Matrix algebra
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An Overview of Low-Rank Matrix Recovery From Incomplete Observations Open
Low-rank matrices play a fundamental role in modeling and computational methods for signal processing and machine learning. In many applications where low-rank matrices arise, these matrices cannot be fully sampled or directly observed, an…
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Nonconvex Optimization Meets Low-Rank Matrix Factorization: An Overview Open
Substantial progress has been made recently on developing provably accurate\nand efficient algorithms for low-rank matrix factorization via nonconvex\noptimization. While conventional wisdom often takes a dim view of nonconvex\noptimizatio…
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Supervised Matrix Factorization Hashing for Cross-Modal Retrieval Open
The target of cross-modal hashing is to embed heterogeneous multimedia data into a common low-dimensional Hamming space, which plays a pivotal part in multimedia retrieval due to the emergence of big multimodal data. Recently, matrix facto…
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Multi-label Classifier Performance Evaluation with Confusion Matrix Open
Confusion matrix is a useful and comprehensive presentation of the classifier performance.It is commonly used in the evaluation of multi-class, single-label classification models, where each data instance can belong to just one class at an…
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Light Field Inpainting Propagation via Low Rank Matrix Completion Open
Building up on the advances in low rank matrix completion, this article presents a novel method for propagating the inpainting of the central view of a light field to all the other views. After generating a set of warped versions of the in…
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Covariance Matrix Estimation in Massive MIMO Open
Interference during the uplink training phase significantly deteriorates the performance of a massive MIMO system. The impact of the interference can be reduced by exploiting second order statistics of the channel vectors, e.g., to obtain …
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Set Stability and Stabilization of Switched Boolean Networks With State-Based Switching Open
This paper is devoted to studying the set stability and stabilization of switched Boolean networks (SBNs) with state-based switching using the semi-tensor product (STP) of matrices. First, the algebraic form of an SBN is obtained by STP. T…
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Structurally Incoherent Low-Rank Nonnegative Matrix Factorization for Image Classification Open
As a popular dimensionality reduction method, nonnegative matrix factorization (NMF) has been widely used in image classification. However, the NMF does not consider discriminant information from the data themselves. In addition, most NMF-…
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A Characterization of Deterministic Sampling Patterns for Low-Rank Matrix Completion Open
Low-rank matrix completion (LRMC) problems arise in a wide variety of\napplications. Previous theory mainly provides conditions for completion under\nmissing-at-random samplings. This paper studies deterministic conditions for\ncompletion.…
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Vandermonde Factorization of Hankel Matrix for Complex Exponential Signal Recovery—Application in Fast NMR Spectroscopy Open
Many signals are modeled as a superposition of exponential functions in spectroscopy of chemistry, biology, and medical imaging. This paper studies the problem of recovering exponential signals from a random subset of samples. We exploit t…
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Analysis of a key exchange protocol based on tropical matrix algebra Open
In this paper, we consider a two party key-exchange protocol proposed in [D. Grigoriev and V. Shpilrain, Tropical cryptography , Comm. Algebra 43 (2014), 2624–2632, Section 2], which uses tropical matrix algebra as the platform. Our analys…
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On Persistency of Excitation and Formulas for Data-driven Control Open
In a paper by Willems and coworkers it was shown that persistently exciting data could be used to represent the input-output trajectory of a linear system. Inspired by this fundamental result, we derive a parametrization of linear feedback…
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A Sliding Mode Observer for Infinitely Unobservable Descriptor Systems Open
In existing work of sliding mode observers (SMOs) for descriptor systems, a necessary condition is that the system must be infinitely observable. This paper presents a scheme that circumvents that condition, by reformulating the system as …
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An improved bound for the lengths of matrix algebras Open
Let [math] be a set of [math] matrices over a field [math] . We show that the [math] -linear span of the words in [math] of length at most\n¶\n\n\n2\nn\n\n\nlog\n\n\n2\n\n\nn\n+\n4\nn\n\n\n¶ is the full [math] -algebra generated by [math] …
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Low-Complexity Modeling of Partially Available Second-Order Statistics: Theory and an Efficient Matrix Completion Algorithm Open
State statistics of linear systems satisfy certain structural constraints\nthat arise from the underlying dynamics and the directionality of input\ndisturbances. In the present paper we study the problem of completing partially\nknown stat…
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Recent Developments in Boolean Matrix Factorization Open
The goal of Boolean Matrix Factorization (BMF) is to approximate a given binary matrix as the product of two low-rank binary factor matrices, where the product of the factor matrices is computed under the Boolean algebra. While the problem…
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Geometric Algebra in Signal and Image Processing: A Survey Open
Recently, Geometric Algebra (GA) has attracted more and more attention in the field of signal and image processing. GA can treat multi-dimensional signals in a holistic way to keep the correlations among multiple dimensions and avoid infor…
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Isomorphism between the <i>R</i>-matrix and Drinfeld presentations of quantum affine algebra: Type <i>C</i> Open
An explicit isomorphism between the R-matrix and Drinfeld presentations of the quantum affine algebra in type A was given by Ding and Frenkel [Commun. Math. Phys. 156, 277–300 (1993)]. We show that this result can be extended to types B, C…
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Hankel Low-Rank Matrix Completion: Performance of the Nuclear Norm Relaxation Open
Accepted version.
