Search

Dynamic Time Warping (DTW) is a well-known similarity measure for time series. The standard dynamic programming approach to compute the DTW distance of two length-n time series, however, requires $$O(n^2)$$ O ( n 2 ) time, which is often too slow for real-world applications. Therefore, many heuristics have been proposed to speed up the DTW computation. These are often based on lower bounding techniques, approximating the DTW distance, or considering special input data such as binary or piecewise constant time series. In this paper, we present a first exact algorithm to compute the DTW distance of two run-length encoded time series whose running time only depends on the encoding lengths of the inputs. The worst-case running time is cubic in the encoding length. In experiments we show that our algorithm is indeed fast for time series with short encoding lengths.

We provide evidence for partial deconfinement -- the deconfinement of a SU($M$) subgroup of the SU($N$) gauge group -- by using lattice Monte Carlo simulations. We take matrix models as concrete examples. By appropriately fixing the gauge, we observe that the $M\times M$ submatrices deconfine. This gives direct evidence for partial deconfinement at strong coupling. We discuss the applications to QCD and holography., Comment: 49 pages, 24 figures, 3 tables. Version accepted for publication on JHEP

In the article the authors present improved Dijkstra's method for the military communication system by using the incidence matrix of nodes and communication lines instead of the incidence matrix of nodes. The improved method was adapted to the model of the military communication system, which is formalized by a block matrix of the incidence of nodes and communication lines with the division of matrix blocks by types and components of the military communication system. The improvement implies in the introduction of additional blocks to the standard Dijkstra algorithm for preliminary, more accurate calculation of the weighting factors of communication lines. At the same time, the authors propose a number of new analytical expressions based on the use of the block matrix of secondary incidence, as well as the quadratic form of the incidence matrix. Mathematical modeling based on a simplified model of the military communication system confirmed the efficiency of the improved method. The improved method synthesized by the authors is more relevant to the real conditions of managing the military communication system and can be used for the needs of the system management process automation as a basis for the development of information and analytical tasks., У статті удосконалено метод Дейкстри для системи військового зв’язку завдяки використанню матриці інцидентності вузлів і ліній зв’язку замість матриці інцидентності вузлів. Удосконалений метод адаптовано до моделі системи військового зв’язку, що формалізується блоковою матрицею інцидентності вузлів і ліній зв’язку з поділом блоків матриці за родами і складовими системи військового зв’язку. Суть удосконалення полягає у введені додаткових блоків до стандартного алгоритму Дейкстри з метою попереднього, точнішого обчислення вагових коефіцієнтів ліній зв’язку. Водночас, на основі використання блокової матриці вторинної інцидентності, а також квадратичної форми матриці інцидентності, запропоновано низку нових аналітичних виразів. Математичне моделювання, на основі спрощеної моделі системи військового зв’язку, підтвердило ефективність удосконаленого методу. Синтезований удосконалений метод точніше відповідає реальним умовам управління системою військового зв’язку і може бути використаний для потреб автоматизації процесу управління системою як основи для розробки інформаційно-аналітичних завдань.

The maximum weighted submatrix coverage problem is a recently introduced problem with applications in data mining. It is concerned with selecting K submatrices of a given numerical matrix such that the sum of the matrix-entries, which occur in at least one of the selected submatrices, is maximized. In the paper introducing the problem, a problem-specific constraint programming approach was developed and embedded in a large neighborhood-search to obtain a heuristic. A compact integer linear programming formulation was also presented, but deemed inefficient due to its size. In this paper, we introduce new integer linear programming formulations for the problem, one of them is based on Benders decomposition. The obtained Benders decomposition-based formulation has a nice combinatorial structure, i.e., there is no need to solve linear programs to separate Benders cuts. We present preprocessing procedures and valid inequalities for all formulations. We also develop a greedy randomized adaptive search procedure for the problem, which is enhanced with a local search. A computational study using the instances from literature is done to evaluate the effectiveness of our new approaches. Our algorithms manage to find improved primal solutions for ten out of 17 real-world instances, and optimality is proven for two real-world instances. Moreover, for over 700 of 1617 large-scale synthetic instances, our algorithms find improved primal solutions compared to the heuristics from the literature.

Let A,B be subsets of a finite abelian group G. Suppose that A+B does not contain a unique sum, i.e., there is no g∈G with a unique representation g=a+b, a∈A, b∈B. From such sets A,B, sparse linear systems over the rational numbers arise. We obtain a new determinant bound on invertible submatrices of the coefficient matrices of these linear systems. Under the condition that |A|+|B| is small compared to the order of G, these bounds provide essential information on the Smith Normal Form of these coefficient matrices. We use this information to prove that A and B admit coset partitions whose parts have properties resembling those of A and B. As a consequence, we improve previously known sufficient conditions for the existence of unique sums in A+B and show how our structural results can be used to classify sets A and B for which A+B does not contain a unique sum when |A|+|B| is relatively small. Our method also can be applied to subsets of abelian groups which have no unique differences. Ministry of Education (MOE) This research is supported by the Ministry of Education, Singapore, under its Academic Research Fund Tier 1 (RG27/18).

