mp4: done MATLAB
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20 changed files with 1436993 additions and 98 deletions
27493
mp4/3elt_adj.tex
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27493
mp4/3elt_adj.tex
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327369
mp4/3elt_clu.tex
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327369
mp4/3elt_clu.tex
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mp4/3elt_hist.tex
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mp4/3elt_hist.tex
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% This file was created by matlab2tikz.
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%
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\definecolor{mycolor1}{rgb}{0.00000,0.44700,0.74100}%
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%
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\begin{tikzpicture}
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\begin{axis}[%
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width=2.603in,
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height=4.754in,
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at={(1.011in,0.642in)},
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scale only axis,
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xmin=0.3,
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xmax=4.7,
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ymin=0,
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ymax=1800,
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axis background/.style={fill=white}
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]
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\addplot[ybar interval, fill=mycolor1, fill opacity=0.6, draw=black, area legend] table[row sep=crcr] {%
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x y\\
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0.5 1088\\
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2.5 869\\
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};
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\end{axis}
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\begin{axis}[%
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width=2.603in,
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height=4.754in,
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at={(4.436in,0.642in)},
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scale only axis,
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xmin=0.3,
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xmax=4.7,
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ymin=0,
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ymax=3500,
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axis background/.style={fill=white}
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]
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\addplot[ybar interval, fill=mycolor1, fill opacity=0.6, draw=black, area legend] table[row sep=crcr] {%
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x y\\
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0.5 31\\
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2.5 3098\\
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3.5 31\\
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};
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\end{axis}
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\end{tikzpicture}%
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mp4/Project_4_Maggioni_Claudio.pdf
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mp4/Project_4_Maggioni_Claudio.pdf
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\documentclass[unicode,11pt,a4paper,oneside,numbers=endperiod,openany]{scrartcl}
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\usepackage{graphicx}
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\usepackage{subcaption}
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\usepackage{amsmath}
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\input{assignment.sty}
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\usepackage{pgfplots}
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\pgfplotsset{compat=newest}
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\usetikzlibrary{plotmarks}
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\usetikzlibrary{arrows.meta}
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\usepgfplotslibrary{patchplots}
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\usepackage{grffile}
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\usepackage{amsmath}
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\usepackage{subcaption}
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\usepgfplotslibrary{external}
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\tikzexternalize
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\begin{document}
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\setassignment
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\setduedate{Wednesday, 18 November 2020, 11:55 PM}
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@ -26,5 +35,24 @@
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\end{enumerate}
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\begin{figure}
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\centering\input{airfoil1_clu.tex}
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\caption{Graphs for \textit{Airfoil1}}
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\end{figure}
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\begin{figure}
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\centering\input{barth_clu.tex}
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\caption{Graphs for \textit{Barth}}
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\end{figure}
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\begin{figure}
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\centering\input{grid2_clu.tex}
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\caption{Graphs for \textit{Grid2}}
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\end{figure}
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\begin{figure}
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\centering\input{3elt_clu.tex}
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\caption{Graphs for \textit{3elt}}
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\end{figure}
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\begin{figure}
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\end{figure}
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\end{document}
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mp4/Project_4_Maggioni_Claudio/similarityfunc.m
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mp4/Project_4_Maggioni_Claudio/similarityfunc.m
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@ -2,64 +2,74 @@
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% USI, ICS, Lugano
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% Numerical Computing
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clear all;close all;
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clear variables;
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close all;
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warning OFF;
