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We consider two matrix completion problems, in which we are given a matrix with missing entries and the task is to complete the matrix in a way that (1) minimizes the rank, or (2) minimizes the number of distinct rows. We study the…

Data Structures and Algorithms · Computer Science 2018-09-14 Robert Ganian , Iyad Kanj , Sebastian Ordyniak , Stefan Szeider

Processing of missing data by modern neural networks, such as CNNs, remains a fundamental, yet unsolved challenge, which naturally arises in many practical applications, like image inpainting or autonomous vehicles and robots. While…

Machine Learning · Computer Science 2021-11-01 Marcin Przewięźlikowski , Marek Śmieja , Łukasz Struski , Jacek Tabor

A method of modeling data with gaps by a sequence of curves has been developed. The new method is a generalization of iterative construction of singular expansion of matrices with gaps. Under discussion are three versions of the method…

Disordered Systems and Neural Networks · Physics 2007-05-23 A. N. Gorban , A. A. Rossiev , D. C. Wunsch

The main contribution of this paper is the development of a new decision tree algorithm. The proposed approach allows users to guide the algorithm through the data partitioning process. We believe this feature has many applications but in…

Machine Learning · Statistics 2020-10-27 Cédric Beaulac , Jeffrey S. Rosenthal

In this article, we discuss a novel approach to solving number sequence problems, in which sequences of numbers following unstated rules are given, and missing terms are to be inferred. We develop a methodology of decomposing test sequences…

History and Overview · Mathematics 2022-11-29 John Prager

Matrix completion and extrapolation (MCEX) are dealt with here over reproducing kernel Hilbert spaces (RKHSs) in order to account for prior information present in the available data. Aiming at a faster and low-complexity solver, the task is…

Machine Learning · Statistics 2019-10-02 Pere Giménez-Febrer , Alba Pagès-Zamora , Georgios B. Giannakis

Multi-View Representation Learning (MVRL) aims to derive a unified representation from multi-view data by leveraging shared and complementary information across views. However, when views are irregularly missing, the incomplete data can…

Machine Learning · Computer Science 2025-03-03 Xin Gao , Jian Pu

Conventional multi-view clustering seeks to partition data into respective groups based on the assumption that all views are fully observed. However, in practical applications, such as disease diagnosis, multimedia analysis, and…

Machine Learning · Computer Science 2022-08-18 Jie Wen , Zheng Zhang , Lunke Fei , Bob Zhang , Yong Xu , Zhao Zhang , Jinxing Li

This note presents some numerical examples worked out in order to show the reader how to implement, within a widely accessible computational setting, the methodology for achieving zero cancellation in linear multivariable systems discussed…

Systems and Control · Computer Science 2013-12-30 Elena Zattoni

Multi-view problems can be faced with latent variable models since they are able to find low-dimensional projections that fairly capture the correlations among the multiple views that characterise each datum. On the other hand,…

In many applications, e.g., recommender systems and traffic monitoring, the data comes in the form of a matrix that is only partially observed and low rank. A fundamental data-analysis task for these datasets is matrix completion, where the…

Machine Learning · Computer Science 2017-05-02 Natali Ruchansky , Mark Crovella , Evimaria Terzi

In reality, learning from multi-view multi-label data inevitably confronts three challenges: missing labels, incomplete views, and non-aligned views. Existing methods mainly concern the first two and commonly need multiple assumptions to…

Machine Learning · Computer Science 2024-06-12 Xiang Li , Songcan Chen

This paper considers the problem of kernel regression and classification with possibly unobservable response variables in the data, where the mechanism that causes the absence of information is unknown and can depend on both predictors and…

Statistics Theory · Mathematics 2022-12-07 Majid Mojirsheibani , William Pouliot , Andre Shakhbandaryan

Matrix completion is often applied to data with entries missing not at random (MNAR). For example, consider a recommendation system where users tend to only reveal ratings for items they like. In this case, a matrix completion method that…

Machine Learning · Statistics 2019-10-30 Wei Ma , George H. Chen

Point cloud completion is the task of predicting complete geometry from partial observations using a point set representation for a 3D shape. Previous approaches propose neural networks to directly estimate the whole point cloud through…

Computer Vision and Pattern Recognition · Computer Science 2020-10-12 Alexis Mendoza , Alexander Apaza , Ivan Sipiran , Cristian Lopez

We here propose a machine learning approach for monitoring particle detectors in real-time. The goal is to assess the compatibility of incoming experimental data with a reference dataset, characterising the data behaviour under normal…

High Energy Physics - Experiment · Physics 2023-03-10 Gaia Grosso , Nicolò Lai , Marco Letizia , Jacopo Pazzini , Marco Rando , Lorenzo Rosasco , Andrea Wulzer , Marco Zanetti

This paper develops an inferential theory for high-dimensional matrix-variate factor models with missing observations. We propose an easy-to-use all-purpose method that involves two straightforward steps. First, we perform principal…

Methodology · Statistics 2025-03-26 Yongxia Zhang , Jinwen Liang , Liwen Xu , Keming Yu , Maozai Tian

A useful technique for analyzing incomplete tables is to model the missing data mechanisms of the variables using log-linear models. In this paper, we use log-linear parametrization and propose estimation methods for arbitrary three-way and…

Methodology · Statistics 2019-10-29 S. Ghosh , P. Vellaisamy

Railway points are among the key components of railway infrastructure. As a part of signal equipment, points control the routes of trains at railway junctions, having a significant impact on the reliability, capacity, and punctuality of…

Machine Learning · Computer Science 2019-07-03 Zhibin Li , Jian Zhang , Qiang Wu , Yongshun Gong , Jinfeng Yi , Christina Kirsch

A matrix completion problem is to recover the missing entries in a partially observed matrix. Most of the existing matrix completion methods assume a low rank structure of the underlying complete matrix. In this paper, we introduce an…

Machine Learning · Statistics 2020-11-16 Chencheng Cai , Rong Chen , Han Xiao