From 34b290c569385fa5c3b503f2a628b15068acb836 Mon Sep 17 00:00:00 2001 From: "Claudio Maggioni (maggicl)" Date: Wed, 4 Nov 2020 14:59:14 +0100 Subject: [PATCH] mp4: done 1a-c in MATLAB --- mp4/Makefile | 15 +++ mp4/Project_4_Maggioni_Claudio.tex | 30 ++++++ .../datasets/Meshes/3elt.mat | Bin 0 -> 118304 bytes .../datasets/Meshes/airfoil1.mat | Bin 0 -> 105639 bytes .../datasets/Meshes/barth.mat | Bin 0 -> 216236 bytes .../datasets/Meshes/crack_dual.mat | Bin 0 -> 167451 bytes .../datasets/Meshes/grid2.mat | Bin 0 -> 45116 bytes .../datasets/clusterincluster.m | 43 ++++++++ .../datasets/corners.m | 35 +++++++ .../datasets/crescentfullmoon.m | 31 ++++++ .../datasets/getGraphs.m | 30 ++++++ .../datasets/getPoints.m | 63 ++++++++++++ .../datasets/gplotLength.m | 48 +++++++++ .../datasets/halfkernel.m | 32 ++++++ .../datasets/outlier.m | 38 +++++++ .../datasets/twospirals.m | 34 +++++++ .../src/ClusterGraphs.m | 65 ++++++++++++ .../src/ClusterMetrics.m | 13 +++ .../src/ClusterPoints.m | 64 ++++++++++++ .../src/CreateLapl.m | 18 ++++ .../src/epsilonSimGraph.m | 19 ++++ .../src/gplotLength.m | 48 +++++++++ mp4/Project_4_Maggioni_Claudio/src/gplotg.m | 61 +++++++++++ mp4/Project_4_Maggioni_Claudio/src/gplotmap.m | 86 ++++++++++++++++ .../src/isConnected.m | 70 +++++++++++++ .../src/kNNSimGraph.m | 28 ++++++ .../src/kmeans_mod.m | 57 +++++++++++ .../src/minSpanTree.m | 51 ++++++++++ .../src/setfilter.m | 20 ++++ .../src/similarityfunc.m | 19 ++++ mp4/assignment.sty | 95 ++++++++++++++++++ mp4/usi_inf.pdf | Bin 0 -> 34678 bytes 32 files changed, 1113 insertions(+) create mode 100644 mp4/Makefile create mode 100644 mp4/Project_4_Maggioni_Claudio.tex create mode 100644 mp4/Project_4_Maggioni_Claudio/datasets/Meshes/3elt.mat create mode 100644 mp4/Project_4_Maggioni_Claudio/datasets/Meshes/airfoil1.mat create mode 100644 mp4/Project_4_Maggioni_Claudio/datasets/Meshes/barth.mat create mode 100755 mp4/Project_4_Maggioni_Claudio/datasets/Meshes/crack_dual.mat create mode 100644 mp4/Project_4_Maggioni_Claudio/datasets/Meshes/grid2.mat create mode 100755 mp4/Project_4_Maggioni_Claudio/datasets/clusterincluster.m create mode 100755 mp4/Project_4_Maggioni_Claudio/datasets/corners.m create mode 100755 mp4/Project_4_Maggioni_Claudio/datasets/crescentfullmoon.m create mode 100644 mp4/Project_4_Maggioni_Claudio/datasets/getGraphs.m create mode 100644 mp4/Project_4_Maggioni_Claudio/datasets/getPoints.m create mode 100644 mp4/Project_4_Maggioni_Claudio/datasets/gplotLength.m create mode 100755 mp4/Project_4_Maggioni_Claudio/datasets/halfkernel.m create mode 100755 mp4/Project_4_Maggioni_Claudio/datasets/outlier.m create mode 100755 mp4/Project_4_Maggioni_Claudio/datasets/twospirals.m create mode 100644 mp4/Project_4_Maggioni_Claudio/src/ClusterGraphs.m create mode 100644 mp4/Project_4_Maggioni_Claudio/src/ClusterMetrics.m create mode 100644 mp4/Project_4_Maggioni_Claudio/src/ClusterPoints.m create mode 100644 mp4/Project_4_Maggioni_Claudio/src/CreateLapl.m create mode 100644 mp4/Project_4_Maggioni_Claudio/src/epsilonSimGraph.m create mode 100644 mp4/Project_4_Maggioni_Claudio/src/gplotLength.m create mode 100644 mp4/Project_4_Maggioni_Claudio/src/gplotg.m create mode 100644 mp4/Project_4_Maggioni_Claudio/src/gplotmap.m create mode 100644 mp4/Project_4_Maggioni_Claudio/src/isConnected.m create mode 100644 mp4/Project_4_Maggioni_Claudio/src/kNNSimGraph.m create mode 100644 mp4/Project_4_Maggioni_Claudio/src/kmeans_mod.m create