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addpath ../datasets
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addpath ../datasets/Meshes
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load airfoil1.mat
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% load barth.mat
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% load grid2.mat
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% load 3elt.mat
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MATS = {'airfoil1', 'barth', 'grid2', '3elt'};
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% Specify the number of clusters
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K = 4;
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% Read graph
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W = Problem.A;
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Pts = Problem.aux.coord;
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n = size(Pts,1);
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% dummy var
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dummy_map = ones(n,1);
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for i = 1:length(MATS)
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load(strcat(MATS{i}, '.mat'));
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figure;
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spy(W)
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title('Adjacency matrix')
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%% 2a) Create the Laplacian matrix and plot the graph using the 2nd and 3rd eigenvectors
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% \----------------------------/
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% Your implementation
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% \----------------------------/
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% Specify the number of clusters
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K = 4;
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% Read graph
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W = Problem.A;
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Pts = Problem.aux.coord;
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n = size(Pts,1);
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% dummy var
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dummy_map = ones(n,1);
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% Eigen-decomposition
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% \----------------------------/
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% Your implementation
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% \----------------------------/
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figure;
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spy(W)
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xlabel(strcat(MATS{i}, ': adjacency matrix'))
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%matlab2tikz('showInfo', false, strcat('../../', MATS{i}, '_adj.tex'))
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%% 2a) Create the Laplacian matrix and plot the graph using the 2nd and 3rd eigenvectors
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[L,~] = CreateLapl(W);
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[V,~] = eigs(L, 4, 'smallestabs');
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% Plot and compare
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figure;
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subplot(1,2,1);
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gplot(W,Pts)
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xlabel('Nodal coordinates')
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subplot(1,2,2);
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gplot(W,Pts)
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xlabel('TODO: Plot using Eigenvector coordinates')
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% Plot and compare
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figure;
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subplot(2,2,1);
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gplot(W,Pts)
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title(strcat(MATS{i}, ': nodal coordinates'))
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subplot(2,2,2);
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gplot(W,V(:, 2:3))
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title(strcat(MATS{i}, ': eigenvector coordinates'))
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%% 2b) Cluster each graph in K = 4 clusters with the spectral and the
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% k-means method, and compare yourresults visually for each case.
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%% 2b) Cluster each graph in K = 4 clusters with the spectral and the
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% k-means method, and compare yourresults visually for each case.
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% \----------------------------/
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% Your implementation
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% \----------------------------/
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[D_spec,x_spec] = kmeans_mod(V, K, n);
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[D_kmeans,x_kmeans] = kmeans_mod(Pts, K, n);
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% Compare and visualize
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subplot(2,2,3);
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gplotmap(W,Pts,x_spec)
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title(strcat(MATS{i}, ': spectral clusters'))
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subplot(2,2,4);
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gplotmap(W,Pts,x_kmeans)
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title(strcat(MATS{i}, ': k-means clusters'))
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matlab2tikz('showInfo', false, strcat('../../', MATS{i}, '_clu.tex'))
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% Compare and visualize
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figure;
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subplot(1,2,1);
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gplotmap(W,Pts,dummy_map)
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title('TODO: Plot the spectral clusters')
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subplot(1,2,2);
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gplotmap(W,Pts,dummy_map)
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title('TODO: Plot the K-means clusters')
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%% 2c) Calculate the number of nodes per cluster
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[Spec_nodes,Kmeans_nodes] = USI_ClusterMetrics(K,dummy_map,dummy_map);
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cx = sum(x_spec == 1:4);
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ck = sum(x_kmeans == 1:4);
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fprintf('%10s spectral: %4d %4d %4d %4d k-means: %4d %4d %4d %4d\n', ...
