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Related papers: Geometric Matrix Completion: A Functional View

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We consider a problem of significant practical importance, namely, the reconstruction of a low-rank data matrix from a small subset of its entries. This problem appears in many areas such as collaborative filtering, computer vision and…

Machine Learning · Computer Science 2009-11-04 Raghunandan H. Keshavan , Andrea Montanari , Sewoong Oh

This research article suggests that there are significant benefits in exposing demand planners to forecasting methods using matrix completion techniques. This study aims to contribute to a better understanding of the field of forecasting…

Applications · Statistics 2020-09-10 Rodrigo Rivera-Castro , Ivan Nazarov , Evgeny Burnaev

In this paper, we present an approach, namely Lexical Semantic Image Completion (LSIC), that may have potential applications in art, design, and heritage conservation, among several others. Existing image completion procedure is highly…

Computer Vision and Pattern Recognition · Computer Science 2020-03-03 Shengyu Zhang , Tan Jiang , Qinghao Huang , Ziqi Tan , Zhou Zhao , Siliang Tang , Jin Yu , Hongxia Yang , Yi Yang , Fei Wu

We introduce and study a mathematical framework for a broad class of regularization functionals for ill-posed inverse problems: Regularization Graphs. Regularization graphs allow to construct functionals using as building blocks linear…

Optimization and Control · Mathematics 2022-09-28 Kristian Bredies , Marcello Carioni , Martin Holler

Functional equations satisfied by additive functions have a special interest not only in the theory of functional equations, but also in the theory of (commutative) algebra because the fundamental notions such as derivations and…

Classical Analysis and ODEs · Mathematics 2018-02-22 Eszter Gselmann , Gergely Kiss , Csaba Vincze

Several complex tasks that arise in organizations can be simplified by mapping them into a matrix completion problem. In this paper, we address a key challenge faced by our company: predicting the efficiency of artists in rendering visual…

Machine Learning · Computer Science 2020-05-19 Emanuele Bugliarello , Swayambhoo Jain , Vineeth Rakesh

Low rank matrix recovery problems, including matrix completion and matrix sensing, appear in a broad range of applications. In this work we present GNMR -- an extremely simple iterative algorithm for low rank matrix recovery, based on a…

Optimization and Control · Mathematics 2022-04-28 Pini Zilber , Boaz Nadler

Scientific and commercial data is often incomplete. Recovery of the missing information is an important pre-processing step in data analysis. Real-world data can in many cases be represented as a superposition of two or more different types…

Functional Analysis · Mathematics 2017-05-31 Emily J. King , James M. Murphy

We consider the symmetric Toeplitz matrix completion problem, whose matrix under consideration possesses specific row and column structures. This problem, which has wide application in diverse areas, is well-known to be computationally…

Optimization and Control · Mathematics 2024-03-15 Xihong Yan , Jiahao Guo , Yi Xu

In a previous paper [1] it was discussed the viability of functional analysis using as a basis a couple of generic functions, and hence vectorial decomposition. Here we complete the paradigm exploiting one of the analysis methodologies…

Numerical Analysis · Computer Science 2013-11-26 Sossio Vergara

This paper presents the first step of a wider research effort to apply tree automata completion to the static analysis of functional programs. Tree Automata Completion is a family of techniques for computing or approximating the set of…

Logic in Computer Science · Computer Science 2014-10-14 Thomas Genet

Noncommutative rational functions, i.e., elements of the universal skew field of fractions of a free algebra, can be defined through evaluations of noncommutative rational expressions on tuples of matrices. This interpretation extends their…

Rings and Algebras · Mathematics 2018-04-24 Jurij Volčič

This paper considers the problem of matrix completion when the observed entries are noisy and contain outliers. It begins with introducing a new optimization criterion for which the recovered matrix is defined as its solution. This…

Machine Learning · Statistics 2017-12-29 Raymond K. W. Wong , Thomas C. M. Lee

Shape completion, i.e., predicting the complete geometry of an object from a partial observation, is highly relevant for several downstream tasks, most notably robotic manipulation. When basing planning or prediction of real grasps on…

Computer Vision and Pattern Recognition · Computer Science 2026-01-21 Matthias Humt , Dominik Winkelbauer , Ulrich Hillenbrand

Multiresolution analysis and matrix factorization are foundational tools in computer vision. In this work, we study the interface between these two distinct topics and obtain techniques to uncover hierarchical block structure in symmetric…

Computer Vision and Pattern Recognition · Computer Science 2017-05-17 Vamsi K. Ithapu , Risi Kondor , Sterling C. Johnson , Vikas Singh

This paper studies the problem of completing a low-rank matrix from a few of its random entries with the aid of prior information. We suggest a strategy to incorporate prior information into the standard matrix completion procedure by…

Information Theory · Computer Science 2020-07-15 Xu Zhang , Wei Cui , Yulong Liu

Roughly speaking, functional analysis is the study of vector spaces of arbitrary dimension over the field of real or complex numbers, and the continuous linear mappings between such spaces. Naturally, the notion of continuity requires a…

Functional Analysis · Mathematics 2025-10-09 Christoph Bock

This work studies the strong duality of non-convex matrix factorization problems: we show that under certain dual conditions, these problems and its dual have the same optimum. This has been well understood for convex optimization, but…

Data Structures and Algorithms · Computer Science 2018-04-26 Maria-Florina Balcan , Yingyu Liang , David P. Woodruff , Hongyang Zhang

The increasing demand for Fourier transforms on geometric algebras has resulted in a large variety. Here we introduce one single straight forward definition of a general geometric Fourier transform covering most versions in the literature.…

Algebraic Geometry · Mathematics 2013-06-11 Roxana Bujack , Gerik Scheuermann , Eckhard Hitzer

For a rational function of several variables with nonnegative imaginary part on the upper poly-half-plane, the matrix representations are obtained.

Complex Variables · Mathematics 2021-11-30 M. F. Bessmertnyi