mode 100644 mp4/Project_4_Maggioni_Claudio/src/minSpanTree.m create mode 100644 mp4/Project_4_Maggioni_Claudio/src/setfilter.m create mode 100644 mp4/Project_4_Maggioni_Claudio/src/similarityfunc.m create mode 100644 mp4/assignment.sty create mode 100644 mp4/usi_inf.pdf diff --git a/mp4/Makefile b/mp4/Makefile new file mode 100644 index 0000000..1b05f7f --- /dev/null +++ b/mp4/Makefile @@ -0,0 +1,15 @@ +filename=template + +pdf: + pdflatex ${filename} + #bibtex ${filename} + pdflatex ${filename} + pdflatex ${filename} + make clean + +read: + evince ${filename}.pdf & + + +clean: + rm -f *.out *.log *.bbl *.blg *.aux ${filename}.log ${filename}.ps ${filename}.aux ${filename}.out ${filename}.dvi ${filename}.bbl ${filename}.blg diff --git a/mp4/Project_4_Maggioni_Claudio.tex b/mp4/Project_4_Maggioni_Claudio.tex new file mode 100644 index 0000000..b07e936 --- /dev/null +++ b/mp4/Project_4_Maggioni_Claudio.tex @@ -0,0 +1,30 @@ +\documentclass[unicode,11pt,a4paper,oneside,numbers=endperiod,openany]{scrartcl} + +\input{assignment.sty} + + + + +\begin{document} + + +\setassignment +\setduedate{Wednesday, 18 November 2020, 11:55 PM} + +\serieheader{Numerical Computing}{2020}{Student: FULL NAME}{Discussed with: FULL NAME}{Solution for Project 4}{} +\newline + +\assignmentpolicy + + +\begin{enumerate} + +\item \textbf{Spectral clustering of non-convex sets [60 points]:} + + +\item \textbf{Spectral clustering of real-world graphs [40 points]:} + +\end{enumerate} + + +\end{document} diff --git 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sparse(ai(ind),aj(ind),1); +[gpx,gpy] = gplot(thisa,x); +if (~isempty(gpx)), + ph(i) = plot(gpx,gpy,'-','Color',cm(i,:),'LineWidth',linewidth); + axis off +end + +end + diff --git a/mp4/Project_4_Maggioni_Claudio/datasets/halfkernel.m b/mp4/Project_4_Maggioni_Claudio/datasets/halfkernel.m new file mode 100755 index 0000000..1cb07a7 --- /dev/null +++ b/mp4/Project_4_Maggioni_Claudio/datasets/halfkernel.m @@ -0,0 +1,32 @@ +function data = halfkernel(N, minx, r1, r2, noise, ratio) + +if nargin < 1 + N = 1000; +end +if mod(N,2) ~= 0 + N = N + 1; +end +if nargin < 2 + minx = -20; +end +if nargin < 3 + r1 = 20; +end +if nargin < 4 + r2 = 35; +end +if nargin < 5 + noise = 4; +end +if nargin < 6 + ratio = 0.6; +end + +phi1 = rand(N/2,1) * pi; +inner = [minx + r1 * sin(phi1) - .5 * noise + noise * rand(N/2,1) r1 * ratio * cos(phi1) - .5 * noise + noise * rand(N/2,1) ones(N/2,1)]; + +phi2 = rand(N/2,1) * pi; +outer = [minx + r2 * sin(phi2) - .5 * noise + noise * rand(N/2,1) r2 * ratio * cos(phi2) - .5 * noise + noise * rand(N/2,1) zeros(N/2,1)]; + +data = [inner/4; outer/4]; +end \ No newline at end of file diff --git a/mp4/Project_4_Maggioni_Claudio/datasets/outlier.m b/mp4/Project_4_Maggioni_Claudio/datasets/outlier.m new file mode 100755 index 0000000..2992e2f --- /dev/null +++ b/mp4/Project_4_Maggioni_Claudio/datasets/outlier.m @@ -0,0 +1,38 @@ +function data = outlier(N, r, dist, outliers, noise) + + if nargin < 1 + N = 600; + end + if nargin < 2 + r = 20; + end + if nargin < 3 + dist = 30; + end + if nargin < 4 + outliers = 0.04; + end + if nargin < 5 + noise = 5; + end + + N1 = round(N * (.5-outliers)); + N2 = N1; + N3 = round(N * outliers); + N4 = N-N1-N2-N3; + + phi1 = rand(N1,1) * pi; + r1 = sqrt(rand(N1,1))*r; + P1 = [-dist + r1.*sin(phi1) r1.*cos(phi1) zeros(N1,1)]; + + phi2 = rand(N2,1) * pi; + r2 = sqrt(rand(N2,1))*r; + P2 = [dist - r2.*sin(phi2) r2.