sds.m

%SDS
%
%     [TARGET_DATA, OUTLIER_DATA] = SDS(X,K,THRESHOLD)
%
% INPUT
%   X        	Dataset
%   K     		Number of nearest neighbors ( default = ceil(5 * log10(size(x, 1))) )
%   THRESHOLD  	Decision threshold (default = 0.1)
%
% OUTPUT
%   TARGET_DATA		Pseudo targets generated by shifting target data along positive direction
%   OUTLIER_DATA	Pseudo outliers generated by shifting edge patterns along negative direction
%
%
% DESCRIPTION
%
% Generate binary data to tune a one class classifier according to the following paper:
% Wang, S. et al. 2018. Hyperparameter selection of one-class support vector machine by self-adaptive data
% shifting. Pattern Recognition. 74, 2018.

function [target_data, outlier_data] = sds(x, k, threshold)

if nargin < 3 || isempty(threshold), threshold = 0.1; end
if nargin < 2 || isempty(k), k = ceil(5 * log10(size(x, 1))); end
if nargin < 1 || isempty(x)
	error('Incorrect call to SDS: Empty dataset');
end

%make sure we have a OneClass dataset
x = +target_class(x);
   
%calculate the euclidian distance matrix
distmat = sqrt(sqeucldistm(x, x));
%sort the distances
[sD, idx] = sort(distmat, 2);

edge_idx = [];
norm_vec = [];
target_data = [];
l_ns = 0;

%finding the edge patterns
for i = 1:size(x, 1)
	v_ij = repmat(x(i,:), k, 1) - x(idx(i, 2:k+1),:);
	for j = 1:k
		v_ij(j,:) = v_ij(j,:)/norm(v_ij(j,:));
	end
	n_i = sum(v_ij, 1);
	theta_ij = sum(v_ij .* repmat(n_i, k, 1), 2);
	l_i = 1/k * sum(theta_ij >= 0);
	n_i = n_i/norm(n_i);

	if l_i >= 1 - threshold
		%add new edge
		edge_idx = [edge_idx i];
		norm_vec = [norm_vec; n_i];
		l_ns = l_ns + (1 / k * sum(sD(i, 2:k+1)));
	end

	%generate pseudo targets
	lambda_i_positive = sum(repmat(-n_i, k, 1) .* (x(idx(i, 2:k+1),:) - repmat(x(i,:), k, 1)),2);
	if (length(lambda_i_positive(lambda_i_positive > 0)) > 0)
		%shift along positive direction of data density gradient
		x_ij_min_positive = min(lambda_i_positive(lambda_i_positive > 0));
		target_data = [target_data; x(i,:) + x_ij_min_positive * -n_i];
	end
end

l_ns = l_ns / length(edge_idx);

%generate pseudo outliers by shifting along negative direction
outlier_data = x(edge_idx,:) + norm_vec * l_ns;

target_data = gendatoc(target_data);
outlier_data = gendatoc([], outlier_data);
  
return