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demo1_clust_spcm_emb.m
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demo1_clust_spcm_emb.m
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Main demo script for the SPCM-CRP-MM Clustering Algorithm proposed in:
%
% N. Figueroa and A. Billard, “Transform-Invariant Clustering of SPD Matrices
% and its Application on Joint Segmentation and Action Discovery}”
% Arxiv, 2019.
%
% Author: Nadia Figueroa, PhD Student., Robotics
% Learning Algorithms and Systems Lab, EPFL (Switzerland)
% Email address: nadia.figueroafernandez@epfl.ch
% Website: http://lasa.epfl.ch
% December 2018; Last revision: 10-Feb-2019
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Step 1 (DATA LOADING): Load Datasets %%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
close all; clear all; clc
%% %%%%%%%%%%%%%%%%%%%%%%% Select a Dataset %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 1: Non-deformed+Deformed Ellips. (3D) / (80 Samples c1:3, c2:3, c2:3 c4:)
% 2: SPD sampled from Wishart (3D) / (120 Samples c1:40, c2:40, c2:40)
% 3: SPD sampled from Wishart (6D) / (200 Samples c1:50, c2:50, c3:50 c4:50)
% 4: Real 6D Task-Ellipsoids (6D) / (105 Samples c1:63, c2:21, c3:21)
% 5: Manipulability Ellipsoids 1 (3D) / (727 Samples 5 classes)
% 6: Real Diffusion Tensors (Rat) (3D) / (1024 Samples 5 classes)
% ...
% 9: ETH-80 Object Dataset Feats. (18D) ... TODO (Rotated Objects)
% 10 : HMM Emission Models - Task1 (13D) ... TODO (Polishing)
% 11 : HMM Emission Models - Task2 (7D) ... TODO (Grating)
% 12 : HMM Emission Models - Task3 (13D) ... TODO (Rolling)
% 13: HMM Emission Models - Task4 (26D) ... TODO (Peeling)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%% Data Loading Parameter Description %%%%%%%%%%%%%%%%%%%%%%
% display: [0,1] -- Display Covariance matrices in their own format
% randomize: [0,1] -- Randomize the Covariance Matrices indices
% pkg_dir: {'./data/'} -- Path to data folder
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
pkg_dir = '/home/nbfigueroa/Dropbox/PhD_papers/journal-draft/new-code/SPCM-CRP';
display = 1; % display SDP matrices (if applicable)
randomize = 0; % randomize idx
dataset = 4; % choosen dataset from index above
sample_ratio = 1; % sub-sample dataset [0.01 - 1]
[sigmas, true_labels, dataset_name] = load_SPD_dataset(dataset, pkg_dir, display, randomize);
% Generate Random Labels for Baseline Clustering Comparison
M = length(sigmas);
if exist('true_labels', 'var')
K = length(unique(true_labels));
end
random_labels = zeros(1,length(true_labels));
for i=1:M
random_labels(i) = randsample(K,1);
end
[Purity_random, NMI_random, F_random, ARI_random] = cluster_metrics(true_labels, random_labels);
fprintf('------ Results for Random Clustering ------\n K: %d, Purity: %1.2f, NMI: %1.2f, ARI: %1.2f, F measure: %1.2f \n', ...