*cos(phi2) 3*ones(N2,1)]; + + P3 = [rand(N3,1)*noise dist+rand(N3,1)*noise 2*ones(N3,1)]; + + P4 = [rand(N4,1)*noise -dist+rand(N4,1)*noise ones(N4,1)]; + + data = [P1/4.5; P2/4.5; P3/4.5; P4/4.5]; + +end \ No newline at end of file diff --git a/mp4/Project_4_Maggioni_Claudio/datasets/twospirals.m b/mp4/Project_4_Maggioni_Claudio/datasets/twospirals.m new file mode 100755 index 0000000..52ffa8b --- /dev/null +++ b/mp4/Project_4_Maggioni_Claudio/datasets/twospirals.m @@ -0,0 +1,34 @@ +function data = twospirals(N, degrees, start, noise) +% Generate "two spirals" dataset with N instances. +% degrees controls the length of the spirals +% start determines how far from the origin the spirals start, in degrees +% noise displaces the instances from the spiral. +% 0 is no noise, at 1 the spirals will start overlapping + + if nargin < 1 + N = 2000; + end + if nargin < 2 + degrees = 570; + end + if nargin < 3 + start = 90; + end + if nargin < 5 + noise = 0.2; + end + + deg2rad = (2*pi)/360; + start = start * deg2rad; + + N1 = floor(N/2); + N2 = N-N1; + + n = start + sqrt(rand(N1,1)) * degrees * deg2rad; + d1 = [-cos(n).*n + rand(N1,1)*noise sin(n).*n+rand(N1,1)*noise zeros(N1,1)]; + + n = start + sqrt(rand(N1,1)) * degrees * deg2rad; + d2 = [cos(n).*n+rand(N2,1)*noise -sin(n).*n+rand(N2,1)*noise ones(N2,1)]; + + data = [d1/2;d2/2]; +end \ No newline at end of file diff --git a/mp4/Project_4_Maggioni_Claudio/src/ClusterGraphs.m b/mp4/Project_4_Maggioni_Claudio/src/ClusterGraphs.m new file mode 100644 index 0000000..f854021 --- /dev/null +++ b/mp4/Project_4_Maggioni_Claudio/src/ClusterGraphs.m @@ -0,0 +1,65 @@ +% Cluster 2D real-world graphs with spectral clustering and compare with k-means +% USI, ICS, Lugano +% Numerical Computing + +clear all;close all; +warning OFF; + +addpath ../datasets +addpath ../datasets/Meshes + +load airfoil1.mat +% load barth.mat +% load grid2.mat +% load 3elt.mat + +% 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); + +figure; +spy(W) +title('Adjacency matrix') +%% 2a) Create the Laplacian matrix and plot the graph using the 2nd and 3rd eigenvectors +% \----------------------------/ +% Your implementation +% \----------------------------/ + +% Eigen-decomposition +% \----------------------------/ +% Your implementation +% \----------------------------/ + +% 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') + +%% 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 +% \----------------------------/ + + +% 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 diff --git a/mp4/Project_4_Maggioni_Claudio/src/ClusterMetrics.m b/mp4/Project_4_Maggioni_Claudio/src/ClusterMetrics.m new file mode 100644 index 0000000..9ee5c89 --- /dev/null +++ b/mp4/Project_4_Maggioni_Claudio/src/ClusterMetrics.m @@ -0,0 +1,13 @@ +function [Spec_nodes,Kmeans_nodes] = ClusterMetrics(K,x_spec,x_kmeans) +%% METRICS +Spec_nodes = 0; +Kmeans_nodes = 0; + + % 2c) Calculate the number of nodes per cluster (for k-means and spectral + % clustering) and plot them in a histogram. + +% \----------------------------/ +% Your implementation +% \----------------------------/ + +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 new file mode 100644 index 0000000..7154f3f --- /dev/null +++ b/mp4/Project_4_Maggioni_Claudio/src/ClusterPoints.m @@ -0,0 +1,64 @@ +% 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') \ No newline at end of file diff --git a/mp4/Project_4_Maggioni_Claudio/src/CreateLapl.m b/mp4/Project_4_Maggioni_Claudio/src/CreateLapl.m