Penalized Orthogonal Iteration for Sparse Estimation of Generalized Eigenvalue Problem

We propose a new algorithm for sparse estimation of eigenvectors in generalized eigenvalue problems (GEP). The GEP arises in a number of modern data-analytic situations and statistical methods, including principal component analysis (PCA), multiclass linear discriminant analysis (LDA), canonical correlation analysis (CCA), sufficient dimension reduction (SDR) and invariant co-ordinate selection. We propose to modify the standard generalized orthogonal iteration with a sparsity-inducing penalty for the eigenvectors. To achieve this goal, we generalize the equation-solving step of orthogonal iteration to a penalized convex optimization problem. The resulting algorithm, called penalized orthogonal iteration, provides accurate estimation of the true eigenspace, when it is sparse. Also proposed is a computationally more efficient alternative, which works well for PCA and LDA problems. Numerical studies reveal that the proposed algorithms are competitive, and that our tuning procedure works well. We demonstrate applications of the proposed algorithm to obtain sparse estimates for PCA, multiclass LDA, CCA and SDR. Supplementary materials are available online

Siyasi komiserler yeni başbakanı ayaklarına kadar getirttiler:Ali Rıza Paşa İngiliz yardımını talep etti

Taha Toros Arşivi, Dosya Adı: Milli Mücadele İstiklal Harbi GazetesiUnutma İstanbul projesi İstanbul Kalkınma Ajansı'nın 2016 yılı "Yenilikçi ve Yaratıcı İstanbul Mali Destek Programı" kapsamında desteklenmiştir. Proje No: TR10/16/YNY/010

Media 16: Variations in optical coherence tomography resolution and uniformity: a multi-system performance comparison

Originally published in Biomedical Optics Express on 01 July 2014 (boe-5-7-2066