3,072 research outputs found
Fast and Robust Archetypal Analysis for Representation Learning
We revisit a pioneer unsupervised learning technique called archetypal
analysis, which is related to successful data analysis methods such as sparse
coding and non-negative matrix factorization. Since it was proposed, archetypal
analysis did not gain a lot of popularity even though it produces more
interpretable models than other alternatives. Because no efficient
implementation has ever been made publicly available, its application to
important scientific problems may have been severely limited. Our goal is to
bring back into favour archetypal analysis. We propose a fast optimization
scheme using an active-set strategy, and provide an efficient open-source
implementation interfaced with Matlab, R, and Python. Then, we demonstrate the
usefulness of archetypal analysis for computer vision tasks, such as codebook
learning, signal classification, and large image collection visualization
A Fast Gradient Method for Nonnegative Sparse Regression with Self Dictionary
A nonnegative matrix factorization (NMF) can be computed efficiently under
the separability assumption, which asserts that all the columns of the given
input data matrix belong to the cone generated by a (small) subset of them. The
provably most robust methods to identify these conic basis columns are based on
nonnegative sparse regression and self dictionaries, and require the solution
of large-scale convex optimization problems. In this paper we study a
particular nonnegative sparse regression model with self dictionary. As opposed
to previously proposed models, this model yields a smooth optimization problem
where the sparsity is enforced through linear constraints. We show that the
Euclidean projection on the polyhedron defined by these constraints can be
computed efficiently, and propose a fast gradient method to solve our model. We
compare our algorithm with several state-of-the-art methods on synthetic data
sets and real-world hyperspectral images
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