From 0f44ec9e386982835cd3c3c7fe99627a15b1914a Mon Sep 17 00:00:00 2001 From: Ramon Correa Date: Fri, 30 Oct 2020 13:21:24 -0400 Subject: [PATCH 1/4] initial commit --- Ex01_testPCA.m | 61 +++++++++++++++++++- Ex01_testPCA.m~ | 88 +++++++++++++++++++++++++++++ Ex02_testEigenAnalysisPowerMethod.m | 6 ++ 3 files changed, 154 insertions(+), 1 deletion(-) create mode 100644 Ex01_testPCA.m~ diff --git a/Ex01_testPCA.m b/Ex01_testPCA.m index 1181070..a466451 100644 --- a/Ex01_testPCA.m +++ b/Ex01_testPCA.m @@ -1,4 +1,5 @@ -% Principal component analysis +% Ramon Correa (rlcorre@emory.edu) +%Principal component analysis % % BMI500 Course % Lecture: An Introduction to Blind Source Separation and Independent Component Analysis @@ -35,4 +36,62 @@ N = size(x, 1); % The number of channels T = size(x, 2); % The number of samples per channel +PlotECG(x,4,'b',fs,'Raw data channels'); + +x_demeaned = x - mean(x,2)*ones(1,size(x,2)); + +Cx = cov(x_demeaned'); + +[V,D] = eig(Cx,'vector'); + +figure +subplot(1,2,1) +plot(D(end:-1:1)) +grid +xlabel('Index') +ylabel('Eigenvalues'); +title('Eighenvalues in linear scale') +subplot(122) +plot(10*log10(D(end:-1:1)/D(end)) ) +grid +xlabel('Index'); +ylabel('Eigenvalue ratios in dB') +title('Normalzied eighenvalues in log scale') + +x_var = var(x_demeaned,[] ,2 ) %formula 1 +x_var2 = diag(Cx); % formula 2 +% decorrelate the channels +y = V' * x_demeaned; +Cy = cov(y'); +y_var = diag(Cy) + +%check total energy match +x_total_energy = sum(x_var) +Cx_trace = trace(Cx) +eigenvale_sum = sum(D) +Cy_trace = trace(Cy); + +%these values should all be the same as the rotaion doesn't change relative +%distances we are still looking at the same distances. +x_partial_energy = 100.0 * cumsum(D(end:-1:1))./x_total_energy; + +th = 99.9; +N_eighs_to_keep = find(x_partial_energy <= th,1,'last') + +x_compressed = V(:,N - N_eighs_to_keep + 1:N)*y(N-N_eighs_to_keep + 1:N,:); + + +t = (0: T-1)/fs; + +for ch = 1:N + figure + hold on + plot(t,x(ch,:)); + plot(t,x_compressed(ch,:)); + legend(['channel ',num2str(ch),'compressed')]) +end + + + + diff --git a/Ex01_testPCA.m~ b/Ex01_testPCA.m~ new file mode 100644 index 0000000..6cec15c --- /dev/null +++ b/Ex01_testPCA.m~ @@ -0,0 +1,88 @@ +% Ramon Correa (rlcorre@emory.edu) +%Principal component analysis +% +% BMI500 Course +% Lecture: An Introduction to Blind Source Separation and Independent Component Analysis +% By: R. Sameni +% Department of Biomedical Informatics, Emory University, Atlanta, GA, USA +% Fall 2020 +% +% Dependency: The open-source electrophysiological toolbox (OSET): +% https://github.com/alphanumericslab/OSET.git +% OR +% https://gitlab.com/rsameni/OSET.git +% + +clc +clear +close all + +example = 1; +switch example + case 1 % Load a sample EEG signal + load EEGdata textdata data % A sample EEG from the OSET package + fs = 250; + x = data'; % make the data in (channels x samples) format + % Check the channel names + disp(textdata) + case 2 % Load a sample ECG signal + load SampleECG2 data % A sample ECG from the OSET package + fs = 1000; + x = data(:, 2:end)'; % make the data in (channels x samples) format + x = x - LPFilter(x, 1.0/fs); % remove the lowpass baseline + otherwise + error('unknown example'); +end + +N = size(x, 1); % The number of channels +T = size(x, 2); % The number of samples per channel +PlotECG(x,4,'b',fs,'Raw data channels'); + +x_demeaned = x - mean(x,2)*ones(1,size(x,2)); + +Cx = cov(x_demeaned'); + +[V,D] = eig(Cx,'vector'); + +figure +subplot(1,2,1) +plot(D(end:-1:1)) +grid +xlabel('Index') +ylabel('Eigenvalues'); +title('Eighenvalues in linear scale') +subplot(122) +plot(10*log10(D(end:-1:1)/D(end)) ) +grid +xlabel('Index'); +ylabel('Eigenvalue ratios in dB') +title('Normalzied eighenvalues in log scale') + +x_var = var(x_demeaned,[] ,2 ) %formula 1 +x_var2 = diag(Cx); % formula 2 +% decorrelate the channels +y = V' * x_demeaned; +Cy = cov(y'); +y_var = diag(Cy) + +%check total energy match +x_total_energy = sum(x_var) +Cx_trace = trace(Cx) +eigenvale_sum = sum(D) +Cy_trace = trace(Cy); + +%these values should all be the same as the rotaion doesn't change relative +%distances we are still looking at the same distances. +x_partial_energy = 100.0 * cumsum(D(end:-1:1))./x_total_energy; + +th = 99.9; +N_eighs_to_keep = find(x_partial_energy <= th,1,'last') + +x_compressed = V(:,N - N_eighs_to_keep + 1:N)*y(N-N_eighs_to_keep + 1:N,:); + + + + + + + diff --git a/Ex02_testEigenAnalysisPowerMethod.m b/Ex02_testEigenAnalysisPowerMethod.m index f1d95be..1b1e7d5 100644 --- a/Ex02_testEigenAnalysisPowerMethod.m +++ b/Ex02_testEigenAnalysisPowerMethod.m @@ -12,6 +12,12 @@ % https://gitlab.com/rsameni/OSET.git % + +%note that eigs gives you the first few eigenvectors. i guess we can +%estimate this +% i think we have to do power method of slide 57 +%keep doing this to converge onto the eigen vectors +% this converges onto the first eigen vector. close all; clear clc; From 09dab5bba268ff95f1443489079fb900ba2c5209 Mon Sep 17 00:00:00 2001 From: Ramon Correa Date: Fri, 30 Oct 2020 14:02:31 -0400 Subject: [PATCH 2/4] adding example 4 --- Ex04_testEOGArtifactRemoval.m | 15 ++++++++++++ Ex04_testEOGArtifactRemoval.m~ | 45 ++++++++++++++++++++++++++++++++++ 2 files changed, 60 insertions(+) create mode 100644 Ex04_testEOGArtifactRemoval.m~ diff --git a/Ex04_testEOGArtifactRemoval.m b/Ex04_testEOGArtifactRemoval.m index b6c4122..8d9f591 100644 --- a/Ex04_testEOGArtifactRemoval.m +++ b/Ex04_testEOGArtifactRemoval.m @@ -32,3 +32,18 @@ T = size(x, 2); % The number of samples per channel t = (0 : T - 1)/fs; +approach = 'symm'; +g = 'tanh'; +lastEigfastica = N; +numOfIC= N; +interactivePA = ' off'; +[ s_fastica, A_fatsica] = fastica(x,'approach',approach,'g',g,'lastEig',lastEigfastica,'numOfIC',numOfIC,'interactivePCA','off') +Cs = cov(s_fastica'); +lastEigJADE = N; +W_JADE = jadeR(x,lastEigJade); +s_jade = W_JADE * x; +lastEigSOBI = N; +num_cov_matrices = 100; +[W_SOBI,s_sobi] = sobi(x,lastEigSOBI,num_cov_matrices); +PlotECG(s_fastica,4,'r',fs,' Sources extracted by fatsica') + diff --git a/Ex04_testEOGArtifactRemoval.m~ b/Ex04_testEOGArtifactRemoval.m~ new file mode 100644 index 0000000..d3556bf --- /dev/null +++ b/Ex04_testEOGArtifactRemoval.m~ @@ -0,0 +1,45 @@ +% Removing EOG artifacts from EEG signals +% +% BMI500 Course +% Lecture: An Introduction to Blind Source Separation and Independent Component Analysis +% By: R. Sameni +% Department of Biomedical Informatics, Emory University, Atlanta, GA, USA +% Fall 2020 +% +% Dependency: The open-source electrophysiological toolbox (OSET): +% https://github.com/alphanumericslab/OSET.git +% OR +% https://gitlab.com/rsameni/OSET.git +% + +clc +clear +close all + +example = 1; +switch example + case 1 % A sample EEG from the OSET package + load EEGdata textdata data % Load a sample EEG signal + fs = 250; + x = data'; % make the data in (channels x samples) format + % Check the channel names + disp(textdata) + otherwise + error('unknown example'); +end + +N = size(x, 1); % The number of channels +T = size(x, 2); % The number of samples per channel +t = (0 : T - 1)/fs; + +approach = 'symm'; +g = 'tanh'; +lastEigfastica = N; +numOfIC N; +interactivePA = ' off'; +[ s_fastica, A_fatsica] = fastica(x,'approach',approach,'g',g,'lastEig',lastEigfastica,'numOfIC',numOfIC,'interactive','off') +Cs = cov(s_fastica'); +lastEigJADE = N; +W_JADE = jadeR(x,lastEigJade); +s_jade = W + From 7f12816500558e543bc314f25eb28e82a0578802 Mon Sep 17 00:00:00 2001 From: Ramon Correa Date: Wed, 4 Nov 2020 20:44:32 -0500 Subject: [PATCH 3/4] hw commit --- Ex01_testPCA.m | 112 ++++++++++++++-------------- Ex01_testPCA.m~ | 88 ---------------------- Ex02_testEigenAnalysisPowerMethod.m | 32 ++++++-- Ex03_testICAmethods.m | 40 ++++++++++ Ex04_testEOGArtifactRemoval.m | 94 +++++++++++++++++++---- Ex04_testEOGArtifactRemoval.m~ | 45 ----------- Ex05_testFetalECGExtraction.m | 17 ++++- README.md | 75 ++++++++++++++++++- eig_val_time.png | Bin 0 -> 29187 bytes eig_ve_component.png | Bin 0 -> 24732 bytes fastica_pow3_out.png | Bin 0 -> 63004 bytes fastica_skew_out.png | Bin 0 -> 64194 bytes fastica_tanh_out.png | Bin 0 -> 62482 bytes hw.m | 71 ++++++++++++++++++ 14 files changed, 360 insertions(+), 214 deletions(-) delete mode 100644 Ex01_testPCA.m~ delete mode 100644 Ex04_testEOGArtifactRemoval.m~ create mode 100644 eig_val_time.png create mode 100644 eig_ve_component.png create mode 100644 fastica_pow3_out.png create mode 100644 fastica_skew_out.png create mode 100644 fastica_tanh_out.png create mode 100644 hw.m diff --git a/Ex01_testPCA.m b/Ex01_testPCA.m index a466451..99474dd 100644 --- a/Ex01_testPCA.m +++ b/Ex01_testPCA.m @@ -1,5 +1,4 @@ -% Ramon Correa (rlcorre@emory.edu) -%Principal component analysis +% Principal component analysis % % BMI500 Course % Lecture: An Introduction to Blind Source Separation and Independent Component Analysis @@ -16,8 +15,7 @@ clc clear close all - -example = 1; +example = 2; %changing dataset considered switch example case 1 % Load a sample EEG signal load EEGdata textdata data % A sample EEG from the OSET package @@ -33,65 +31,69 @@ otherwise error('unknown example'); end - N = size(x, 1); % The number of channels T = size(x, 2); % The number of samples per channel -PlotECG(x,4,'b',fs,'Raw data channels'); - -x_demeaned = x - mean(x,2)*ones(1,size(x,2)); - -Cx = cov(x_demeaned'); - -[V,D] = eig(Cx,'vector'); - +% Plot the channels +PlotECG(x, 4, 'b', fs, 'Raw data channels'); +% Remove the channel means +x_demeaned = x - mean(x, 2) * ones(1, size(x, 2)); +% Plot the zero-mean channels +% PlotECG(x_demeaned, 4, 'r', fs, 'Zero-mean data channels'); +% Covariance matrix of the input +Cx = cov(x_demeaned') +% Eigenvalue decomposition +[V, D] = eig(Cx, 'vector'); figure -subplot(1,2,1) -plot(D(end:-1:1)) -grid -xlabel('Index') -ylabel('Eigenvalues'); -title('Eighenvalues in linear scale') +subplot(121) +plot(D(end:-1:1)); +grid +xlabel('Index'); +ylabel('Eigenvalue'); +title('Eigenvalues in linear scale'); subplot(122) -plot(10*log10(D(end:-1:1)/D(end)) ) -grid +plot(10*log10(D(end:-1:1)/D(end))); +grid xlabel('Index'); -ylabel('Eigenvalue ratios in dB') -title('Normalzied eighenvalues in log scale') - -x_var = var(x_demeaned,[] ,2 ) %formula 1 -x_var2 = diag(Cx); % formula 2 -% decorrelate the channels -y = V' * x_demeaned; -Cy = cov(y'); +ylabel('Eigenvalue ratios in dB'); +title('Normalized eigenvalues in log scale'); +% Check signal evergy +x_var = var(x_demeaned, [], 2) % Formula 1 +x_var2 = diag(Cx) % formula 2 +% Decorrelate the channels +y = V' * x_demeaned; +Cy = cov(y') y_var = diag(Cy) - -%check total energy match -x_total_energy = sum(x_var) -Cx_trace = trace(Cx) -eigenvale_sum = sum(D) -Cy_trace = trace(Cy); - -%these values should all be the same as the rotaion doesn't change relative -%distances we are still looking at the same distances. -x_partial_energy = 100.0 * cumsum(D(end:-1:1))./x_total_energy; - -th = 99.9; -N_eighs_to_keep = find(x_partial_energy <= th,1,'last') - -x_compressed = V(:,N - N_eighs_to_keep + 1:N)*y(N-N_eighs_to_keep + 1:N,:); - - -t = (0: T-1)/fs; - -for ch = 1:N - figure - hold on - plot(t,x(ch,:)); - plot(t,x_compressed(ch,:)); - legend(['channel ',num2str(ch),'compressed')]) +% PlotECG(y, 4, 'r', fs, 'Decorrelated data channels'); +% Check total energy match +x_total_energy = sum(x_var) +Cx_trace = trace(Cx) +eigenvale_sum = sum(D) +Cy_trace = trace(Cy) +% partial energy in eigenvalues +x_partial_energy = 100.0 * cumsum(D(end : -1 : 1))./x_total_energy +% set a cut off threshold for the eigenvalues +th = 90; % change threshold from 99 to 90 +N_eigs_to_keep = find(x_partial_energy <= th, 1, 'last') + +% find a compressed version of x +x_compressed = V(:, N - N_eigs_to_keep + 1 : N) * y(N - N_eigs_to_keep + 1 : N, :); +% eig(cov(x_compressed')) + +t = (0 : T - 1)/fs; +for ch = 1 : N + figure + hold on + plot(t, x(ch, :)); + plot(t, x_compressed(ch, :)); + legend(['channel ' num2str(ch)], 'compressed'); + grid end - +%here we change the dataset to use the sample dataset two. Our primary +%change was to look into the 90th percentile in signal instead of the 99th +%percentile. It is clearly evident that in some channels a lot of the +%variability is no longer captured. Yet most of the trends are kept as one +%would expect from PCA. diff --git a/Ex01_testPCA.m~ b/Ex01_testPCA.m~ deleted file mode 100644 index 6cec15c..0000000 --- a/Ex01_testPCA.m~ +++ /dev/null @@ -1,88 +0,0 @@ -% Ramon Correa (rlcorre@emory.edu) -%Principal component analysis -% -% BMI500 Course -% Lecture: An Introduction to Blind Source Separation and Independent Component Analysis -% By: R. Sameni -% Department of Biomedical Informatics, Emory University, Atlanta, GA, USA -% Fall 2020 -% -% Dependency: The open-source electrophysiological toolbox (OSET): -% https://github.com/alphanumericslab/OSET.git -% OR -% https://gitlab.com/rsameni/OSET.git -% - -clc -clear -close all - -example = 1; -switch example - case 1 % Load a sample EEG signal - load EEGdata textdata data % A sample EEG from the OSET package - fs = 250; - x = data'; % make the data in (channels x samples) format - % Check the channel names - disp(textdata) - case 2 % Load a sample ECG signal - load SampleECG2 data % A sample ECG from the OSET package - fs = 1000; - x = data(:, 2:end)'; % make the data in (channels x samples) format - x = x - LPFilter(x, 1.0/fs); % remove the lowpass baseline - otherwise - error('unknown example'); -end - -N = size(x, 1); % The number of channels -T = size(x, 2); % The number of samples per channel -PlotECG(x,4,'b',fs,'Raw data channels'); - -x_demeaned = x - mean(x,2)*ones(1,size(x,2)); - -Cx = cov(x_demeaned'); - -[V,D] = eig(Cx,'vector'); - -figure -subplot(1,2,1) -plot(D(end:-1:1)) -grid -xlabel('Index') -ylabel('Eigenvalues'); -title('Eighenvalues in linear scale') -subplot(122) -plot(10*log10(D(end:-1:1)/D(end)) ) -grid -xlabel('Index'); -ylabel('Eigenvalue ratios in dB') -title('Normalzied eighenvalues in log scale') - -x_var = var(x_demeaned,[] ,2 ) %formula 1 -x_var2 = diag(Cx); % formula 2 -% decorrelate the channels -y = V' * x_demeaned; -Cy = cov(y'); -y_var = diag(Cy) - -%check total energy match -x_total_energy = sum(x_var) -Cx_trace = trace(Cx) -eigenvale_sum = sum(D) -Cy_trace = trace(Cy); - -%these values should all be the same as the rotaion doesn't change relative -%distances we are still looking at the same distances. -x_partial_energy = 100.0 * cumsum(D(end:-1:1))./x_total_energy; - -th = 99.9; -N_eighs_to_keep = find(x_partial_energy <= th,1,'last') - -x_compressed = V(:,N - N_eighs_to_keep + 1:N)*y(N-N_eighs_to_keep + 1:N,:); - - - - - - - diff --git a/Ex02_testEigenAnalysisPowerMethod.m b/Ex02_testEigenAnalysisPowerMethod.m index 1b1e7d5..fce2c52 100644 --- a/Ex02_testEigenAnalysisPowerMethod.m +++ b/Ex02_testEigenAnalysisPowerMethod.m @@ -12,12 +12,6 @@ % https://gitlab.com/rsameni/OSET.git % - -%note that eigs gives you the first few eigenvectors. i guess we can -%estimate this -% i think we have to do power method of slide 57 -%keep doing this to converge onto the eigen vectors -% this converges onto the first eigen vector. close all; clear clc; @@ -30,3 +24,29 @@ % Cx = x * x'; Cx = cov(x'); +% Apply eigenvalue decomposition +% Read 'eig' help and compare with 'eigs' +[V,D] = eig(Cx) + +Itr = 20; % The number of power method iterations + +v0 = rand(N, 1); +v1 = EigenAnalysisPowerMethod(Cx, v0, Itr); +scale1 = (Cx*v1)./v1; +lambda1 = mean(scale1) + +C = Cx - lambda1 * (v1 * v1'); +v2 = EigenAnalysisPowerMethod(C, v0, Itr); +scale2 = (Cx*v2)./v2; +lambda2 = mean(scale2) + +C = C - mean(lambda2) * (v2 * v2'); +v3 = EigenAnalysisPowerMethod(C, v0, Itr); +scale3 = (Cx*v3)./v3; +lambda3 = mean(scale3) + +%For thsi section we modified the iteration accunt to see how small the +%iteration count could get to reliably estimate the eigne value. Around +%the 20 iteration count we see stable