A Smoothed Matrix Multivariate Elliptical Distribution-Based Projection Method for Feature Extraction

Algorithm 2

SMEDP.

	Input: a dataset of n training image matrices{Xi^c}∈R^m×n, m = p×q, and an image matrix Y ∈ R^p×q
(1)	Use Algorithm 1 to calculate the weight vector αi for each Xi.
(2)	Apply PCA to reduce the dimensions of X = [Vec(X1^1), Vec(X2^1), …, Vec(Xn1^1), Vec(X1^2), Vec(X2^2), …, Vec(Xn2^2), …, Vec(X1^C), Vec(X2^C), …, Vec(XnC^C)] and denote WPCA as the PCA-transformation matrix.
(3)	Compute the local scatter matrix XαβX^T and the total scatter matrix (X−) (X−)^T in the PCA subspace.
(4)	Calculate the P = [p1, p2, …, pd] of corresponding to the first d largest eigenvalues.
	Output: the optimal projection matrix P and the final projection matrix W=P^TW^TPCA