K, Purity_random, NMI_random, ARI_random, F_random);
%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Step 2: Compute Similarity Matrix from B-SPCM Function for dataset %%
%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%% Set Hyper-parameter %%%%%%%%%%%%%%%%%%%%%%%%%%%
% Tolerance for SPCM decay function
dis_type = 2; % Choose dis-similarity type
% 1:'var' use the variance of homothetic ratios
% 2:'cv' use the coefficient of variation of homo. ratios
gamma = 4;
% %%%%%%%%%%%%%%% Compute Confusion Matrix of Similarities %%%%%%%%%%%%%%%%
spcm = ComputeSPCMfunctionMatrix(sigmas, gamma, dis_type);
D = spcm(:,:,1);
S = spcm(:,:,2);
%%%%%%% Visualize Bounded Similarity Confusion Matrix %%%%%%%%%%%%%%
% if exist('h0','var') && isvalid(h0), delete(h0); end
title_str = 'SPCM Similarity Matrix';
h0 = plotSimilarityConfMatrix(S, title_str);
% if exist('h1','var') && isvalid(h1), delete(h1); end
title_str = 'SPCM Dis-similarity Matrix';
h1 = plotSimilarityConfMatrix(D, title_str);
% Compute Negative Eigenfraction of similarity matrix (NEF)
lambda_S = eig(S);
NEF_S = sum(abs(lambda_S(lambda_S < 0)))/sum(abs(lambda_S));
%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Step 3: Embed SDP Matrices in Approximate Euclidean Space %%
%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Choose Embedding implementation
show_plots = 0; % Show plot of similarity matrices+eigenvalues
pow_eigen = 4; % (L^+)^(pow_eigen) for dimensionality selection
emb_type = 2; % 0: Graph-Subspace Projection
% 1: Kernel-PCA on L^+
% 2: Kernel-PCA on deformed Kernel with L
switch emb_type
case 0
[x_emb, Y, d_L_pow] = graphEuclidean_Embedding(S, show_plots, pow_eigen);
emb_name = '(SPCM) Graph-Subspace Projection';
case 1
norm_K = 1; % Choose to normalize K, ends up being unneccesary for L^+
[x_emb, Y] = graphKernelPCA_Embedding(S, show_plots, norm_K, pow_eigen);
emb_name = '(SPCM) Graph Kernel PCA Projection';
case 2
emb_options = [];
emb_options.l_sensitivity = 2; % This changes the embedding/results ALOT!
emb_options.distance_name = 'SPCM';
emb_options.norm_K = 1; % Normalize the Kernel Matrix
emb_options.pow_eigen = pow_eigen; % K^(pow_eigen) for dimensionality selection
emb_options.show_plots = show_plots; % 0/1 display plots
emb_options.deform = 1;
%%%%%%%%%%%%%%%%%%%%%% Choose SDP distance %%%%%%%%%%%%%%%%%%%%%%%%
choosen_distance = 1; % 1: Log-Euclidean Riemannian Distance (LERM)
% 3: LogDet-Divergence (JBLD)
[D, distance_name] = computeSDP_distances(sigmas, choosen_distance);
[x_emb, Y, K, K_SP, gamma_le] = deformedKernelPCA_Embedding(D, S, emb_options);
if emb_options.deform
emb_name = 'Kernel PCA on deformed $k_{LE}^{SP}(\cdot,\cdot)$';
if exist('h0a','var') && isvalid(h0a), delete(h0a); end
title_str = '(un-deformed) log-Euclidean RBF kernel $k_{LE}(\cdot,\cdot)$';
h0a = plotSimilarityConfMatrix(K, title_str);
if exist('h0b','var') && isvalid(h0b), delete(h0b); end
title_str = 'Deformed log-Euclidean RBF kernel $k_{LE}^{SP}(\cdot,\cdot)$';
h0b = plotSimilarityConfMatrix(K_SP, title_str);
else
emb_name = 'Kernel PCA on (un-deformed) $k_{LE}(\cdot,\cdot)$';
end
end
M = size(Y,1);
show_emb = 0;
%% %%%%%% Visualize Approximate Euclidean Embedding %%%%%%%%
plot_options = [];
plot_options.labels = true_labels;
plot_options.title = emb_name;
ml_plot_data(Y',plot_options);
axis equal;
%%%%%%%% Visualize Full Euclidean Embedding %%%%%%%%
if show_emb
plot_options = [];
plot_options.labels = true_labels;
plot_options.title = emb_name;
ml_plot_data(x_emb',plot_options);
end
%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Step 4: Discover Clusters of Covariance Matrices %%
%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Discover Clusters with GMM-based Clustering Variants on Embedding %%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0: sim-CRP-MM (Collapsed Gibbs Sampler) on Preferred Embedding
% 1: GMM-EM Model Selection via BIC on Preferred Embedding
% 2: CRP-GMM (Gibbs Sampler/Collapsed) on Preferred Embedding
est_options = [];
est_options.type = 0; % Clustering Estimation Algorithm Type
% If algo 1 selected:
est_options.maxK = 15; % Maximum Gaussians for Type 1
est_options.fixed_K = 2; % Fix K and estimate with EM for Type 1
% If algo 0 or 2 selected:
est_options.samplerIter = 150; % Maximum Sampler Iterations
% For type 0: 50-200 iter are needed
% For type 2: 200-1000 iter are needed
% Plotting options
est_options.do_plots = 1; % Plot Estimation Stats
est_options.dataset_name = dataset_name; % Dataset name
est_options.true_labels = true_labels; % To plot against estimates
% Fit GMM to Trajectory Data
tic;
clear Priors Mu Sigma
[Priors, Mu, Sigma, est_labels, stats] = fitgmm_sdp(S, Y, est_options);
toc;
%%%%%%%%%% Compute Cluster Metrics %%%%%%%%%%%%%
[Purity, NMI, F, ARI] = cluster_metrics(true_labels, est_labels');
if exist('true_labels', 'var')
K = length(unique(true_labels));
end
switch est_options.type
case 0
fprintf('---%s Results---\n Iter:%d, LP: %d, Clusters: %d/%d with Purity: %1.2f, NMI Score: %1.2f, ARI: %1.2f, F measure: %1.2f \n', ...