new file mode 100644 index 0000000..5068fbd --- /dev/null +++ b/mp4/Project_4_Maggioni_Claudio/src/CreateLapl.m @@ -0,0 +1,18 @@ +function [L,Diag] = CreateLapl(W) +% Create the Laplacian matrix of a graph +% Input +% W : Adjacency matrix +% Output +% L : Laplacian + + +% Degree matrix +Diag = zeros(size(W,1)); +for i = 1:size(W,1) + Diag(i,i) = sum(W(:,i)); +end + +% Construct the Laplacian +L = Diag - W; + +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 new file mode 100644 index 0000000..58faba2 --- /dev/null +++ b/mp4/Project_4_Maggioni_Claudio/src/epsilonSimGraph.m @@ -0,0 +1,19 @@ +function [G] = epsilonSimGraph(epsilon, Pts, S) +% Construct an epsilon similarity graph +% Input +% epsilon: size of neighborhood (calculate from Prim's Algorithm) +% Pts : coordinate list of the sample +% +% Output +% A : the epsilon similarity matrix +% +% USI, ICS, Lugano +% Numerical Computing + +fprintf('----------------------------\n'); +fprintf('epsilon similarity graph\n'); +fprintf('----------------------------\n'); + +G = S <= epsilon; + +end \ No newline at end of file diff --git a/mp4/Project_4_Maggioni_Claudio/src/gplotLength.m b/mp4/Project_4_Maggioni_Claudio/src/gplotLength.m new file mode 100644 index 0000000..a891f4f --- /dev/null +++ b/mp4/Project_4_Maggioni_Claudio/src/gplotLength.m @@ -0,0 +1,48 @@ +function [d] = gplotLength(a, x, linewidth) +% function [d] = gplotLength(a, x,linewidth) +% +% plot with colors depending on lengths of +% edges in x, +% a: Adjacency +% x: coords +% linewidth: for ploting + +[ai,aj] = find(a); +m = length(ai); +d = double(a); + +for i = 1:m, + d(ai(i),aj(i)) = norm(x(ai(i),:)-x(aj(i),:)); +end + +[di,dj,dv] = find(d); + +sdv = sort(dv); +l = length(sdv); + +ran = [64:-1:0]/64; +ran = ran.^2; +ran = 1-ran; + +ll = round([1:l/65:l]); +ranges = sdv(ll); + +clf; hold on; +set(gca,'Color',[0 0 0]) + +cm = jet; + +%cm = .3+.7*cm; + +for i = 1:64; +ind = (dv <= ranges(i+1))&(dv>ranges(i)); + +thisa = sparse(ai(ind),aj(ind),1); +[gpx,gpy] = gplot(thisa,x); +if (~isempty(gpx)), + ph(i) = plot(gpx,gpy,'-','Color',cm(i,:),'LineWidth',linewidth); + axis off +end + +end + diff --git a/mp4/Project_4_Maggioni_Claudio/src/gplotg.m b/mp4/Project_4_Maggioni_Claudio/src/gplotg.m new file mode 100644 index 0000000..65acf22 --- /dev/null +++ b/mp4/Project_4_Maggioni_Claudio/src/gplotg.m @@ -0,0 +1,61 @@ +function handle = gplotg(A,xy,lc) +% GPLOTG : Plot a "graph theoretic" graph. +% +% handle = gplotg(A,xy) plots the graph specified by A and xy. +% A graph, G, is a set of nodes numbered from 1 to n, +% and a set of connections, or edges, between them. +% In order to plot G, two matrices are needed. +% The adjacency matrix, A, has a(i,j) nonzero if and +% only if node i is connected to node j. The coordinates +% array, xy, is an n-by-2 or n-by-3 matrix with the position +% for node i in the i-th row, xy(i,:) = [x(i) y(i)], +% or xy(i,:) = [x(i) y(i) z(i)]. +% +% gplotg(A,xy,lc) uses line type and color instead of the +% default, 'r-'. For example, lc = 'g:'. See PLOT. +% +% Unlike gplot, gplotg sets 'erasemode' to 'none' +% so a graph won't redraw if something is drawn over it. +% Also, gplotg returns the handle to the plot. +% Also, gplotg can handle graphs with 3D coordinates. +% +% See also: SPY, TPLOT, SUBMESH, UNMESH. +% +% John Gilbert, 1991. +% Modified 1-21-91, LS; 2-28-92, CBM; 6-14-01, JRG; +% Copyright (c) 1991-92 by the MathWorks, Inc. +% John