A Geometric Approach to Archetypal Analysis and Nonnegative Matrix Factorization. Issue 3 (3rd July 2017)

• Record Type: Journal Article
• Authors: Damle, Anil; Sun, Yuekai
• Is Part Of: Technometrics. Volume 59:Issue 3(2017)
• Page Start: 361
• Page End: 370
• Publication Date: 2017-07-03
• Subjects: Convex hull -- Group lasso -- Random projections; Statistical physics -- Periodicals; Chemistry -- Statistical methods -- Periodicals; Engineering -- Statistical methods -- Periodicals; 519.5
• DOI: 10.1080/00401706.2016.1247017
• Languages: English
• ISSNs: 0040-1706

Abstract

ABSTRACT: Archetypal analysis and nonnegative matrix factorization (NMF) are staples in a statistician's toolbox for dimension reduction and exploratory data analysis. We describe a geometric approach to both NMF and archetypal analysis by interpreting both problems as finding extreme points of the data cloud. We also develop and analyze an efficient approach to finding extreme points in high dimensions. For modern massive datasets that are too large to fit on a single machine and must be stored in a distributed setting, our approach makes only a small number of passes over the data. In fact, it is possible to obtain the NMF or perform archetypal analysis with just two passes over the data.