'spcm-CRP-MM (Collapsed-Gibbs)', stats.Psi.Maxiter, stats.Psi.MaxLogProb, length(unique(est_labels)), K, Purity, NMI, ARI, F);
case 1
fprintf('---%s Results---\n Clusters: %d/%d with Purity: %1.2f, NMI Score: %1.2f, ARI: %1.2f, F measure: %1.2f \n', ...
'Finite-GMM (MS-BIC)', length(unique(est_labels)), K, Purity, NMI, ARI, F);
case 2
if isfield(stats,'collapsed')
fprintf('---%s Results---\n Clusters: %d/%d with Purity: %1.2f, NMI Score: %1.2f, ARI: %1.2f, F measure: %1.2f \n', ...
'CRP-GMM (Collapsed-Gibbs)', length(unique(est_labels)), K, Purity, NMI, ARI, F);
else
fprintf('---%s Results---\n Clusters: %d/%d with Purity: %1.2f, NMI Score: %1.2f, ARI: %1.2f, F measure: %1.2f \n', ...
'CRP-GMM (Gibbs)', length(unique(est_labels)), K, Purity, NMI, ARI, F);
end
end
%% Visualize Estimated Parameters
re_estimate = 1;
if M < 4
est_options.emb_name = emb_name;
if re_estimate
[Priors0, Mu0, Sigma0] = gmmOracle(Y, est_labels);
tot_dilation_factor = 1; rel_dilation_fact = 0.2;
Sigma0 = adjust_Covariances(Priors0, Sigma0, tot_dilation_factor, rel_dilation_fact);
[~, est_labels0] = my_gmm_cluster(Y, Priors0, Mu0, Sigma0, 'hard', []);
[h_gmm, h_pdf] = visualizeEstimatedGMM(Y, Priors0, Mu0, Sigma0, est_labels0, est_options);
else
[h_gmm, h_pdf] = visualizeEstimatedGMM(Y, Priors, Mu, Sigma, est_labels, est_options);
end
end
%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Compute/Show GMM-Oracle Results %%
%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% GMM-Oracle Estimation
[Priors0, Mu0, Sigma0] = gmmOracle(Y, true_labels);
[~, est_labels0] = my_gmm_cluster(Y, Priors0, Mu0, Sigma0, 'hard', []);
est_K0 = length(unique(est_labels0));
[Purity, NMI, F, ARI] = cluster_metrics(true_labels, est_labels0);
fprintf('(GMM-Oracle) Number of estimated clusters: %d/%d, Purity: %1.2f, NMI Score: %1.2f, ARI: %1.2f, F measure: %1.2f \n',est_K0,K, Purity, NMI, ARI, F);
if M < 4
oracle_options = [];
oracle_options.type = -1;
oracle_options.emb_name = emb_name;
[h_gmm] = visualizeEstimatedGMM(Y, Priors0, Mu0, Sigma0, est_labels0, oracle_options);
axis equal
end
%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% %%%%%%% For Dataset 6: Visualize cluster labels for DTI %%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Visualize Estimated Cluster Labels as DTI
% if exist('h3a','var') && isvalid(h3a), delete(h3a);end
title = 'Estimated Cluster Labels of Diffusion Tensors';
h3a = plotlabelsDTI(est_labels, title);
% if exist('h3b','var') && isvalid(h3b), delete(h3b);end
title = 'Ground Truth Cluster Labels of Diffusion Tensors';
h3b = plotlabelsDTI(true_labels, title);