Related papers: Finding minimum Tucker submatrices
It is well-known that every 3-connected planar graph has a unique planar embedding on the sphere. We study the extension to triangulated 1-planar graphs, T1P graphs for short, which admit an embedding in which each edge is crossed at most…
Recently, $l_{2,1}$ matrix norm has been widely applied to many areas such as computer vision, pattern recognition, biological study and etc. As an extension of $l_1$ vector norm, the mixed $l_{2,1}$ matrix norm is often used to find…
Superregular matrices have the property that all of their submatrices, which can be full rank are so. Lower triangular superregular matrices are useful for e.g., maximum distance separable convolutional codes as well as for (sequential)…
In this paper, we study the problems of detection and recovery of hidden submatrices with elevated means inside a large Gaussian random matrix. We consider two different structures for the planted submatrices. In the first model, the…
Submodular optimization has received significant attention in both practice and theory, as a wide array of problems in machine learning, auction theory, and combinatorial optimization have submodular structure. In practice, these problems…
A matrix algorithm is said to be superfast (that is, runs at sublinear cost) if it involves much fewer scalars and flops than the input matrix has entries. Such algorithms have been extensively studied and widely applied in modern…
Let A, B, C, D be given finite sets of pairs of n-by-n complex matrices. We describe an algorithm to determine, with finitely many computations, whether there is a single unitary matrix U such that each pair of matrices in A is unitarily…
In this article we discuss the presentation of a random binary matrix using sequence of whole nonnegative numbers. We examine some advantages and disadvantages of this presentation as an alternative of the standard presentation using…
A 0-1 matrix $M$ contains a 0-1 matrix pattern $P$ if we can obtain $P$ from $M$ by deleting rows and/or columns and turning arbitrary 1-entries into 0s. The saturation function $\mathrm{sat}(P,n)$ for a 0-1 matrix pattern $P$ indicates the…
It is now well known that the performance of a linear code $C$ under iterative decoding on a binary erasure channel (and other channels) is determined by the size of the smallest stopping set in the Tanner graph for $C$. Several recent…
Dimensionality reduction is a popular approach to tackle high-dimensional data with low-dimensional nature. Subspace Restricted Isometry Property, a newly-proposed concept, has proved to be a useful tool in analyzing the effect of…
We study tensor networks as a model of arithmetic computation for evaluating multilinear maps. These capture any algorithm based on low border rank tensor decompositions, such as $O(n^{\omega+\epsilon})$ time matrix multiplication, and in…
We study three fundamental problems of Linear Algebra, lying in the heart of various Machine Learning applications, namely: 1)"Low-rank Column-based Matrix Approximation". We are given a matrix A and a target rank k. The goal is to select a…
We establish a list of characterizations of bounded twin-width for hereditary, totally ordered binary structures. This has several consequences. First, it allows us to show that a (hereditary) class of matrices over a finite alphabet either…
To efficiently express tensor data using the Tucker format, a critical task is to minimize the multilinear rank such that the model would not be over-flexible and lead to overfitting. Due to the lack of rank minimization tools in tensor,…
Frick and Grohe [J. ACM 48 (2006), 1184-1206] introduced a notion of graph classes with locally bounded tree-width and established that every first order logic property can be decided in almost linear time in such a graph class. Here, we…
In this work we propose a method for reducing the dimensionality of tensor objects in a binary classification framework. The proposed Common Mode Patterns method takes into consideration the labels' information, and ensures that tensor…
In this paper, we study feature cross search as a fundamental primitive in feature engineering. The importance of feature cross search especially for the linear model has been known for a while, with well-known textbook examples. In this…
We study an iterative matrix conditioning algorithm due to Osborne (1960). The goal of the algorithm is to convert a square matrix into a balanced matrix where every row and corresponding column have the same norm. The original algorithm…
Originally developed for imputing missing entries in low rank, or approximately low rank matrices, matrix completion has proven widely effective in many problems where there is no reason to assume low-dimensional linear structure in the…