Rank Constraint Research Articles

Calmness of partial perturbation to composite rank constraint systems and its applications

This paper is concerned with the calmness of a partial perturbation to the composite rank constraint system, an intersection of the rank constraint set and a general closed set, which is shown to be equivalent to a local Lipschitz-type error bound and also a global Lipschitz-type error bound under a certain compactness. Based on its lifted formulation, we derive two criteria for identifying those closed sets such that the associated partial perturbation possesses the calmness, and provide a collection of examples to demonstrate that the criteria are satisfied by common nonnegative and positive semidefinite rank constraint sets. Then, we use the calmness of this perturbation to obtain several global exact penalties for rank constrained optimization problems, and a family of equivalent DC surrogates for rank regularized problems.

Analyzing constraints of smallholders' chickpea (Cicer arietinum L.) production systems in Gondar Zuria Woreda of Ethiopia using the Henry Garrett’s ranking technique

In Ethiopian, pulses are the second top most grain crops, of which chickpea takes the first place. However, chickpea production by smallholder farmers has been facing several constraints and this has not been adequately studied using the appropriate techniques. As a result, this study used Henry Garrett’s ranking technique to analyze and rank constraints in the production of chickpeas. . Using the multistage sampling technique, the data were gathered from 140 randomly chosen samples. The findings indicate the smallholder chickpea producers face input, marketing, economic, institutional, and environmental constraints. As to the Henry Garrett’s ranking, higher price of seed (65%), higher price of chemicals (64.3%), delays in supply of improved seed (64%), capital shortage (60.5%), shortage of improved seed (58%), and disease infestation (56.4%) are the major constraints noted in average values. It is noted that. The study concludes that ranking constraints using the Henry Garrett technique are better as compared to simple frequencies. Key prerequisites for a robust chickpea production include addressing of constraints relating to irregularity and shortage in the supply of improved chickpea seed varieties, higher cost of inputs, diseases and pests, and inability to access in-kind credit.

3-D Inter-Robot Relative Localization via Semidefinite Optimization

In this letter, the 3-D inter-robot relative localization problem is addressed using noise-corrupted odometric and distance measurements. Unlike the existing solutions, we are devoted to providing a relative localization method that has an “overall best performance,” which means that the tradeoffs between the estimation accuracy (EA), the number of measurements (NoMs), and the computation efficiency (CE) are considered. We demonstrate that an existing formulation of the 3-D relative localization problem, the square distances weighted least square (SD-WLS), can be equivalently reformulated as a non-convex quadratic constrained quadratic programming (QCQP) problem. Further, to handle the non-convex nature of the QCQP problem, we adopt the semidefinite programming (SDP) relaxation approach, which drops the rank constraint and recovers the solution of the QCQP via an eigenvalue decomposition strategy. Finally, a refinement step is introduced to solve the problem that the quadratic constraints might not be satisfied due to the SDP relaxation. The simulation and experiment results show that, compared to existing methods, our method has the best overall performance when the three factors, i.e., EA, NoMs, and CE, are important for a relative localization application.

An augmented Lagrangian method for optimization problems with structured geometric constraints

This paper is devoted to the theoretical and numerical investigation of an augmented Lagrangian method for the solution of optimization problems with geometric constraints. Specifically, we study situations where parts of the constraints are nonconvex and possibly complicated, but allow for a fast computation of projections onto this nonconvex set. Typical problem classes which satisfy this requirement are optimization problems with disjunctive constraints (like complementarity or cardinality constraints) as well as optimization problems over sets of matrices which have to satisfy additional rank constraints. The key idea behind our method is to keep these complicated constraints explicitly in the constraints and to penalize only the remaining constraints by an augmented Lagrangian function. The resulting subproblems are then solved with the aid of a problem-tailored nonmonotone projected gradient method. The corresponding convergence theory allows for an inexact solution of these subproblems. Nevertheless, the overall algorithm computes so-called Mordukhovich-stationary points of the original problem under a mild asymptotic regularity condition, which is generally weaker than most of the respective available problem-tailored constraint qualifications. Extensive numerical experiments addressing complementarity- and cardinality-constrained optimization problems as well as a semidefinite reformulation of MAXCUT problems visualize the power of our approach.

