Related papers: Image space projection for low-rank signal estimat…

Non linear regression models are a standard tool for modeling real phenomena, with several applications in machine learning, ecology, econometry... Estimating the parameters of the model has garnered a lot of attention during many years. We…

We consider the problem of finding a low rank symmetric matrix satisfying a system of linear equations, as appears in phase retrieval. In particular, we solve the gauge dual formulation, but use a fast approximation of the spectral…

In this paper, we propose a new algorithm for recovery of low-rank matrices from compressed linear measurements. The underlying idea of this algorithm is to closely approximate the rank function with a smooth function of singular values,…

We consider the problem of recovering an unknown low-rank matrix X with (possibly) non-orthogonal, effectively sparse rank-1 decomposition from measurements y gathered in a linear measurement process A. We propose a variational formulation…

This contribution revisits the classical approximate realization problem, which involves determining matrices of a state-space model based on estimates of a truncated series of Markov parameters. A Hankel matrix built up by these Markov…

Layer factorization has emerged as a widely used technique for training memory-efficient neural networks. However, layer factorization methods face several challenges, particularly a lack of robustness during the training process. To…

In this paper, we consider the estimation of a low Tucker rank tensor from a number of noisy linear measurements. The general problem covers many specific examples arising from applications, including tensor regression, tensor completion,…

Low rank approximation of matrices has been well studied in literature. Singular value decomposition, QR decomposition with column pivoting, rank revealing QR factorization (RRQR), Interpolative decomposition etc are classical deterministic…

We consider the problem of finding for a given $N$-tuple of polynomials (real or complex) the closest $N$-tuple that has a common divisor of degree at least $d$. Extended weighted Euclidean seminorm of the coefficients is used as a measure…

This paper presents a novel adaptive reduced-rank {multi-input multi-output} (MIMO) equalization scheme and algorithms based on alternating optimization design techniques for MIMO spatial multiplexing systems. The proposed reduced-rank…

In this work, we propose a new randomized algorithm for computing a low-rank approximation to a given matrix. Taking an approach different from existing literature, our method first involves a specific biased sampling, with an element being…

Recently, low-rank matrix recovery theory has been emerging as a significant progress for various image processing problems. Meanwhile, the group sparse coding (GSC) theory has led to great successes in image restoration (IR) problem with…

We propose a new iteratively reweighted least squares (IRLS) algorithm for the recovery of a matrix $X \in \mathbb{C}^{d_1\times d_2}$ of rank $r \ll\min(d_1,d_2)$ from incomplete linear observations, solving a sequence of low complexity…

Inference and simulation in the context of high-dimensional dynamical systems remain computationally challenging problems. Some form of dimensionality reduction is required to make the problem tractable in general. In this paper, we propose…

We develop time integration methods in low-rank representation that can adaptively adjust approximation ranks to achieve a prescribed accuracy, while ensuring that these ranks remain proportional to the corresponding best approximation…

A weighted regression procedure is proposed for regression type problems where the innovations are heavy-tailed. This method approximates the least absolute regression method in large samples, and the main advantage will be if the sample is…

For three decades, carrier-phase observations have been used to obtain the most accurate location estimates using global navigation satellite systems (GNSS). These estimates are computed by minimizing a nonlinear mixed-integer least-squares…

We propose a new technique for constructing low-rank approximations of matrices that arise in kernel methods for machine learning. Our approach pairs a novel automatically constructed analytic expansion of the underlying kernel function…

Matrix low rank approximation including the classical PCA and the robust PCA (RPCA) method have been applied to solve the background modeling problem in video analysis. Recently, it has been demonstrated that a special weighted low rank…

Low-rankness plays an important role in traditional machine learning, but is not so popular in deep learning. Most previous low-rank network compression methods compress networks by approximating pre-trained models and re-training. However,…