【域适应】基于散度成分分析（SCA）的四分类任务典型方法实现

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关于

SCA（scatter component analysis）是基于一种简单的几何测量，即分散，它在再现内核希尔伯特空间上进行操作。 SCA找到一种在最大化类的可分离性、最小化域之间的不匹配和最大化数据的可分离性之间进行权衡的表示；每一个都通过分散进行量化。

参考论文：Shibboleth Authentication Request

工具

MATLAB

方法实现

SCA变换实现

function [test_accuracy, predicted_labels, Zs, Zt] = SCA(X_s_cell, Y_s_cell, X_t, Y_t, params)INPUT(params is optional):X_s_cell          - cell of (n_s*d) matrix, each matrix corresponds to the instance features of a source domainY_s_cell          - cell of (n_s*1) matrix, each matrix corresponds to the instance labels of a source domainX_t               - (n_t*d) matrix, rows correspond to instances and columns correspond to featuresY_t               - (n_t*1) matrix, each row is the class label of corresponding instances in X_t[params]          - params.beta:      vector of validated values of betaparams.delta:     vector of validated values of deltaparams.k_list:    vector of validated dimension of the transformed spaceparams.X_v:       (n_v*d) matrix of instance features of validation set (use the source instances if not provided)params.Y_v:       (n_v*1) matrix of instance labels of validation set (use the source instances if not provided)params.verbose:   if true, show the validation accuracy of each parameter settingOUTPUT:test_accuracy     - test accuracy on target instancespredicted_labels  - predicted labels of target instancesZs                - projected source domain instancesZt                - projected target domain instancesShoubo Hu (shoubo.sub [at] gmail.com)
2019-06-02Reference
[1] Ghifary, M., Balduzzi, D., Kleijn, W. B., & Zhang, M. (2017). Scatter component analysis: A unified framework for domain adaptation and domain generalization. IEEE transactions on pattern analysis and machine intelligence, 39(7), 1414-1430.
%}if nargin < 4error('Error. \nOnly %d input arguments! At least 4 required', nargin);elseif nargin == 4% default params valuesbeta = [0.1 0.3 0.5 0.7 0.9];delta = [1e-3 1e-2 1e-1 1 1e1 1e2 1e3 1e4 1e5 1e6];k_list = [2];X_v = cat(1, X_s_cell{:});Y_v = cat(1, Y_s_cell{:});verbose = false;elseif nargin == 5if ~isfield(params, 'beta')beta = [0.1 0.3 0.5 0.7 0.9];elsebeta = params.beta;endif ~isfield(params, 'delta')delta = [1e-3 1e-2 1e-1 1 1e1 1e2 1e3 1e4 1e5 1e6];elsedelta = params.delta;endif ~isfield(params, 'k_list')k_list = [2];elsek_list = params.k_list;endif ~isfield(params, 'verbose')verbose = false;elseverbose = params.verbose;endif ~isfield(params, 'X_v')X_v = cat(1, X_s_cell{:});Y_v = cat(1, Y_s_cell{:});elseif ~isfield(params, 'Y_v')error('Error. Labels of validation set needed!');endX_v = params.X_v;Y_v = params.Y_v;endend% ----- training phase% ----- ----- source domainsX_s = cat(1, X_s_cell{:});Y_s = cat(1, Y_s_cell{:});fprintf('Number of source domains: %d, Number of classes: %d.\n', length(X_s_cell), length(unique(Y_s)) );fprintf('Validating hyper-parameters ...\n');dist_s_s = pdist2(X_s, X_s);dist_s_s = dist_s_s.^2;sgm_s = compute_width(dist_s_s);% ----- ----- validation setdist_s_v = pdist2(X_s, X_v);dist_s_v = dist_s_v.^2;sgm_v = compute_width(dist_s_s);n_s = size(X_s, 1);n_v = size(X_v, 1);H_s = eye(n_s) - ones(n_s)./n_s;H_v = eye(n_v) - ones(n_v)./n_v;K_s_s = exp(-dist_s_s./(2 * sgm_s * sgm_s));K_s_v = exp(-dist_s_v./(2 * sgm_v * sgm_v));K_s_v_bar = H_s * K_s_v * H_v;[P, T, D, Q, K_s_s_bar] = SCA_terms(K_s_s, X_s_cell, Y_s_cell);acc_mat = zeros(length(k_list), length(beta), length(delta));for i = 1:length(beta)cur_beta = beta(i);for j = 1:length(delta)cur_delta = delta(j);[B, A] = SCA_trans(P, T, D, Q, K_s_s_bar, cur_beta, cur_delta, 1e-5);for k = 1:length(k_list)[acc, ~, ~, ~] = SCA_test(B, A, K_s_s_bar, K_s_v_bar, Y_s, Y_v, k_list( k ) );acc_mat(k, i, j) = acc;if verbosefprintf('beta: %f, delta: %f, acc: %f\n', cur_beta, cur_delta, acc);endendendendfprintf('Validation done! Classifying the target domain instances ...\n');% ----- test phase% ----- ----- get optimal parametersacc_tr_best = max( acc_mat(:) );ind = find( acc_mat == acc_tr_best );[k, i, j] = size( acc_mat );[best_k, best_i, best_j] = ind2sub([k, i, j], ind(1));best_beta = beta(best_i);best_delta = delta(best_j);best_k = k_list(best_k);% ----- ----- test on the target domaindist_s_t = pdist2(X_s, X_t);dist_s_t = dist_s_t.^2;sgm = compute_width(dist_s_t);K_s_t = exp(-dist_s_t./(2 * sgm * sgm));n_s = size(X_s, 1);H_s = eye(n_s) - ones(n_s)./n_s;n_t = size(X_t, 1);H_t = eye(n_t) - ones(n_t)./n_t;K_s_t_bar = H_s * K_s_t * H_t;[B, A] = SCA_trans(P, T, D, Q, K_s_s_bar, best_beta, best_delta, 1e-5);[test_accuracy, predicted_labels, Zs, Zt] = SCA_test(B, A, K_s_s_bar, K_s_t_bar, Y_s, Y_t, best_k );fprintf('Test accuracy: %f\n', test_accuracy);end

基于SCA的域迁移分类实现

clear all
clcaddpath('./modules');
load('./syn_data/data.mat');% ----- parameters
% target / all / source domains
tgt_dm = [5];
val_dm = [3 4];
src_dm = [1 2];data_cell = XY_cell;
X_t = data_cell{tgt_dm(1)}(:, 1:2);
Y_t = data_cell{tgt_dm(1)}(:, 3);% ----- training data
X_s_cell = cell(1,length(src_dm));
Y_s_cell = cell(1,length(src_dm));    
for idx = 1:length(src_dm)cu_dm = src_dm(1, idx);X_s_cell{idx} = data_cell{cu_dm}(:, 1:2);Y_s_cell{idx} = data_cell{cu_dm}(:, 3);
end
% ----- validation data
X_v = [];
Y_v = [];
for idx = 1:length(val_dm)cu_dm = val_dm(1, idx);X_v = [X_v; data_cell{cu_dm}(:, 1:2)];Y_v = [Y_v; data_cell{cu_dm}(:, 3)];
endparams.X_v = X_v;
params.Y_v = Y_v;
params.verbose = true;
[test_accuracy, predicted_labels, Zs, Zt] = SCA(X_s_cell, Y_s_cell, X_t, Y_t, params);