levels of performance. This is a +%simpler signal and could perhaps not generalzie to larger matrices. + diff --git a/Ex03_testICAmethods.m b/Ex03_testICAmethods.m index af123be..7125312 100644 --- a/Ex03_testICAmethods.m +++ b/Ex03_testICAmethods.m @@ -16,6 +16,7 @@ clear close all +rng(123) %added rng number example = 3; switch example case 1 % A sample EEG from the OSET package @@ -46,3 +47,42 @@ N = size(x, 1); % The number of channels T = size(x, 2); % The number of samples per channel +% Plot the channels +PlotECG(x, 4, 'b', fs, 'Raw data channels'); + +% Run fastica +approach = 'symm'; % 'symm' or 'defl' +g = 'skew'; % 'pow3', 'tanh', 'gauss', 'skew' +lastEigfastica = N; % PCA stage +numOfIC = N; % ICA stage +interactivePCA = 'off'; +[s_fastica, A_fatsica, W_fatsica] = fastica (x, 'approach', approach, 'g', g, 'lastEig', lastEigfastica, 'numOfIC', numOfIC, 'interactivePCA', interactivePCA, 'verbose', 'off', 'displayMode', 'off'); + +% Check the covariance matrix +Cs = cov(s_fastica'); + +% Run JADE +lastEigJADE = N; % PCA stage +W_JADE = jadeR(x, lastEigJADE); +s_jade = W_JADE * x; + +% Run SOBI +lastEigSOBI = N; % PCA stage +num_cov_matrices = 100; +[W_SOBI, s_sobi] = sobi(x, lastEigSOBI, num_cov_matrices); + +% Plot the sources +PlotECG(s_fastica, 4, 'r', fs, 'Sources extracted by fatsica'); + +% Plot the sources +PlotECG(s_jade, 4, 'k', fs, 'Sources extracted by JADE'); + +% Plot the sources +PlotECG(s_sobi, 4, 'm', fs, 'Sources extracted by SOBI'); + +%for this section we compared the changes caused by different +%appriximation approaches. We observed tanh,pow3, and skew to view a small +%subset of variability. We notice that tanh and po3 have the greatest +%agreeement. Meanwhile skew produces slightly different results + + diff --git a/Ex04_testEOGArtifactRemoval.m b/Ex04_testEOGArtifactRemoval.m index 8d9f591..6d0ae4f 100644 --- a/Ex04_testEOGArtifactRemoval.m +++ b/Ex04_testEOGArtifactRemoval.m @@ -32,18 +32,84 @@ T = size(x, 2); % The number of samples per channel t = (0 : T - 1)/fs; -approach = 'symm'; -g = 'tanh'; -lastEigfastica = N; -numOfIC= N; -interactivePA = ' off'; -[ s_fastica, A_fatsica] = fastica(x,'approach',approach,'g',g,'lastEig',lastEigfastica,'numOfIC',numOfIC,'interactivePCA','off') -Cs = cov(s_fastica'); -lastEigJADE = N; -W_JADE = jadeR(x,lastEigJade); -s_jade = W_JADE * x; -lastEigSOBI = N; -num_cov_matrices = 100; -[W_SOBI,s_sobi] = sobi(x,lastEigSOBI,num_cov_matrices); -PlotECG(s_fastica,4,'r',fs,' Sources extracted by fatsica') +% Plot the channels +%PlotECG(x, 4, 'b', fs, 'Raw data channels'); + +% Run JADE +lastEigJADE = N; % PCA stage +W_JADE = jadeR(x, lastEigJADE); +s_jade = W_JADE * x; +A_jade = pinv(W_JADE); % The mixing matrix + +% Plot the sources +% PlotECG(s_jade, 4, 'k', fs, 'Sources extracted by JADE'); + +% Channel denoising by JADE +eog_channel = [2 3]; % check from the plots to visually detect the EOG +s_jade_denoised = s_jade; +s_jade_denoised(eog_channel, :) = 0; +x_denoised_jade = A_jade * s_jade_denoised; + +% Channel denoising by NSCA +eog_channel = 24; +eog_ref = x(eog_channel, :); +energy_envelope_len = round(0.25*fs); +eog_envelope = sqrt(filtfilt(ones(1, energy_envelope_len), energy_envelope_len, eog_ref.^2)); +med = median(eog_envelope); +mx = max(eog_envelope); +%eog_detection_threshold = 0.95 * med + 0.05 * mx; +eog_detection_threshold = 0.90 * med + 0.1 * mx; + +J = eog_envelope >= eog_detection_threshold; +I = 1 : T; + +[s_nsca, W_nsca, A_nsca] = NSCA(x,J, I); +% Channel denoising by JADE +eog_channel = [1 2]; % check from the plots to visually detect the EOG +s_nsca_denoised = s_nsca; +s_nsca_denoised(eog_channel, :) = 0; +x_denoised_nsca = A_nsca * s_nsca_denoised; +% PlotECG(s_nsca, 4, 'r', fs, 'Sources extracted by NSCA'); + +%figure +%hold on +%plot(t, eog_ref); +%plot(t, eog_envelope); +%plot(t, eog_detection_threshold(ones(1, T))); +%grid +%legend('EOG reference channel', 'EOG envelope'); + +% Plot the denoised signals +for ch = 1 : 3 + figure + hold on + plot(t, x(ch, :)); + plot(t, x_denoised_jade(ch, :)); + plot(t, x_denoised_nsca(ch, :)); + legend(['channel ' num2str(ch)], 'denoised by JADE', 'denoised by NSCA'); + disp('Signal change') + disp(std(x(ch,:))) + disp( std(x_denoised_jade(ch, :))); + disp(std( x_denoised_nsca(ch, :))); + grid +end + + +% Run the following script from the OSET package for a more advanced method +%testEOGRemoval + + +%noise removal utilizing NCSA seems to be more aggresive than using jade +%this is reflected in the summary statistics where the standard devieaiton +%of the signal is smallest with nsca. At a high level observation the +%signals appear to be rather similar. On closer inspection we can see +%differences in denoising ocmparing signals from channel 1 and channel 3 +%in the region with a rapid change seen in the 31 second mark we see that +%jade trails behind the NSCA method. Suggesting that jade is more sensitive +%to rapid changes in signals. Meanwhile for regions with a consistent +%signal( i.e flat) both methods are in agreement + + + + diff --git a/Ex04_testEOGArtifactRemoval.m~ b/Ex04_testEOGArtifactRemoval.m~ deleted file mode 100644 index d3556bf..0000000 --- a/Ex04_testEOGArtifactRemoval.m~ +++ /dev/null @@ -1,45 +0,0 @@ -% Removing EOG artifacts from EEG signals -% -% BMI500 Course -% Lecture: An Introduction to Blind Source Separation and Independent Component Analysis -% By: R. Sameni -% Department of Biomedical Informatics, Emory University, Atlanta, GA, USA -% Fall 2020 -% -% Dependency: The open-source electrophysiological toolbox (OSET): -% https://github.com/alphanumericslab/OSET.git -% OR -% https://gitlab.com/rsameni/OSET.git -% - -clc -clear -close all - -example = 1; -switch example - case 1 % A sample EEG from the OSET package - load EEGdata textdata data % Load a sample EEG signal - fs = 250; - x = data'; % make the data in (channels x samples) format - % Check the channel names - disp(textdata) - otherwise - error('unknown example'); -end - -N = size(x, 1); % The number of channels -T = size(x, 2); % The number of samples per channel -t = (0 : T - 1)/fs; - -approach = 'symm'; -g = 'tanh'; -lastEigfastica = N; -numOfIC N; -interactivePA = ' off'; -[ s_fastica, A_fatsica] = fastica(x,'approach',approach,'g',g,'lastEig',lastEigfastica,'numOfIC',numOfIC,'interactive','off') -Cs = cov(s_fastica'); -lastEigJADE = N; -W_JADE = jadeR(x,lastEigJade); -s_jade = W - diff --git a/Ex05_testFetalECGExtraction.m b/Ex05_testFetalECGExtraction.m index 3ac2f31..69af298 100644 --- a/Ex05_testFetalECGExtraction.m +++ b/Ex05_testFetalECGExtraction.m @@ -13,9 +13,18 @@ % % Uncomment the following lines to run advanced demos -testPCAICAPiCAfECGExtraction % Call this demo from the OSET package -% testECGICAPCAPiCAPlot1 +%testPCAICAPiCAfECGExtraction % Call this demo from the OSET package + %testECGICAPCAPiCAPlot1 + % testECGICAPCAPiCAPlot1 -% testAveragefECGbyDeflationAndKF + testAveragefECGbyDeflationAndKF % testICAPiCAAfterMECGCancellation % (using the deflation algorithm + Kalman filter) -% testPCAICAPiCAfECGDenoising % (denoising using BSS and semi-BSS methods) \ No newline at end of file +% testPCAICAPiCAfECGDenoising % (denoising using BSS and semi-BSS methods) + + +% this script appears to be using several model estimation techniques to +% fit a polynomial curve onto the the ECG signal. It allows for an +% interective interpretatatio nof the data which i find quite useful. +% Interestingly enough we can get an ok fit with just 2 parameters to be +% fit producing an error of 1.82% +% meanwhile for the \ No newline at end of file diff --git a/README.md b/README.md index a14ae45..63fab35 100644 --- a/README.md +++ b/README.md @@ -1,2 +1,73 @@ -# BSSPackage -Simplified illustration of blind-source separation algorithms +# question 1 +A) include the writting section of letters + + +B) + +We obtain similar eigenvalues to the one obtained by matlab eig. For the eigenvector we had some