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‎Makefile

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# Makefile to generate fig23.pdf, fig4.pdf
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# Michael Tschannen, 2016
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all: fig23.pdf fig4.pdf
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fig23.pdf: ceskm-distobslen.dat ceskm-distsigman.dat ceskm-obslenp.dat ceskm-obslensigman.dat ceskmfp-distobslen.dat ceskmfp-distsigman.dat ceskmfp-obslenp.dat ceskmfp-obslensigman.dat cesnnpc-distobslen.dat cesnnpc-distsigman.dat cesnnpc-obslenp.dat cesnnpc-obslensigman.dat
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pdflatex -halt-on-error -interaction=batchmode fig23.tex
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ceskm-distobslen.dat:
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matlab -nojvm -r "synthPhaseDiag; exit(0);"
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ceskm-distsigman.dat:
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ceskm-obslenp.dat:
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ceskm-obslensigman.dat:
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ceskmfp-distobslen.dat:
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ceskmfp-distsigman.dat:
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ceskmfp-obslenp.dat:
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ceskmfp-obslensigman.dat:
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cesnnpc-distobslen.dat:
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cesnnpc-distsigman.dat:
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cesnnpc-obslenp.dat:
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cesnnpc-obslensigman.dat:
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fig4.pdf: cesnnpc.dat ceskm.dat
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pdflatex -halt-on-error -interaction=batchmode fig4.tex
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cesnnpc.dat:
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matlab -nojvm -r "testeeg; exit(0);"
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ceskm.dat:
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clean:
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rm *.dat *.log *.gz *.aux
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cleanall:
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rm *.dat *.log *.pdf *.gz *.aux
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‎NNPCDist.m

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% NNPC for precomputed dissimilarity matrix
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% D: Dissimilarity matrix
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% q: Number of nearest neighbors
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% L: Number of clusters
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% labels: Labels assigned to the data points
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function labels = NNPCDist(D,q,L)
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N = size(D,1);
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Z = zeros(N,N);
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% Compute nearest neighbor graph
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for i=1:N
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di = D(:,i);
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di(i) = inf; % avoid that the ith point is selected
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[dio,order] = sort(di, 'ascend');
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Z(i, order(1:q) ) = exp(-2*dio(1:q));
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end
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Z = Z + Z';
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% Normalized spectral clustering
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Dsum = diag(1./sqrt(sum(Z)+eps));
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LN = eye(N) - Dsum*Z*Dsum;
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[~,S,V] = svd(LN);
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if nargin < 3
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singvals = diag(S);
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[~,minidx] = min(diff(singvals(1:(end-1))));
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L = N - minidx;
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end
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VL = V(:,N-L+1:N);
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VL = normr(VL);
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[labels,~] = kmeans(VL,L,'maxiter',1000,'replicates',200,'EmptyAction','singleton');
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end
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‎README.md

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### Instructions for reproducing the numerical results in "Robust nonparametric nearest neighbor random process clustering", 2016, by Michael Tschannen and Helmut Bölcskei
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Requirements: matlab, make, pdflatex
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#### Comparison of NNPC and TSC (see Section 4 in the paper)
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Run "synthDataNNPCvsTSC(0.2)" in Matlab (the argument indicates the noise variance). This will produce a figure showing the clustering error as a function of the observation length M for NNPC and TSC clustering observations stemming from three different generative models. The generative model PSDs will be shown in a separate figure.
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### Figures 2 and 3:
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In terminal, cd to the folder "supp_material_rpc_ext" and type "make fig23.pdf".
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### Table 1:
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1. Download the file "amc_to_matrix.m" from "http://mocap.cs.cmu.edu/tools.php" and move it to "robust_rpc".
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2. Download the motion capture files listed below from "http://mocap.cs.cmu.edu" and move them to the corresponding folders in "robust_rpc".
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3. Run "testMOCAP(1)" and "testMOCAP(2)" in Matlab to reproduce the first and second row of Table 1, respectively.
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File list "MOCAP_S16":
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16_08.amc
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16_11.amc
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16_12.amc
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16_13.amc
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16_14.amc
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16_15.amc
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16_16.amc
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16_17.amc
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16_18.amc
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16_19.amc
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16_20.amc
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16_21.amc
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16_22.amc
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16_23.amc
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16_24.amc
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16_25.amc
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16_26.amc
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16_27.amc
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16_28.amc
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16_29.amc
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16_30.amc
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16_31.amc
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16_32.amc
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16_33.amc
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16_34.amc
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16_35.amc
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16_36.amc
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16_37.amc
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16_38.amc
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16_39.amc
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16_40.amc
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16_41.amc
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16_42.amc
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16_43.amc
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16_44.amc
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16_45.amc
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16_46.amc
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16_47.amc
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16_48.amc
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16_49.amc
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16_50.amc
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16_51.amc
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16_52.amc
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16_53.amc
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16_54.amc
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16_55.amc
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16_56.amc
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16_57.amc
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16_58.amc
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File list "MOCAP_S35":
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35_01.amc
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35_02.amc
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35_03.amc
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35_04.amc
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35_05.amc
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35_06.amc
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35_07.amc
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35_08.amc
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35_09.amc
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35_10.amc
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35_11.amc
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35_12.amc
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35_13.amc
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35_14.amc
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35_15.amc
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35_16.amc
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35_17.amc
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35_18.amc
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35_19.amc
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35_20.amc
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35_21.amc
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35_22.amc
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35_23.amc
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35_24.amc
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35_25.amc
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35_26.amc
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35_28.amc
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35_29.amc
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35_30.amc
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35_31.amc
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35_32.amc
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35_33.amc
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35_34.amc
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#### Table 2 and Figure 4:
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1. Download Set A ("Z.zip") and Set E ("S.zip") from http://ntsa.upf.edu/downloads/andrzejak-rg-et-al-2001-indications-nonlinear-deterministic-and-finite-dimensional and unpack the zip files in the folder "robust_rpc".
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2. In terminal, cd to the folder "robust_rpc" and type "make fig4.pdf".
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‎TSC.m