Distributed Robust Dictionary Pair Learning and Its Application to Aluminum Electrolysis Industrial Process

In modern industrial systems, high-dimensional process data provide rich information for process monitoring. To make full use of local information of industrial process, a distributed robust dictionary pair learning (DRDPL) is proposed for refined process monitoring. Firstly, the global system is divided into several sub-blocks based on the reliable prior knowledge of industrial processes, which achieves dimensionality reduction and reduces process complexity. Secondly, a robust dictionary pair learning (RDPL) method is developed to build a local monitoring model for each sub-block. The sparse constraint with l2,1 norm is added to the analytical dictionary, and a low rank constraint is applied to the synthetical dictionary, so as to obtain robust dictionary pairs. Then, Bayesian inference method is introduced to fuse local monitoring information to global anomaly detection, and the block contribution index and variable contribution index are used to realize anomaly isolation. Finally, the effectiveness of the proposed method is verified by a numerical simulation experiment and Tennessee Eastman benchmark tests, and the proposed method is then successfully applied to a real-world aluminum electrolysis process.

Projection onto the Set of Rank-Constrained Structured Matrices for Reduced-Order Controller Design

In this paper, we propose an efficient numerical computation method of reduced-order controller design for linear time-invariant systems. The design problem is described by linear matrix inequalities (LMIs) with a rank constraint on a structured matrix, due to which the problem is non-convex. Instead of the heuristic method that approximates the matrix rank by the nuclear norm, we propose a numerical projection onto the rank-constrained set based on the alternating direction method of multipliers (ADMM). Then the controller is obtained by alternating projection between the rank-constrained set and the LMI set. We show the effectiveness of the proposed method compared with existing heuristic methods, by using 95 benchmark models from the COMPLeib library.

Multi-view clustering with graph regularized optimal transport

For a multi-view learning task, it is crucial to assign appropriate weights to each view in order to learn complementary and consistent information across different views. In the field of multi-view clustering, most existing methods have been able to handle the weights of different views. However, these algorithms face the problem of unacceptable time complexity when dealing with large-scale datasets, and the learned similarity matrix fails to satisfy the graph regularization. In this paper, we propose an auto-weight learning method called multi-view clustering with graph regularized optimal transport. First, an anchor-based method is employed to overcome the problem of heavy time complexity when processing large-scale datasets, and it is able to automatically learn an appropriate weight for each view. Second, by introducing optimal transport we learn a regularized doubly-stochastic similarity matrix applicable to multi-view clustering tasks. Third, the optimal regularized anchor graph can be classified into specific clusters by adding a rank constraint. Finally, an effective optimization method is designed to optimize the formulated problem. Comprehensive experiments on multiple real-world datasets demonstrate that the proposed algorithm achieves superior performance to other state-of-the-arts algorithms.

High-Performance Estimation of Jamming Covariance Matrix for IRS-Aided Directional Modulation Network With a Malicious Attacker

In this paper, we investigate the anti-jamming problem of a directional modulation (DM) system with the aid of intelligent reflecting surface (IRS). As an efficient tool to combat malicious jamming, receive beamforming (RBF) is usually designed by using the statistical properties of the jamming received by Bob. Thus, it is very necessary to estimate the receive jamming covariance matrix (JCM) at Bob. To achieve a precise JCM estimation, three JCM estimation methods, including eigenvalue decomposition (EVD), parametric estimation method by gradient descend (PEM-GD) and parametric estimation method by alternating optimization (PEM-AO), are proposed. Here, the proposed EVD is derived according to the rank-2 constraint of JCM. The PEM-GD method fully explores the structure features of JCM and the PEM-AO is proposed to decrease the computational complexity of the former via dimensionality reduction. The simulation results show that the proposed three methods perform better than directly using sample covariance matrix. Additionally, the proposed PEM-GD and PEM-AO outperform EVD method and the clutter and disturbance covariance estimator RCML.

Random translation-invariant Hamiltonians and their spectral gaps

We consider random translation-invariant frustration-free quantum spin Hamiltonians on ZD in which the nearest-neighbor interaction in every direction is randomly sampled and then distributed across the lattice. Our main result is that, under a small rank constraint, the Hamiltonians are automatically frustration-free and they are gapped with a positive probability. This extends previous results on 1D spin chains to all dimensions. The argument additionally controls the local gap. As an application, we obtain a 2D area law for a cut-dependent ground state via recent AGSP methods of Anshu-Arad-Gosset.

Semisupervised Feature Selection via Generalized Uncorrelated Constraint and Manifold Embedding.

Ridge regression is frequently utilized by both supervised learning and semisupervised learning. However, the results cannot obtain the closed-form solution and perform manifold structure when ridge regression is directly applied to semisupervised learning. To address this issue, we propose a novel semisupervised feature selection method under generalized uncorrelated constraint, namely SFS. The generalized uncorrelated constraint equips the framework with the elegant closed-form solution and is introduced to the ridge regression with embedding the manifold structure. The manifold structure and closed-form solution can better save data's topology information compared to the deep network with gradient descent. Furthermore, the full rank constraint of the projection matrix also avoids the occurrence of excessive row sparsity. The scale factor of the constraint that can be adaptively obtained also provides the subspace constraint more flexibility. Experimental results on data sets validate the superiority of our method to the state-of-the-art semisupervised feature selection methods.