initial diferences when it comes to the final values +We were abled to obtain similar direction vectors but their individiual values are different. We ere able to rectify this by normalizing the vectors to +unit norm. The script hw.m also includes the + + + +# question 2 + +![alt text](./eig_val_time.png ) + +![alt text](./eig_ve_component.png) + + + +# question 3: execrises + +## Ex 1 + + +here we change the dataset to use the sample dataset two. Our primary +change was to look into the 90th percentile in signal instead of the 99th +percentile. It is clearly evident that in some channels a lot of the +variability is no longer captured. Yet most of the trends are kept as one +would expect from PCA. + +## Ex 2 + +For thsi section we modified the iteration accunt to see how small the +iteration count could get to reliably estimate the eigne value. Around +the 20 iteration count we see stable levels of performance. This is a +simpler signal and could perhaps not generalzie to larger matrices. + +## Ex 3 +for this section we compared the changes caused by different +appriximation approaches. We observed tanh,pow3, and skew to view a small +subset of variability. We notice that tanh and po3 have the greatest +agreeement. Meanwhile skew produces slightly different results. Bellow we have the skew and tanh example outputs of fastica. + +![alt text](./fastica_skew_out.png) +![alt text](./fastica_tanh_out.png) + + +## Ex 4 +noise removal utilizing NCSA seems to be more aggresive than using jade +this is reflected in the summary statistics where the standard devieaiton +of the signal is smallest with nsca. At a high level observation the +signals appear to be rather similar. On closer inspection we can see +differences in denoising ocmparing signals from channel 1 and channel 3 +in the region with a rapid change seen in the 31 second mark we see that +jade trails behind the NSCA method. Suggesting that jade is more sensitive +to rapid changes in signals. Meanwhile for regions with a consistent +signal( i.e flat) both methods are in agreement + +## Ex 5 + + +this script appears to be using several model estimation techniques to +fit a polynomial curve onto the the ECG signal. It allows for an +interective interpretatatio nof the data which i find quite useful. +Interestingly enough we can get an ok fit with just 2 parameters to be fit producing an error of 1.82% + meanwhile for the + +# Reading report + +A comparison of PCA, KPCA, and ICA for dimensionality reduction in support vector machine + +SVM was adopted "due to its remarkable characteristics such as good generalization performance, the absense of local minima and the sparse representation no solution" . SVMs are liked since they have the tendency to minimize the upper bound of the generalization error. Traditionally most applications would have used the raw feature space to do classification, but this is meant with a few limitations. Model performance is impacted by the correlated nature of the raw features. The scientific community therefore adopted several feature selection and/or extractions to minimize the number of unnecessary techniques. One series of feature extraction techniques that gained prominence was the dimensionality reduction techniques seen in PCA and KPCA. PCA using singular value decomposition produced a sieres of uncorrelated features. Meanwhile kernel PCA focuses on project the data onto a new space and applying linear PCA onto it. This allows KPCA to better generalize for non-linear features. ICA on the other hand focuses on identifying features that are statistically independent for each other. These different feature projection schemes result in varying feature sets, therefore, to validate their usefulness the researchers looked into 3 different datasets. They trained a SVM regression model of several openly available datasets. All 3 datasets had variables that provided a summary value of multiple events making their behavior nonlinear in most cases. It is for this reason that the best performing model was thus the KPCA followed by ICA. Although the data appeared to originate from different smaller sources which could have benefited from ICAs source separations abilities the top performer was still It is important to note that although KPCA was best performing it was also the slowest to run . PCA was the fastest model followed by ICA. Suggesting there are potential trade off considerations to be had when deciding which program to be used. 