Gilbert and Shanghua Teng, 1992-1993. +% Copyright (c) 1990-1996 by Xerox Corporation. All rights reserved. +% HELP COPYRIGHT for complete copyright and licensing notice. + +if nargin < 3, + lc = 'r-'; +end; + +[i,j] = find(A); +[ignore, p] = sort(max(i,j)); +i = i(p); +j = j(p); + +% Create a long, NaN-seperated list of line segments, +% rather than individual segments. + +X = [ xy(i,1) xy(j,1) NaN*ones(size(i))]'; +Y = [ xy(i,2) xy(j,2) NaN*ones(size(i))]'; +X = X(:); +Y = Y(:); + +if size(xy,2) == 2 + h = plot (X, Y, lc, 'erasemode', 'none'); +else + set(gca,'drawmode','fast'); + Z = [ xy(i,3) xy(j,3) NaN*ones(size(i))]'; + Z = Z(:); + h = plot3 (X, Y, Z, lc, 'erasemode', 'none'); +end; + +axis equal; +axis off; +if nargout >= 1 + handle = h; +end; diff --git a/mp4/Project_4_Maggioni_Claudio/src/gplotmap.m b/mp4/Project_4_Maggioni_Claudio/src/gplotmap.m new file mode 100644 index 0000000..51aeb1d --- /dev/null +++ b/mp4/Project_4_Maggioni_Claudio/src/gplotmap.m @@ -0,0 +1,86 @@ +function handle = gplotmap(A,xy,map,pcolor,ecolor) +% GPLOTMAP : Plot a partitioned graph in 2 or 3 dimensions. +% +% gplotmap(A,xy,map) plots the n-vertex graph specified +% by the n by n adjacency (or Laplacian) matrix A +% and the n by 2 or 3 matrix of coordinates xy. +% Argument map is an n-vector of part numbers, which +% assigns each vertex to a part. +% +% By default, edges that join different parts are omitted, and +% the picture shows each part in a different color. The call +% +% gplotmap(A,xy,map,pcolor,ecolor) +% +% uses color "pcolor" for the parts and "ecolor" for the +% edges between the parts. If "pcolor" has multiple rows, +% each part gets the color of one row (in cyclic order). +% +% See also GPLOTPART. +% +% John Gilbert 2 August 1994 +% Copyright (c) 1990-1996 by Xerox Corporation. All rights reserved. +% HELP COPYRIGHT for complete copyright and licensing notice. + +[n,n] = size(A); +if nargin < 3, + map = zeros(1,n); +end; +if nargin < 4 + pcolor = []; +end; +if nargin < 5, + ecolor = []; +end; + +parts = setfilter(map); +nparts = length(parts); +if length(pcolor) == 0, + pcolor = hsv(nparts); + pcolor = pcolor(randperm(nparts),:); +end; + +% clf reset +% colordef(gcf,'black') +if size(xy,2) == 2 + axis([min(xy(:,1)) max(xy(:,1)) min(xy(:,2)) max(xy(:,2))]); +else + axis([min(xy(:,1)) max(xy(:,1)) min(xy(:,2)) max(xy(:,2)) ... + min(xy(:,3)) max(xy(:,3))]); +end; + +axis equal; +axis off; +lighting gouraud; +hold on + +% Count and plot the separating edges. +[i,j] = find(A); +f = find(map(i) > map(j)); +if length(f) +% xlabel( [int2str(length(f)) ' cut edges on ' int2str(nparts) ' partitions'],'visible','on'); + if length(ecolor) + cut = sparse(i(f),j(f),1,n,n); + set(gplotg(cut,xy,'-'),'color',ecolor); + end; +else +% xlabel('0 cut edges','visible','on'); +end; + +% Plot each piece. +ncolor = 1; +for partnumber = parts; + c = pcolor(ncolor,:); + ncolor = rem(ncolor, size(pcolor,1)) + 1; + part = find(map == partnumber); + set(gplotg(A(part,part),xy(part,:),'-'),'color',c); + if n < 500, + if size(xy,2) == 2 + set(plot(xy(part,1),xy(part,2),'o'),'color',c); + else + set(plot3(xy(part,1),xy(part,2),xy(part,3),'o'),'color',c); + end; + end; +end; + +hold off diff --git a/mp4/Project_4_Maggioni_Claudio/src/isConnected.m b/mp4/Project_4_Maggioni_Claudio/src/isConnected.m new file mode 100644 index 0000000..1a398d8 --- /dev/null +++ b/mp4/Project_4_Maggioni_Claudio/src/isConnected.m @@ -0,0 +1,70 @@ +%################################################################## +% Determine if a graph is connected +% Idea by Ed Scheinerman, circa 2006, source: http://www.ams.jhu.edu/~ers/matgraph/ +% routine: matgraph/@graph/isconnected.m +% +% INPUTS: adjacency matrix, nxn +% OUTPUTS: Boolean variable, 0 or 1 +% +% Note: This function works only for undirected graphs. +% GB: last updated, Sep 23 2012 +%################################################################## + +function S = isConnected(adj) + +if not(isempty(find(sum(adj)==0))); S = false; return; end + +n = length(adj); +x = [1; zeros(n-1,1)]; % [1,0,...0] nx1 vector + +while 1 + y = x; + x = adj*x + x; + x = x>0; + + if x==y; break; end + +end + +S = true; +if sum(x) 0 then the graph is connected +% a=algebraic_connectivity(adj); +% S = false; if a>0; S = true; end + +% Alternative 2 ========================================================== +% Uses the fact that multiplying the adj matrix to itself k times give the +% number of ways to get from i to j in k steps. If the end of the +% multiplication in the sum of all matrices there are 0 entries then the +% graph is disconnected. Computationally intensive, but can be sped up by +% the fact that in practice the diameter is very short compared to n, so it +% will terminate in order of log(n)? steps. +% function S=isconnected(el): +% +% S=false; +% +% adj=edgeL2adj(el); +% n=numnodes(adj); % number of nodes +% adjn=zeros(n); +% +% adji=adj; +% for i=1:n +% adjn=adjn+adji; +% adji=adji*adj; +% +% if length(find(adjn==0))==0 +% S=true; +% return +% end +% end + +% Alternative 3 ========================================================== +% Find all connected components, if their number is 1, the graph is +% connected. Use find_conn_comp(adj). \ No newline at end of file diff --git a/mp4/Project_4_Maggioni_Claudio/src/kNNSimGraph.m b/mp4/Project_4_Maggioni_Claudio/src/kNNSimGraph.m new file mode 100644 index 0000000..8584804 --- /dev/null +++ b/mp4/Project_4_Maggioni_Claudio/src/kNNSimGraph.m @@ -0,0 +1,28 @@ +function [G] = kNNSimGraph(Pts) +% Construct a k-nearest neighbors similarity graph +% Input +% k : # of neighbors +% Pts : coordinate list of the sample +% +% Output +% G : the kNN similarity matrix + + +n = length(Pts(:,1)); +kn = ceil(2*log(n)); + + +fprintf('kNN similarity graph\n'); + for i = 1:n + s = repmat(Pts(i,:),n,1); + d = Pts - s; +% e = diag(d*d'); + e = sum(d.^2,2); + [val,ind] = sort(e); + ind(1) = []; + nbrs = ind(1:kn); + G(i,nbrs) = 1; + G(nbrs,i) = 1; + 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 new file mode 100644 index 0000000..b38e2c5 --- /dev/null +++ b/mp4/Project_4_Maggioni_Claudio/src/kmeans_mod.m @@ -0,0 +1,57 @@ +function [D,x] = kmeans_mod(Y,K,n) +% Function to perform k-means clustering +% -------------------------------------- +% Input +% Y: data matrix +% K: # of clusters +% n: number of points +% Output +% D: centroids +% x: assignment(indicator) vector + + +cand = unique(round(10000*Y)/10000,'rows'); +c = datasample(cand,K,'Replace',false); % pick K random input pts as initial centroids +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 + D_old = D; + % Assign points to clusters + for i = 1:n + min = inf; + for k = 1:K + dist = norm(Y(i,:) - D(k,:)); + if dist < min + min = dist; + x(i) = k; + end + end + end + + % Update centroid locations + for k = 1:K + ind = find(x == k); + if length(ind) == 1 + D(k,:) = Y(ind,:); + else + D(k,:) = mean(Y(ind,:)); + end + end + + count = count + 1; +end + +for i = 1:n + min = inf; + for k = 1:K + dist = norm(Y(i,:) - D(k,:)); + if dist < min + min = dist; + x(i) = k; + end + end +end +end + diff --git a/mp4/Project_4_Maggioni_Claudio/src/minSpanTree.m b/mp4/Project_4_Maggioni_Claudio/src/minSpanTree.m new file mode 100644 index 0000000..57abff4 --- /dev/null +++ b/mp4/Project_4_Maggioni_Claudio/src/minSpanTree.m @@ -0,0 +1,51 @@ +function A_sp = minSpanTree(A) +%MINSPANTREE Prim's minimal spanning tree algorithm + +% @input A, NxN adjacency matrix +% @output A_sp, NxN adjacency matrix of minimum spanning tree + +% Prim's alg idea: +% start at any node, find closest neighbor and mark edges +% for all remaining nodes, find closest to previous cluster, mark edge +% continue until no nodes remain +% +% INPUTS: graph defined by adjacency matrix, nxn +% OUTPUTS: matrix specifying minimum spanning tree (subgraph), nxn +% +% Other routines used: isConnected.m +% Updated: cleaned fprintf + +% IB Last updated: 3/24/14 + + +A_sp = []; + +% check if graph is connected: +if not(isConnected(A)); fprintf('This graph is not connected. No spanning tree exists.\n'); return; end + +n = length(A); % number of nodes +A_sp = sparse(n,n); % initialize tree + +A(A==0)=inf; % set all zeros in the matrix to inf + +conn_nodes = 1; % nodes part of the min-span-tree +rem_nodes = [2:n]; % remaining nodes + +while ~isempty(rem_nodes) + + [minlink]=min(min(A(conn_nodes,rem_nodes))); + ind=find(A(conn_nodes,rem_nodes)==minlink); + + [ind_i,ind_j] = ind2sub([length(conn_nodes),length(rem_nodes)],ind(1)); + + i=conn_nodes(ind_i); j=rem_nodes(ind_j); % gets back to adj indices + A_sp(i,j)=A(i,j); A_sp(j,i)=A(j,i); + conn_nodes = [conn_nodes j]; %#ok + rem_nodes = setdiff(rem_nodes,j); + +end + + + + +end \ No newline at end of file diff --git a/mp4/Project_4_Maggioni_Claudio/src/setfilter.m b/mp4/Project_4_Maggioni_Claudio/src/setfilter.m new file mode 100644 index 0000000..c3dc545 --- /dev/null +++ b/mp4/Project_4_Maggioni_Claudio/src/setfilter.m @@ -0,0 +1,20 @@ +function B = setfilter(A) +% SETFILTER : Sort and remove duplicates. +% +% B = setfilter(A) returns a row vector with one occurrence +% of each different element of A, in sorted order. +% +% Based on code by Asko Huuskonen, Finnish Meteorological Institute, +% Asko.Huuskonen@fmi.fi, posted to comp.soft-sys.matlab. +% This version by John Gilbert, Xerox PARC, 27 Sep 1993 +% Copyright (c) 1990-1996 by Xerox Corporation. All rights reserved. +% HELP COPYRIGHT for complete copyright and licensing notice. + +if length(A) == 0 + B = []; + return; +end; + +B = sort(A(:)); +B(find(diff(B)==0)) = []; +B = B.'; diff --git a/mp4/Project_4_Maggioni_Claudio/src/similarityfunc.m b/mp4/Project_4_Maggioni_Claudio/src/similarityfunc.m new file mode 100644 index 0000000..25e15a8 --- /dev/null +++ b/mp4/Project_4_Maggioni_Claudio/src/similarityfunc.m @@ -0,0 +1,19 @@ +function [S] = similarityfunc(Pts, sigma) +% Create the similarity matrix S from the coordinate list of the input +% points +% dimosthenis.pasadakis@usi.ch +% ICS, USI. + +if nargin < 2 + % Choose \sigma ~ 2*log(n) + n = length(Pts(:,1)); + sigma = log(n); +end + +fprintf('----------------------------\n'); +fprintf('Gaussian similarity function\n'); +fprintf('----------------------------\n'); +S = squareform(pdist(Pts)); +S = exp(-S.