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MATS{i}, cx(1), cx(2), cx(3), cx(4), ck(1), ck(2), ck(3), ck(4));
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figure;
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subplot(1,2,1);
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title(strcat(MATS{i}, ': spectral histogram'));
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histogram(x_spec, [0:4] + 0.5);
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subplot(1,2,2);
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title(strcat(MATS{i}, ': k-means histogram'));
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histogram(x_kmeans, [0:4] + 0.5);
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matlab2tikz('showInfo', false, strcat('../../', MATS{i}, '_hist.tex'));
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%% 2c) Calculate the number of nodes per cluster
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[Spec_nodes,Kmeans_nodes] = ClusterMetrics(K,dummy_map,dummy_map);
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end
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addpath ../datasets
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addpath ../datasets/Meshes
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% Specify the number of clusters
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K = 2;
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%% 1a) Get coordinate list from pointclouds
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% Coords used in this script
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Pts = getPoints();
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figure;
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scatter(Pts(:,1),Pts(:,2))
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title('Two Spirals')
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[Pts_spirals,Pts_clusterin,Pts_corn,Pts_halfk,Pts_fullmoon,Pts_out] = getPoints();
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n = size(Pts, 1);
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TITLES = ["Two Spirals", "Cluster in", "Corn", "Half crescent", "Full crescent", "Outlier"];
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RUNS = {Pts_spirals, Pts_clusterin, Pts_corn, Pts_halfk, Pts_fullmoon, Pts_out};
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KS = {2, 2, 4, 2, 2, 4};
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% Create Gaussian similarity function
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[S] = similarityfunc(Pts(:,1:2));
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for i = 1:6
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% Specify the number of clusters
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Pts = RUNS{i};
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K = KS{i};
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disp(TITLES(i));
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figure;
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scatter(Pts(:,1),Pts(:,2))
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title(TITLES(i))
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%% 1b) Find the minimal spanning tree of the full graph. Use the information
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% to determine a valid value for epsilon
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H = minSpanTree(S);
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epsilon = max(H(H > 0), [], 'all');
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n = size(Pts, 1);
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% Create Gaussian similarity function
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[S] = similarityfunc(Pts(:,1:2), 10 * log(n));
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%% 1c) Create the epsilon similarity graph
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[G] = epsilonSimGraph(epsilon,Pts, S);
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%% 1b) Find the minimal spanning tree of the full graph. Use the information
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% to determine a valid value for epsilon
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H = minSpanTree(S);
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epsilon = max(H(H > 0), [], 'all');
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%% 1d) Create the adjacency matrix for the epsilon case
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W = S .* G;
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figure;
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gplotg(W,Pts(:,1:2))
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title('Adjacency matrix')
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%% 1e) Create the Laplacian matrix and implement spectral clustering
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[L,Diag] = CreateLapl(W);
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%% 1c) Create the epsilon similarity graph
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[G] = epsilonSimGraph(epsilon,Pts);
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% \----------------------------/
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% Your implementation
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% \----------------------------/
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%% 1d) Create the adjacency matrix for the epsilon case
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W = S .* G;
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figure;
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gplotg(W,Pts(:,1:2))
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title('Adjacency matrix')
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% Cluster rows of eigenvector matrix of L corresponding to K smallest
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% eigennalues. Use kmeans for that.
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[D_spec,x_spec] = kmeans_mod(Pts,K,n);
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%% 1e) Create the Laplacian matrix and implement spectral clustering
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[L,Diag] = CreateLapl(W);
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[V,~] = eigs(L, K, 'SA');
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%% 1f) Run K-means on input data
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% \----------------------------/
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% Your implementation
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% \----------------------------/
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[D_kmeans,x_kmeans] = kmeans_mod(Pts,K,n);
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% Cluster rows of eigenvector matrix of L corresponding to K smallest
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% eigennalues. Use kmeans for that.
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[D_spec,x_spec] = kmeans_mod(V,K,n);
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%% 1g) Visualize spectral and k-means clustering results
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figure;
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subplot(1,2,1)
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gplotmap(W,Pts,dummy_map)
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title('TODO: Plot the spectral clusters')
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subplot(1,2,2)
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gplotmap(W,Pts,dummy_map)
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title('TODO: Plot the K-means clusters')
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%% 1f) Run K-means on input data
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[D_kmeans,x_kmeans] = kmeans_mod(Pts,K,n);
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%% 1g) Visualize spectral and k-means clustering results
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figure;
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subplot(1,2,1)
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gplotmap(W,Pts,x_spec)
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title(strcat(TITLES(i), ': Spectral clusters'))
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subplot(1,2,2)
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gplotmap(W,Pts,x_kmeans)
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title(strcat(TITLES(i), ': K-means clusters'))
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end
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function [G] = epsilonSimGraph(epsilon, Pts, S)
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function [G] = epsilonSimGraph(epsilon, Pts)
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% Construct an epsilon similarity graph
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% Input
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% epsilon: size of neighborhood (calculate from Prim's Algorithm)
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fprintf('epsilon similarity graph\n');
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fprintf('----------------------------\n');
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G = S <= epsilon;
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n = size(Pts, 1);
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G = zeros(n, n);
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for i = 1:n
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for j = 1:n
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dist = norm((Pts(i, :) - Pts(j, :)), 2);
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if dist < epsilon
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G(i, j) = 1;
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G(j, i) = 1;
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end
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end
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end
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end
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x = zeros(size(Y,1),1);
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D_old = inf*ones(size(D));
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count = 1;
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while norm(D - D_old) > 0.00001 & count < 500
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while norm(D - D_old) > 0.00001 && count < 500
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D_old = D;
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% Assign points to clusters
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for i = 1:n
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24627
mp4/airfoil1_adj.tex
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mp4/airfoil1_adj.tex
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mp4/airfoil1_clu.tex
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mp4/airfoil1_clu.tex
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mp4/airfoil1_hist.tex
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mp4/airfoil1_hist.tex
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% This file was created by matlab2tikz.