Multi-view clustering has become an active topic in artificial intelligence. Yet, similar investigation for graph-structured data clustering has been absent so far. To fill this gap, we present a Multi-View Graph embedding Clustering network (MVGC). Specifically, unlike traditional multi-view construction methods, which are only suitable to describe Euclidean structure data, we leverage Euler transform to augment the node attribute, as a new view descriptor, for non-Euclidean structure data. Meanwhile, we impose block diagonal representation constraint, which is measured by the l 1 , 2 -norm, on self-expression coefficient matrix to well explore the cluster structure. By doing so, the learned view-consensus coefficient matrix well encodes the discriminative information. Moreover, we make use of the learned clustering labels to guide the learnings of node representation and coefficient matrix, where the latter is used in turn to conduct the subsequent clustering. In this way, clustering and representation learning are seamlessly connected, with the aim to achieve better clustering performance. Extensive experimental results indicate that MVGC is superior to 11 state-of-the-art methods on four benchmark datasets. In particular, MVGC achieves an Accuracy of 96.17% (53.31%) on the ACM (IMDB) dataset, which is an up to 2.85% (1.97%) clustering performance improvement compared with the strongest baseline.

Multi-view subspace clustering is an effective method to partition data into their corresponding categories. Nevertheless, existing multi-view subspace clustering approaches generally operate in a purely unsupervised manner, while ignoring the valuable weakly supervised information that can be readily obtained in many practical applications. In this paper, we consider the weakly supervised form of sample pair constraints, and devote to promoting the performance of multi-view subspace clustering with the aid of such prior knowledge. To achieve this goal, inspired by the intrinsic block diagonal structure of ideal low-rank representation (LRR), we propose a novel regularization to integrate must-link, cannot-link and normalization constraints into a unified formulation. The proposed regularization can be regarded as a general description for sample pairwise constraints, and thus provides a flexible framework for multi-view semi-supervised subspace clustering task. Furthermore, we devise a contrained tensor representation learning (CTRL) model that takes advantage of our proposed regularization to facilitate the learning of the desired representation tensor. An efficient optimization algorithm based on alternating direction minimization strategy is carefully designed to solve the proposed CTRL model. Extensive experiments on eight challenging real-world datasets are conducted, and the results validate the effectiveness of our designed pairwise constraints regularization, as well as the superiority of the proposed CTRL model.

We give a unified proof of the interlacing properties of eigenvalues of principle submatrices of totally positive matrices.

Last decades, there has been an increased interest in the use of the self-potential (SP) method in hydrogeophysics. In response to this strong interest, we develop a novel approach to the inversion of SP data. Mathematically, the SP inverse problem is the source identification problem for the Poisson equation. Our approach substantially differs from the standard regularization approach, which explicitly includes the forward-problem operator into the cost functional. We formulated the inverse problem is as an optimal control problem and then translate it into a variational system. The system is approximated in suitable finite-element spaces giving rise to an algebraic problem with the saddle-point structure. In contrast to the standard approach, which leads to a dense linear system, our method results in a system with a sparse block matrix. It can be efficiently solved by either direct sparse solvers or preconditioned iterative solvers. In this paper, we present the formulation of the problem and its finite-element approximation. We discuss the iterative solution and preconditioning strategies. Our software implementation is based on an industrial finite-element package. We also present a numerical experiment with node-based linear finite elements on tetrahedral grids. Our results suggest that the proposed approach may serve as a rapid and reliable tool for large-scale SP inverse problems. Moreover, the same technique can easily be extended to a wide range of geophysical linear inverse problems, such as inversions of magnetic and gravity data.

This letter proposes a novel sparse recovery method of multiple-input and multiple-output (MIMO) radar compressed sensing (CS) imaging algorithms. This method leverages the prior structure of the measurement matrix to judge targets' locations and to estimate the sparsity level in the grid roughly and finally inhabits the emergence of false targets in the imaging figure. Explicitly, the algorithm we propose is inspired by the orthogonal matching pursuit (OMP) algorithm. First, the measurement matrix can be divided into some submatrices by column. Then, we estimate which submatrices do not contain signal components by the algorithms we propose in this literature to achieve the reconstruction of the measurement matrix. Finally, we use the sparse Bayesian learning algorithm and the sparsity adaptive matching pursuit algorithm to recover the target location and scattering intensity. Experiments validate that the reconstruction error of the algorithm we propose is much lower than other sparse recovery algorithms, and targets in the imaging are more obvious than other algorithms.

