Related papers: Computing DM-decomposition of a partitioned matrix…
This work studies the combinatorial optimization problem of finding an optimal core tensor shape, also called multilinear rank, for a size-constrained Tucker decomposition. We give an algorithm with provable approximation guarantees for its…
We present an algorithm that given any invertible symmetric diagonally dominant M-matrix (SDDM), i.e., a principal submatrix of a graph Laplacian, $\boldsymbol{\mathit{L}}$ and a nonnegative vector $\boldsymbol{\mathit{b}}$, computes an…
We consider a rank-one symmetric matrix corrupted by additive noise. The rank-one matrix is formed by an $n$-component unknown vector on the sphere of radius $\sqrt{n}$, and we consider the problem of estimating this vector from the…
The simulation of the physical movement of multi-body systems at an atomistic level, with forces calculated from a quantum mechanical description of the electrons, motivates a graph partitioning problem studied in this article. Several…
We present the asymptotically fastest known algorithms for some basic problems on univariate polynomial matrices: rank, nullspace, determinant, generic inverse, reduced form. We show that they essentially can be reduced to two computer…
This paper introduces a novel general-purpose algorithm for Pauli decomposition that employs matrix slicing and addition rather than expensive matrix multiplication, significantly accelerating the decomposition of multi-qubit matrices. In a…
The paper looks at a scaled variant of the stochastic gradient descent algorithm for the matrix completion problem. Specifically, we propose a novel matrix-scaling of the partial derivatives that acts as an efficient preconditioning for the…
We consider the problem of reconstructing a low-rank matrix from a small subset of its entries. In this paper, we describe the implementation of an efficient algorithm called OptSpace, based on singular value decomposition followed by local…
Matrix decompositions are fundamental tools in the area of applied mathematics, statistical computing, and machine learning. In particular, low-rank matrix decompositions are vital, and widely used for data analysis, dimensionality…
We address the problem of finding the minimum decomposition of a permutation in terms of transpositions with non-uniform cost. For arbitrary non-negative cost functions, we describe polynomial-time, constant-approximation decomposition…
Integral equations are commonly encountered when solving complex physical problems. Their discretization leads to a dense kernel matrix that is block or hierarchically low-rank. This paper proposes a new way to build a low-rank…
We give an exact algorithm to calculate (under some GKM-restriction) the matrix describing the embedding $\B(\s)_x\subset\B(\s)^x$, where the first module is the costalk and the second one is the stalk at $x$ of a Bott-Samelson module…
In this paper, we study a polynomial decomposition model that arises in problems of system identification, signal processing and machine learning. We show that this decomposition is a special case of the X-rank decomposition --- a powerful…
It is well known that a set of non-defect matrices can be simultaneously diagonalized if and only if the matrices commute. In the case of non-commuting matrices, the best that can be achieved is simultaneous block diagonalization. Here we…
We consider the factorization of a rectangular matrix $X $ into a positive linear combination of rank-one factors of the form $u v^\top$, where $u$ and $v$ belongs to certain sets $\mathcal{U}$ and $\mathcal{V}$, that may encode specific…
This paper is concerned with the problem of low rank plus sparse matrix decomposition for big data. Conventional algorithms for matrix decomposition use the entire data to extract the low-rank and sparse components, and are based on…
We revisit two NP-hard geometric partitioning problems - convex decomposition and surface approximation. Building on recent developments in geometric separators, we present quasi-polynomial time algorithms for these problems with improved…
We show how to compute a relative-error low-rank approximation to any positive semidefinite (PSD) matrix in sublinear time, i.e., for any $n \times n$ PSD matrix $A$, in $\tilde O(n \cdot poly(k/\epsilon))$ time we output a rank-$k$ matrix…
The Dynamic-Mode Decomposition (DMD) is a well established data-driven method of finding temporally evolving linear-mode decompositions of nonlinear time series. Traditionally, this method presumes that all relevant dimensions are sampled…
In this paper we show a new way of constructing deterministic polynomial-time approximation algorithms for computing complex-valued evaluations of a large class of graph polynomials on bounded degree graphs. In particular, our approach…