The principle of dimensionality reduction with PCA is the representation of the dataset ‘X’in terms of eigenvectors ei ∈ RN  of its covariance matrix. The eigenvectors oriented in the direction with the maximum variance of X in RN carry the most      relevant information of X. These eigenvectors are called principal components [8]. Ass...

We consider concave minimization problems over nonconvex sets. Optimization problems with this structure arise in sparse principal component analysis. We analyze both a gradient projection algorithm and an approximate Newton algorithm where the Hessian approximation is a multiple of the identity. Convergence results are established. In numerical experiments arising in sparse principal component...

We study sparse principal components analysis in the high-dimensional setting, where p (the number of variables) can be much larger than n (the number of observations). We prove optimal, non-asymptotic lower and upper bounds on the minimax estimation error for the leading eigenvector when it belongs to an lq ball for q ∈ [0, 1]. Our bounds are sharp in p and n for all q ∈ [0, 1] over a wide cla...

Recent advances in sparse coding and compressed sensing have paved the way for novel techniques in a variety of fields, including face recognition. Following this trend we present in this paper a feature extraction technique based on projection coefficients computed using a number of sparse projection axes. The feasibility of the technique is demonstrated in a series of face verification experi...

q-mode hierarchical cluster (hca) and principal component analysis (pca) were simultaneously applied to groundwater hydrochemical data from the three times in 2004: june, september, and december, along the ain azel aquifer, algeria, to extract principal factors corresponding to the different sources of variation in the hydrochemistry, with the objective of defining the main controls on the h...

targeted extension for heterogeneous farming systems is a challenge in developing countries. farm type identification and characterization based on estimates of income from different farm components allows simplifying diversity in farming systems. use of multivariate statistical techniques, such as principal component analysis (pca) and cluster analysis (ca), help in such farm typology delineat...