International audience; This paper is concerned with the in-domain stabilization of a class of block diagonal infinite-dimensional systems in the presence of an uncertain and time-varying delay in the distributed control input. Two actuation schemes are considered. The first one assumes a control input that is fully distributed over the domain. The second one assumes that the control input is finite-dimensional, acting over the domain via a bounded operator. In both cases, the control design strategy consists in a predictor feedback law synthesized on a finite-dimensional truncated LTI model capturing the unstable dynamics of the original infinitedimensional system. The predictor feedback law is designed based on the knowledge of the nominal value of the uncertain and time-varying input delay. In the second actuation scheme, the case of distinct input delays in the different scalar control input channels is considered. Index Terms-Delayed distributed actuation, partial differential equations, predictor feedback law. H. Lhachemi and R. Shorten acknowledge the support of Science Foundation Ireland (Grant numbers 16/RC/3872 and 16/IA/4610) and I-Form industry partners. C. Prieur acknowledges the support from MIAI@Grenoble Alpes, (ANR-19-P3IA-0003).

There is a dearth of compressed-sensing localization in the domain of underwater acoustic sensor networks (UASNs). To address this limitation, this paper proposes SAP2: a Sparse-sensing Acoustic Positioning scheme for Stratified and Perturbed UASNs. Three conditions of underwater perturbation are defined, namely, Spin perturbation, Rectilinear dispersion condition, and Radially perturbed condition to model the sudden disturbances in the underwater network topology. Then, “Footprint Variation” is proposed to express the behavior of UASN node topology. Theorem 2.2.b is proposed for the exact retrieval of sparsely deployed UASN location under perturbation conditions. The derivation of a unique solution to the insertion vector in Lemma 3.1.a holds the estimated location of target, necessitating the incoherence of the sensing matrix with the basis vector. Block matrix representation of the coefficients is derived in Lemma 3.1.b. Invertibility of the block matrix is proven in Lemma 3.1.c to establish sparsity of underwater sensor networks. An example is illustrated with a realistic scenario to observe parameters such as correlation of sparse coefficients, distinctness of discretized samples and footprint variation based on perturbation. Footprint variation is found to be below 100m2 for uncorrelated discrete measurements using SAP2 technique. Through rigorous mathematical justification and realistic underwater channel scenario, it is established that compressed sensing based underwater localization is feasible for a sparse sensor network.

Two-level fractional factorial designs are often used in screening scenarios to identify active factors. This article investigates the block diagonal structure of the information matrix of nonregul...

The subspace clustering methods for motion segmentation are widely used in the field of computer vision. However, the existing methods ignore the low-rank property of motion trajectory with nonlinear structure and are sensitive to non-Gaussian noise. To this end, we seek to improve the performance of motion segmentation by effectively modeling some important characteristics of the motion trajectories, such as nonlinear structure and contained non-Gaussian noise. Specifically, we propose to use kernel function to model motion trajectory, design a variant of the correntropy-induced metric to measure noise, and integrate the block diagonal regularizer into the kernel subspace clustering to strengthen the block diagonal structure of the learned affinity matrix. More importantly, we propose a unified rank-constrained block diagonal subspace clustering method for motion segmentation, which can handle not only rigid body motion segmentation, but also non-rigid motion segmentation. And we further extend this method to deal with various noises in motion data, such as missing trajectories, corrupted trajectory and outlying trajectory. An effective algorithm HQ& AM, which is integrated by Half-quadratic theory and alternating minimization, is designed to optimize these models. Experimental results on several commonly used motion datasets indicate the effectualness and robustness of our methods.

The main goal of this paper is to elaborate some results on the spectral properties of $$2 \times 2$$ block matrix linear relations with unbounded entries and with a domain consisting of vectors which satisfy certain relations between their components. We present some conditions to prove some Frobenius–Schur decompositions for linear relations and characterize the stability of the essential spectra of these linear relations. Our results generalize many known ones in the literature, in particular those obtained by Alvarez et al. (in Math Methods Appl Sci 37:620–644, 2014) and Batkai et al. (in Math Nachr 278:1408–1429, 2005).

LU factorization is extensively used in engineering and scientific computations for solution of large set of linear equations. Particularly, circuit simulators rely heavily on sparse version of LU factorization for solution involving circuit matrices. One of the recent advances in this field is exploiting the emerging computing platform of graphics processing units (GPUs) for parallel and sparse LU factorization. In this article, following contributions are made to advance the state of the art in hybrid right-looking algorithm (RLA): 1) a novel GPU kernel based on parallel column and block size optimization (PCBSO) is developed for adaptively allocating the block size while optimizing the number of columns for parallel execution based on the size of their associated submatrices at every level. The proposed approach helps to minimize the resource contention and to improve the computational performance and 2) an algorithm is developed to enable the execution of the new adaptive mode with dynamic parallelism. Also, a comprehensive performance comparison using a set of benchmark circuit examples is presented. The results indicate that, the proposed advancements can improve the results of state-of-the-art right looking sparse LU factorization in GPU by $1.54\times $ (Arithmetic Mean).

This article considers two inverse eigenvalue problems for Lefkovitch and doubly Lefkovitch matrices. The problems consist of constructing these matrices from the maximal eigenvalues of all its leading principal submatrices, eigenvectors associated with some of these eigenvalues, and some diagonal entries. We give sufficient conditions for the existence of such matrices. In particular, when the matrices have constant diagonal entries. In addition, we provide numerical examples to show the results obtained.