2,466 research outputs found
A geometric approach to archetypal analysis and non-negative matrix factorization
Archetypal analysis and non-negative matrix factorization (NMF) are staples
in a statisticians 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.Comment: 36 pages, 13 figure
Consistent Estimation of Mixed Memberships with Successive Projections
This paper considers the parameter estimation problem in Mixed Membership
Stochastic Block Model (MMSB), which is a quite general instance of random
graph model allowing for overlapping community structure. We present the new
algorithm successive projection overlapping clustering (SPOC) which combines
the ideas of spectral clustering and geometric approach for separable
non-negative matrix factorization. The proposed algorithm is provably
consistent under MMSB with general conditions on the parameters of the model.
SPOC is also shown to perform well experimentally in comparison to other
algorithms
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