12e67c0412c24410VgnVCM100000c2b1d38dRCRDapproved/UMICH/stats/Home/News & Events/Statistics SeminarDepartment Seminar Series: Genevera Allen, Sparse and Functional Principal Components Analysis###@###(Fri, 4 Apr 2014)Department Seminar Series: Genevera Allen, Sparse and Functional Principal Components Analysis###@###(Fri, 4 Apr 2014)340 WHstats1396625400000139662540000011:30 AM<p style=" margin-bottom: .0001pt; font-family: 'Times New Roman', serif; color: black; margin: 0in; font-size: 10.0pt;">Abstract: &nbsp;Regularized principal components analysis, especially Sparse PCA and Functional PCA, has become widely used for dimension reduction in high-dimensional settings. Many examples of massive data, however, may benefit from estimating both sparse AND functional factors. These include neuroimaging data where there are discrete brain regions of activation (sparsity) but these regions tend to be smooth spatially (functional). Here, we introduce an optimization framework that can encourage both sparsity and smoothness of the row and/or column PCA factors. This framework generalizes many of the existing approaches to Sparse PCA, Functional PCA and two-way Sparse PCA and Functional PCA, as these are all special cases of our method. In particular, our method permits flexible combinations of sparsity and smoothness that lead to improvements in feature selection and signal recovery as well as more interpretable PCA factors. We demonstrate our method on simulated data and a neuroimaging example on EEG data. This work provides a unified optimization framework for regularized PCA that can form the foundation for a cohesive approach to regularization in high-dimensional multivariate analysis.</p>Nlorieannbzuniga1394119274323e1e67c0412c24410VgnVCM100000c2b1d38d____once11112newnewGenevera Allen, PhD., Assistant Professor, Department of Statistics, Rice Universityhttp://www.stat.rice.edu/~gallen/