Multi-task learning (MTL) seeks to improve the generalization performance by sharing information among multiple tasks. Many existing MTL approaches aim to learn the lowrank structure on the weight matrix, which stores the model parameters of all tasks, to achieve task sharing, and as a consequence the trace norm regularization is widely used in the MTL literature. A major limitation of these ap...

The problem of minimizing the rank of a matrix subject to affine constraints has many applications in machine learning, and is known to be NP-hard. One of the tractable relaxations proposed for this problem is nuclear norm (or trace norm) minimization of the matrix, which is guaranteed to find the minimum rank matrix under suitable assumptions. In this paper, we propose a family of Iterative Re...

It is well known that the parabolic partial differential equations in two or more space dimensions with overspecified boundary data, feature in the mathematical modeling of many phenomena. In this article, an inverse problem of determining an unknown time-dependent source term of a parabolic equation in general dimensions is considered. Employing some transformations, we change the inverse prob...

Low-rank matrix approximation plays an important role in the area of computer vision and image processing. Most of the conventional low-rank matrix approximation methods are based on the l2 -norm (Frobenius norm) with principal component analysis (PCA) being the most popular among them. However, this can give a poor approximation for data contaminated by outliers (including missing data), becau...

We characterize T-measures on weakly generated tribes, where T is a strict triangular norm and we give a Liapunoff Theorem for these measures. This generalizes previous results obtained for monotonic T-measures or for Frank triangular norms.

This note addresses the question if and why the nuclear norm heuristic can recover an impulse response generated by a stable singlereal-pole system, if elements of the upper-triangle of the associated Hankel matrix are given. Since the setting is deterministic, theories based on stochastic assumptions for low-rank matrix recovery do not apply in the considered situation. A ’certificate’ which g...

A(t) is an hX« matrix with complex-valued elements which are measurable and bounded for ¿^0, and p is an «-vector with measurable, complex-valued elements. The norm of a vector (matrix) will be denoted by || -|| and is defined as the sum of the magnitudes of the elements. A vector (matrix) will be called bounded if its norm is bounded on i^O and convergent if its elements tend to finite limits ...

This brief develops two algorithms for the order reduction of two-dimensional (2-D) FIR digital filters, which lead to two indirect design methods. Specifically, we show how an optimal L2 design can be derived as a matrix approximation problem in the Frobenius norm, and how a suboptimal L1 design can be obtained by solving a matrix approximation problem in the 2-norm using the Davis–Kahan–Weinb...

Rosen, Park, and Glick proposed the structured total least norm (STLN) algorithm for solving problems in which both the matrix and the right-hand side contain errors. We extend this algorithm for ill-posed problems by adding regularization, and we use the resulting algorithm to solve blind deconvolution problems as encountered in image deblurring when both the image and the blurring function ha...

We consider the problem of approximation of matrix functions of class L on the unit circle by matrix functions analytic in the unit disk in the norm of L, 2 ≤ p < ∞. For an m × n matrix function Φ in L, we consider the Hankel operator HΦ : H(C) → H −(C), 1/p + 1/q = 1/2. It turns out that the space of m × n matrix functions in L splits into two subclasses: the set of respectable matrix function...