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%
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\definecolor{mycolor1}{rgb}{0.00000,0.44700,0.74100}%
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%
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\begin{tikzpicture}
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\begin{axis}[%
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width=2.603in,
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height=4.754in,
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at={(1.011in,0.642in)},
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scale only axis,
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xmin=0.3,
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xmax=4.7,
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ymin=0,
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ymax=1200,
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axis background/.style={fill=white}
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]
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\addplot[ybar interval, fill=mycolor1, fill opacity=0.6, draw=black, area legend] table[row sep=crcr] {%
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x y\\
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2.5 1150\\
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4.5 1082\\
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};
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\end{axis}
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\begin{axis}[%
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width=2.603in,
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height=4.754in,
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at={(4.436in,0.642in)},
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scale only axis,
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xmin=0.3,
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xmax=4.7,
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ymin=0,
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ymax=2000,
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axis background/.style={fill=white}
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]
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\addplot[ybar interval, fill=mycolor1, fill opacity=0.6, draw=black, area legend] table[row sep=crcr] {%
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x y\\
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4.5 1301\\
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};
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\end{axis}
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\end{tikzpicture}%
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46256
mp4/barth_adj.tex
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mp4/barth_adj.tex
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File diff suppressed because it is too large
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551415
mp4/barth_clu.tex
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551415
mp4/barth_clu.tex
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File diff suppressed because it is too large
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48
mp4/barth_hist.tex
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mp4/barth_hist.tex
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@ -0,0 +1,48 @@
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% This file was created by matlab2tikz.
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%
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\definecolor{mycolor1}{rgb}{0.00000,0.44700,0.74100}%
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%
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\begin{tikzpicture}
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\begin{axis}[%
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width=2.603in,
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height=4.754in,
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at={(1.011in,0.642in)},
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scale only axis,
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xmin=0.3,
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xmax=4.7,
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ymin=0,
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ymax=2500,
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axis background/.style={fill=white}
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]
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\addplot[ybar interval, fill=mycolor1, fill opacity=0.6, draw=black, area legend] table[row sep=crcr] {%
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x y\\
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0.5 1588\\
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2.5 2206\\
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3.5 1407\\
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4.5 1407\\
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};
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\end{axis}
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\begin{axis}[%
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width=2.603in,
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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}%
|
||||
12901
mp4/grid2_adj.tex
Normal file
12901
mp4/grid2_adj.tex
Normal file
File diff suppressed because it is too large
Load diff
153583
mp4/grid2_clu.tex
Normal file
153583
mp4/grid2_clu.tex
Normal file
File diff suppressed because it is too large
Load diff
48
mp4/grid2_hist.tex
Normal file
48
mp4/grid2_hist.tex
Normal file
|
|
@ -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}%
|
||||
BIN
mp4/usi_inf-.png
Normal file
BIN
mp4/usi_inf-.png
Normal file
Binary file not shown.
|
After Width: | Height: | Size: 97 KiB |
Reference in a new issue