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% TSC algorithm
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% X: Data matrix containing data points as columns
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% q: Number of nearest neighbors
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% L: Number of clusters
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% labels: Labels assigned to the data points
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function labels = TSC(X,q,L)
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N = size(X,2);
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Z = zeros(N,N);
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D = abs(X'*X);
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Xnorm = normc(X);
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Dnorm = abs(Xnorm'*Xnorm);
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% Compute nearest neighbor graph
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for i=1:N
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di = D(:,i);
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di(i) = -inf; % avoid that the ith point is selected
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[~,order] = sort(di, 'descend');
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dion = Dnorm(order,i);
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Z(i, order(1:q) ) = exp(-2*acos(dion(1:q)));
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end
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Z = Z + Z';
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% Normalized spectral clustering
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Dsum = diag(1./sqrt(sum(Z)+eps));
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LN = eye(N) - Dsum*Z*Dsum;
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[~,S,V] = svd(LN);
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if nargin < 3
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singvals = diag(S);
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[~,minidx] = min(diff(singvals(1:(end-1))));
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L = N - minidx;
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end
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VL = V(:,N-L+1:N);
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VL = normr(VL);
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[labels,~] = kmeans(VL,L,'maxiter',1000,'replicates',200,'EmptyAction','singleton');
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end
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‎clusconfent2.m

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% Compute the entropy of the 2x2 clustering confustion matrix corresponding
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% to labels 'labels' and the ground truth 'gt' (column or row vectors)
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function S = clusconfent2(labels,gt)
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% Swap label indices if needed
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if sum(labels ~= gt) > 0.5
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labels = labels - 1;
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labels(labels == 0) = 2;
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end
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% Compute clustering confusion matrix
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M = zeros(2,2);
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M(1,1) = sum(labels(gt == 1) == 1);
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M(1,2) = sum(labels(gt == 2) == 1);
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M(2,1) = sum(labels(gt == 1) == 2);
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M(2,2) = sum(labels(gt == 2) == 2);
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% Compute entropy
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S = 0;
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for i = 1:2
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for j = 1:2
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if M(i,j) ~= 0
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S = S + M(i,j)*log(sum(M(i,:))/M(i,j));
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end
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end
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end
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S = S/sum(M(:));
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end

‎computece.m

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% Compute minimum clustering error w.r.t. all label permutations (brute
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% force)
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% labels: Vector containing label assignments (values in 1:L)
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% gt: Vector containing ground truth labels (values in 1:L)
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function cemin = computece(labels,gt)
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% Transpose if needed
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if size(labels,2) < size(labels,1); labels = labels'; end
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if size(gt,2) > size(gt,1); gt = gt'; end
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L = max(gt);
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N = length(gt);
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cemin = 1;
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% L! label permutations
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per = perms(1:L)';
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indmatrix = (per(:,1)*ones(1,N) == ones(L,1)*labels);
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for i = 1:size(per,2)
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% Map labels and compute clustering error
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mapmatrix = repmat(per(:,i),1,N);
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ce = sum(mapmatrix(indmatrix) ~= gt)/N;
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if ce < cemin
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cemin = ce;
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end
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end
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end

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