^2 ./ (2*sigma^2)); + +end \ No newline at end of file diff --git a/mp4/assignment.sty b/mp4/assignment.sty new file mode 100644 index 0000000..54ff904 --- /dev/null +++ b/mp4/assignment.sty @@ -0,0 +1,95 @@ +\usepackage{ifthen} +\usepackage[utf8]{inputenc} +\usepackage{graphics} +\usepackage{graphicx} +\usepackage{hyperref} + +\pagestyle{plain} +\voffset -5mm +\oddsidemargin 0mm +\evensidemargin -11mm +\marginparwidth 2cm +\marginparsep 0pt +\topmargin 0mm +\headheight 0pt +\headsep 0pt +\topskip 0pt +\textheight 255mm +\textwidth 165mm + +\newcommand{\duedate} {} +\newcommand{\setduedate}[1]{% +\renewcommand\duedate {Due date:~ #1}} +\newcommand\isassignment {false} +\newcommand{\setassignment}{\renewcommand\isassignment {true}} +\newcommand{\ifassignment}[1]{\ifthenelse{\boolean{\isassignment}}{#1}{}} +\newcommand{\ifnotassignment}[1]{\ifthenelse{\boolean{\isassignment}}{}{#1}} + +\newcommand{\assignmentpolicy}{ +\begin{table}[h] +\begin{center} +\scalebox{0.8} {% +\begin{tabular}{|p{0.02cm}p{16cm}|} +\hline +&\\ +\multicolumn{2}{|c|}{\Large\textbf{Numerical Computing 2020 --- Submission Instructions}}\\ +\multicolumn{2}{|c|}{\large\textbf{(Please, notice that following instructions are mandatory: }}\\ +\multicolumn{2}{|c|}{\large\textbf{submissions that don't comply with, won't be considered)}}\\ +&\\ +\textbullet & Assignments must be submitted to \href{https://www.icorsi.ch/course/view.php?id=10018}{iCorsi} (i.e. in electronic format).\\ +\textbullet & Provide both executable package and sources (e.g. C/C++ files, Matlab). +If you are using libraries, please add them in the file. Sources must be organized in directories called:\\ +\multicolumn{2}{|c|}{\textit{Project\_number\_lastname\_firstname}}\\ +& and the file must be called:\\ +\multicolumn{2}{|c|}{\textit{project\_number\_lastname\_firstname.zip}}\\ +\multicolumn{2}{|c|}{\textit{project\_number\_lastname\_firstname.pdf}}\\ +\textbullet & The TAs will grade your project by reviewing your project write-up, and looking at the implementation + you attempted, and benchmarking your code's performance.\\ + +\textbullet & You are allowed to discuss all questions with anyone you like; however: (i) your submission must list anyone you discussed problems with and (ii) you must write up your submission independently.\\ +\hline +\end{tabular} +} +\end{center} +\end{table} +} +\newcommand{\punkte}[1]{\hspace{1ex}\emph{\mdseries\hfill(#1~\ifcase#1{Points}\or{Points}\else{Points}\fi)}} + + +\newcommand\serieheader[6]{ +\thispagestyle{empty}% +\begin{flushleft} +\includegraphics[width=0.4\textwidth]{usi_inf} +\end{flushleft} + \noindent% + {\large\ignorespaces{\textbf{#1}}\hspace{\fill}\ignorespaces{ \textbf{#2}}}\\ \\% + {\large\ignorespaces #3 \hspace{\fill}\ignorespaces #4}\\ + \noindent% + \bigskip + \hrule\par\bigskip\noindent% + \bigskip {\ignorespaces {\Large{\textbf{#5}}} + \hspace{\fill}\ignorespaces \large \ifthenelse{\boolean{\isassignment}}{\duedate}{#6}} + \hrule\par\bigskip\noindent% \linebreak + } + +\makeatletter +\def\enumerateMod{\ifnum \@enumdepth >3 \@toodeep\else + \advance\@enumdepth \@ne + \edef\@enumctr{enum\romannumeral\the\@enumdepth}\list + {\csname label\@enumctr\endcsname}{\usecounter + {\@enumctr}%%%? the following differs from "enumerate" + \topsep0pt% + \partopsep0pt% + \itemsep0pt% + \def\makelabel##1{\hss\llap{##1}}}\fi} +\let\endenumerateMod =\endlist +\makeatother + + + + +\usepackage{textcomp} + + + + diff --git a/mp4/usi_inf.pdf b/mp4/usi_inf.pdf new file mode 100644 index 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