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Text Similarity Estimation Based on Word Embeddings and Matrix Norms for Targeted Marketing Open
Tim vor der Brück, Marc Pouly. Proceedings of the 2019 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies, Volume 1 (Long and Short Papers). 2019.
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A Primal-Dual Analysis of Global Optimality in Nonconvex Low-Rank Matrix Recovery Open
We propose a primal-dual based framework for analyzing the global optimality of nonconvex low-rank matrix recovery. Our analysis are based on the restricted strongly convex and smooth conditions, which can be verified for a broad family of…
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The η-Anti-Hermitian Solution to a System of Constrained Matrix Equations over the Generalized Segre Quaternion Algebra Open
In this paper, we propose three real representations of a generalized Segre quaternion matrix. We establish necessary and sufficient conditions for the existence of the η-anti-Hermitian solution to a system of constrained matrix equations …
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PolSAR Ship Detection Based on Azimuth Sublook Polarimetric Covariance Matrix Open
Polarimetric synthetic aperture radar (PolSAR) is an important tool for marine remote sensing. In the past two decades, subaperture decomposition is considered as an alternative method to extract ship targets, especially in complex conditi…
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MBHGA: A Matrix-Based Hybrid Genetic Algorithm for Solving an Agent-Based Model of Controlled Trade Interactions Open
The article discusses the development and study of a new matrix-based hybrid genetic algorithm (MBHGA) for solving an agent-based model of firms’ behavior with controlled trade interactions. The proposed model employs symmetric strategies …
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Movie Recommendation via Markovian Factorization of Matrix Processes Open
The success of the probabilistic matrix factorization (PMF) model has inspired the rapid development of collaborative filtering algorithms, among which timeSVD++ has demonstrated great performance advantage in solving the movie rating pred…
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Supervised Nonnegative Matrix Factorization to Predict ICU Mortality Risk Open
ICU mortality risk prediction is a tough yet important task. On one hand, due to the complex temporal data collected, it is difficult to identify the effective features and interpret them easily; on the other hand, good prediction can help…
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On the Fundamental Limit of Orthogonal Matching Pursuit for Multiple Measurement Vector Open
Given Y ∈ Rm×I and A ∈ Rm×n, the multiple measurement vector (MMV) problem aims to recover the support of the K-row sparse matrix X from Y = AX + E. In this paper, we present a sufficient condition for exact support recovery of K-row spars…
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Output Control Method of Microgrid VSI Control Network Based on Dynamic Matrix Control Algorithm Open
In recent years, the power control method of the primary control layer in a microgrid hierarchical control system has substantially improved. However, the corresponding improvement in the dynamic response performance of the output controll…
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iMTF-GRN: Integrative Matrix Tri-Factorization for Inference of Gene Regulatory Networks Open
Gene Regulatory Network (GRN) inference using computational approaches has been a highly pursued problem in bioinformatics. Various approaches have been developed to infer GRNs from gene expression data including statistical, machine learn…
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Causality-Constrained Multiple Shift Sequential Matrix Diagonalisation For Parahermitian Matrices Open
Publication in the conference proceedings of EUSIPCO, Lisbon, Portugal, 2014