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0000000..768f579 --- /dev/null +++ b/hw.m @@ -0,0 +1,71 @@ +function main() + %%part 1 + disp('---begin part 1') + C = [4,1;1,3]; + [eig_vals,eig_vec ] = getEig(C); + [true_eig_vec,true_eig_val] = eig(C); + disp('Calculated eigen values') + disp(eig_vals) + disp('Expected eigen values') + disp(true_eig_val) + disp('Calculated eigen vectors') + disp(eig_vec) + disp('Expected eigen vectors') + disp(true_eig_vec) + %%part 2: calculate eigen value using power method + eig_val=powerEsti(C,true) +end + + +function [eig_vals,eig_vec]=getEig(C) + I = eye(size(C)); + L = sym('L') + %%Use system of equation to find eigen value + eq = det(C - (I.*L)); + S = solve(eq ==0,L); + eig_vals = eval(S); + %try a similar apporach for + x_val =1; + eig_vec = [1,1]; + for i =1:length(eig_vals) + lambd = eig_vals(i); + A = C - I*lambd; + A = [rref(A),ones(2,1)]; + v = A(1,1:2) ; + eig_vec(1,i) = x_val; + eig_vec(2,i) = v(2)*x_val; + eig_vec(:,i) = eig_vec(:,i)/ norm(eig_vec(:,i)); + end +end + +function f_eig_val=powerEsti(C,doPlot) +guess = randn(2,1); +num_iter = 20; +eig_val = zeros(1,num_iter); +guess_pred = zeros(2,num_iter); +for i =1:num_iter + guess = C*guess; + guess = guess/norm(guess); + guess_pred(:,i) = guess; + eig_val(i) = ((C*guess)'*guess)/(guess'*guess); +end + if doPlot== true + figure(1) + + plot(1:num_iter,eig_val) + title('Eigen value estimation over time') + xlabel('Iteration') + ylabel('Value') + figure(2) + plot(1:num_iter,guess_pred(1,:)) + hold on + plot(1:num_iter,guess_pred(2,:)) + xlabel('Iteration') + ylabel('value') + legend('eigen vector comp 1','eigen vector comp 2','Location','southeast') + end + f_eig_val = eig_val(end); +end + + + From 724259a69c87b91009ca3d78ffe4c964ff961300 Mon Sep 17 00:00:00 2001 From: Ramon Correa Date: Thu, 5 Nov 2020 16:42:35 -0500 Subject: [PATCH 4/4] final commit --- Ex04_testEOGArtifactRemoval.m | 4 ++-- README.md | 7 ++++--- hand_work_eigen.png | Bin 0 -> 128703 bytes 3 files changed, 6 insertions(+), 5 deletions(-) create mode 100644 hand_work_eigen.png diff --git a/Ex04_testEOGArtifactRemoval.m b/Ex04_testEOGArtifactRemoval.m index 6d0ae4f..5a484a1 100644 --- a/Ex04_testEOGArtifactRemoval.m +++ b/Ex04_testEOGArtifactRemoval.m @@ -57,8 +57,8 @@ eog_envelope = sqrt(filtfilt(ones(1, energy_envelope_len), energy_envelope_len, eog_ref.^2)); med = median(eog_envelope); mx = max(eog_envelope); -%eog_detection_threshold = 0.95 * med + 0.05 * mx; -eog_detection_threshold = 0.90 * med + 0.1 * mx; +eog_detection_threshold = 0.95 * med + 0.05 * mx; +%eog_detection_threshold = 0.90 * med + 0.1 * mx; J = eog_envelope >= eog_detection_threshold; I = 1 : T; diff --git a/README.md b/README.md index 63fab35..909e31b 100644 --- a/README.md +++ b/README.md @@ -1,12 +1,13 @@ # question 1 -A) include the writting section of letters +A) + +![alt text](./hand_work_eigen.png) B) We obtain similar eigenvalues to the one obtained by matlab eig. For the eigenvector we had some initial diferences when it comes to the final values -We were abled to obtain similar direction vectors but their individiual values are different. We ere able to rectify this by normalizing the vectors to -unit norm. The script hw.m also includes the +We were abled to obtain similar direction vectors but their individiual values are different. We ere able to rectify this by normalizing the vectors to unit norm. 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