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 domain
Y_s_cell - cell of (n_s*1) matrix, each matrix corresponds to the instance labels of a source domain
X_t - (n_t*d) matrix, rows correspond to instances and columns correspond to features
Y_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 beta
params.delta: vector of validated values of delta
params.k_list: vector of validated dimension of the transformed space
params.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 setting
OUTPUT:
test_accuracy - test accuracy on target instances
predicted_labels - predicted labels of target instances
Zs - projected source domain instances
Zt - projected target domain instances
Shoubo Hu (shoubo.sub [at] gmail.com)
2019-06-02
Reference
[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 < 4
error('Error. \nOnly %d input arguments! At least 4 required', nargin);
elseif nargin == 4
% default params values
beta = [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 == 5
if ~isfield(params, 'beta')
beta = [0.1 0.3 0.5 0.7 0.9];
else
beta = params.beta;
end
if ~isfield(params, 'delta')
delta = [1e-3 1e-2 1e-1 1 1e1 1e2 1e3 1e4 1e5 1e6];
else
delta = params.delta;
end
if ~isfield(params, 'k_list')
k_list = [2];
else
k_list = params.k_list;
end
if ~isfield(params, 'verbose')
verbose = false;
else
verbose = params.verbose;
end
if ~isfield(params, 'X_v')
X_v = cat(1, X_s_cell{:});
Y_v = cat(1, Y_s_cell{:});
else
if ~isfield(params, 'Y_v')
error('Error. Labels of validation set needed!');
end
X_v = params.X_v;
Y_v = params.Y_v;
end
end
% ----- training phase
% ----- ----- source domains
X_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 set
dist_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 verbose
fprintf('beta: %f, delta: %f, acc: %f\n', cur_beta, cur_delta, acc);
end
end
end
end
fprintf('Validation done! Classifying the target domain instances ...\n');
% ----- test phase
% ----- ----- get optimal parameters
acc_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 domain
dist_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
clc
addpath('./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)];
end
params.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);代码获取
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