368 research outputs found
Rate Optimal Denoising of Simultaneously Sparse and Low Rank Matrices
We study minimax rates for denoising simultaneously sparse and low rank
matrices in high dimensions. We show that an iterative thresholding algorithm
achieves (near) optimal rates adaptively under mild conditions for a large
class of loss functions. Numerical experiments on synthetic datasets also
demonstrate the competitive performance of the proposed method
Nonnegative Matrix Underapproximation for Robust Multiple Model Fitting
In this work, we introduce a highly efficient algorithm to address the
nonnegative matrix underapproximation (NMU) problem, i.e., nonnegative matrix
factorization (NMF) with an additional underapproximation constraint. NMU
results are interesting as, compared to traditional NMF, they present
additional sparsity and part-based behavior, explaining unique data features.
To show these features in practice, we first present an application to the
analysis of climate data. We then present an NMU-based algorithm to robustly
fit multiple parametric models to a dataset. The proposed approach delivers
state-of-the-art results for the estimation of multiple fundamental matrices
and homographies, outperforming other alternatives in the literature and
exemplifying the use of efficient NMU computations
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