By Topic

Sparse Variable PCA Using Geodesic Steepest Descent

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$31 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

2 Author(s)
Ulfarsson, M.O. ; Dept. of Electr. Eng. & Comput. Sci., Univ. of Michigan, Ann Arbor, MI ; Solo, V.

Principal component analysis (PCA) is a dimensionality reduction technique used in most fields of science and engineering. It aims to find linear combinations of the input variables that maximize variance. A problem with PCA is that it typically assigns nonzero loadings to all the variables, which in high dimensional problems can require a very large number of coefficients. But in many applications, the aim is to obtain a massive reduction in the number of coefficients. There are two very different types of sparse PCA problems: sparse loadings PCA (slPCA) which zeros out loadings (while generally keeping all of the variables) and sparse variable PCA which zeros out whole variables (typically leaving less than half of them). In this paper, we propose a new svPCA, which we call sparse variable noisy PCA (svnPCA). It is based on a statistical model, and this gives access to a range of modeling and inferential tools. Estimation is based on optimizing a novel penalized log-likelihood able to zero out whole variables rather than just some loadings. The estimation algorithm is based on the geodesic steepest descent algorithm. Finally, we develop a novel form of Bayesian information criterion (BIC) for tuning parameter selection. The svnPCA algorithm is applied to both simulated data and real functional magnetic resonance imaging (fMRI) data.

Published in:

Signal Processing, IEEE Transactions on  (Volume:56 ,  Issue: 12 )