Related papers: Exact Recovery of Non-Random Missing Multidimensio…

Low-rank tensor completion aims to recover a tensor from partially observed entries, and it is widely applicable in fields such as quantum computing and image processing. Due to the significant advantages of the tensor train (TT) format in…

Time-delay embeddings and dimensionality reduction are powerful techniques for discovering effective coordinate systems to represent the dynamics of physical systems. Recently, it has been shown that models identified by dynamic mode…

We study the low-rank phase retrieval problem, where the objective is to recover a sequence of signals (typically images) given the magnitude of linear measurements of those signals. Existing solutions involve recovering a matrix…

This paper focus on recovering multi-dimensional data called tensor from randomly corrupted incomplete observation. Inspired by reweighted $l_1$ norm minimization for sparsity enhancement, this paper proposes a reweighted singular value…

Tensor completion is a fundamental tool for incomplete data analysis, where the goal is to predict missing entries from partial observations. However, existing methods often make the explicit or implicit assumption that the observed entries…

Data missing is an common issue in seismic data, and many methods have been proposed to solve it. In this paper, we present the low-tubal-rank tensor model and a novel tensor completion algorithm to recover 3D seismic data. This is a fast…

In the wild, we often encounter collections of sequential data such as electrocardiograms, motion capture, genomes, and natural language, and sequences may be multichannel or symbolic with nonlinear dynamics. We introduce a new method to…

Recent studies have demonstrated the great potential of reduced order modeling for parametric dynamical systems using low-rank tensor decompositions (LRTD). In particular, within the framework of interpolatory tensorial reduced order models…

Handling missing data in time series classification remains a significant challenge in various domains. Traditional methods often rely on imputation, which may introduce bias or fail to capture the underlying temporal dynamics. In this…

The Large Margin Distribution Machine (LMDM) is a recent advancement in classifier design that optimizes not just the minimum margin (as in SVM) but the entire margin distribution, thereby improving generalization. However, existing LMDM…

The low-tubal-rank tensor model has been recently proposed for real-world multidimensional data. In this paper, we study the low-tubal-rank tensor completion problem, i.e., to recover a third-order tensor by observing a subset of its…

Since higher-order tensors are naturally suitable for representing multi-dimensional data in real-world, e.g., color images and videos, low-rank tensor representation has become one of the emerging areas in machine learning and computer…

The purpose of this thesis is to develop new theories on high-dimensional structured signal recovery under a rather weak assumption on the measurements that only a finite number of moments exists. High-dimensional recovery has been one of…

Robust tensor recovery plays an instrumental role in robustifying tensor decompositions for multilinear data analysis against outliers, gross corruptions and missing values and has a diverse array of applications. In this paper, we study…

Low-rank Deconvolution (LRD) has appeared as a new multi-dimensional representation model that enjoys important efficiency and flexibility properties. In this work we ask ourselves if this analytical model can compete against Deep Learning…

Time series decomposition into trend, seasonal structure, and residual components is a core primitive for downstream analytics such as anomaly detection, change-point detection, and forecasting. However, most existing seasonal-trend…

Time series with missing or irregularly sampled data are a persistent challenge in machine learning. Many methods operate on the frequency-domain, relying on the Fast Fourier Transform (FFT) which assumes uniform sampling, therefore…

We derive theoretical guarantees for the exact recovery of piecewise constant two-dimensional images from a minimal number of non-uniform Fourier samples using a convex matrix completion algorithm. We assume the discontinuities of the image…

This work studies the problem of high-dimensional data (referred to as tensors) completion from partially observed samplings. We consider that a tensor is a superposition of multiple low-rank components. In particular, each component can be…

In recent years, the prediction of multidimensional time series data has become increasingly important due to its wide-ranging applications. Tensor-based prediction methods have gained attention for their ability to preserve the inherent…