Pts(:,1:2), 10 * log(n)); -%% 1c) Create the epsilon similarity graph -[G] = epsilonSimGraph(epsilon,Pts, S); + %% 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'); -%% 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); + %% 1c) Create the epsilon similarity graph + [G] = epsilonSimGraph(epsilon,Pts); -% \----------------------------/ -% Your implementation -% \----------------------------/ + %% 1d) Create the adjacency matrix for the epsilon case + W = S .* G; + figure; + gplotg(W,Pts(:,1:2)) + title('Adjacency matrix') -% 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); + %% 1e) Create the Laplacian matrix and implement spectral clustering + [L,Diag] = CreateLapl(W); + [V,~] = eigs(L, K, 'SA'); -%% 1f) Run K-means on input data -% \----------------------------/ -% Your implementation -% \----------------------------/ -[D_kmeans,x_kmeans] = kmeans_mod(Pts,K,n); + % 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); -%% 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') \ No newline at end of file + %% 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 + \ No newline at end of file diff --git a/mp4/Project_4_Maggioni_Claudio/src/epsilonSimGraph.m b/mp4/Project_4_Maggioni_Claudio/src/epsilonSimGraph.m index 58faba2..4aea068 100644 --- a/mp4/Project_4_Maggioni_Claudio/src/epsilonSimGraph.m +++ b/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 \ No newline at end of file diff --git a/mp4/Project_4_Maggioni_Claudio/src/kmeans_mod.m b/mp4/Project_4_Maggioni_Claudio/src/kmeans_mod.m index b38e2c5..6942f47 100644 --- a/mp4/Project_4_Maggioni_Claudio/src/kmeans_mod.m +++ b/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 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