346 research outputs found
Two Algorithms for Orthogonal Nonnegative Matrix Factorization with Application to Clustering
Approximate matrix factorization techniques with both nonnegativity and
orthogonality constraints, referred to as orthogonal nonnegative matrix
factorization (ONMF), have been recently introduced and shown to work
remarkably well for clustering tasks such as document classification. In this
paper, we introduce two new methods to solve ONMF. First, we show athematical
equivalence between ONMF and a weighted variant of spherical k-means, from
which we derive our first method, a simple EM-like algorithm. This also allows
us to determine when ONMF should be preferred to k-means and spherical k-means.
Our second method is based on an augmented Lagrangian approach. Standard ONMF
algorithms typically enforce nonnegativity for their iterates while trying to
achieve orthogonality at the limit (e.g., using a proper penalization term or a
suitably chosen search direction). Our method works the opposite way:
orthogonality is strictly imposed at each step while nonnegativity is
asymptotically obtained, using a quadratic penalty. Finally, we show that the
two proposed approaches compare favorably with standard ONMF algorithms on
synthetic, text and image data sets.Comment: 17 pages, 8 figures. New numerical experiments (document and
synthetic data sets
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