Nonlocal ultrasound image despeckling via improved statistics and rank constraint

Nonlocal ultrasound image despeckling via improved statistics and rank constraint

Fast NMR spectroscopy reconstruction with a sliding window based Hankel matrix

Nuclear Magnetic Resonance (NMR) spectroscopy is one of the most promising analytical chemistry techniques, although it takes a long time to acquire data. Non-uniform sampling (NUS) is an effective way to reduce the sampling time, but faithful reconstruction methods are needed. The low rank Hankel matrix (LRHM) approach uses the low rank constraint to obtain high-quality spectra from NUS signals, but the reconstruction has a considerable time overhead. In this work, we propose a sliding window based low rank Hankel matrix approach to speed up the spectra reconstruction from NUS signals. Using the sliding window to construct a matrix can effectively reduce the size of the Hankel matrix for faster reconstructions. To further decrease the reconstruction time, parallel computation is applied in the proposed approach. The experiments on both synthetic data and realistic data demonstrate that the reconstruction speed of the proposed method is the fastest among compared methods without sacrificing the quality of spectra.

Tone and morphological level ordering in Dagaare

AbstractDagaare is a language of northern Ghana and adjoining areas of Burkina Faso. There are two tones, H and L, and contrastive downstep H!H that involves a non-automatic pitch drop between two H tones. The challenge is to explain the extensive morphological conditioning of tonal processes, including dissimilation, downstep and spreading. Our solution involves level ordering: tones are introduced at different morphological levels (stems, words and phrases) and later processes can make earlier processes opaque. Tonal differences between nouns (spreading) versus verbs (no spreading) and stems (dissimilation) versus words (downstep) arise from constraint ranking differences within and across levels. There are two kinds of downsteps: stem-level downsteps are underlying L tones affiliated with some morpheme; word-level downsteps are L tones inserted by a general process of word-final lowering. Only one downstep per word is allowed. If more would arise, the morphologically inner downstep blocks the morphologically outer downstep.

An Aspect of Sinhala Assimilation

This paper deals with the assimilations in Sinhala. Syllable contact, which prohibits a rising sonority across the syllable boundary, plays a critical role in assimilation. If a medial cluster shows a falling sonority, assimilation does not apply. When a medial cluster has either a rising or an equal sonority, leftward assimilation arises, resulting in geminates. If, however, a sequence consists of a consonant and a glide, perseverative assimilation occurs instead. It implies the prominence of the onset position can disappear if the onset segment is a weak glide. Another progressive assimilation occurs in the data in which several phonological processes apply before progressive assimilation. The application of phonological processes creates a segment sequence that calls for progressive assimilation. Assimilation types in Sinhala reveal that a simple input-to-output mapping of the classic OT cannot provide a proper analysis. To explain them, we use a theoretical framework, Harmonic Serialism (HS), which can incorporate both rule-based and constraint-based components. We propose one constraint ranking, which can account for non-assimilating and assimilating data in Sinhala.

Factorization of Binary Matrices: Rank Relations, Uniqueness and Model Selection of Boolean Decomposition

The application of binary matrices are numerous. Representing a matrix as a mixture of a small collection of latent vectors via low-rank decomposition is often seen as an advantageous method to interpret and analyze data. In this work, we examine the factorizations of binary matrices using standard arithmetic (real and nonnegative) and logical operations (Boolean and ℤ 2 ). We examine the relationships between the different ranks, and discuss when factorization is unique. In particular, we characterize when a Boolean factorization X = W ∧ H has a unique W , a unique H (for a fixed W ), and when both W and H are unique, given a rank constraint. We introduce a method for robust Boolean model selection, called BMF k , and show on numerical examples that BMF k not only accurately determines the correct number of Boolean latent features but reconstruct the pre-determined factors accurately.

Privileged multi-task learning for attribute-aware aesthetic assessment

Aesthetic attributes are crucial for aesthetics because they explicitly present some photo quality cues that a human expert might use to evaluate a photo’s aesthetic quality. However, the aesthetic attributes have not been largely and sufficiently exploited for photo aesthetic assessment. In this paper, we propose a novel approach to photo aesthetic assessment with the help of aesthetic attributes. The aesthetic attributes are used as privileged information (PI), which is often available during training phase but unavailable in prediction phase due to the high collection expense. The proposed framework consists of a deep multi-task network as generator and a fully connected network as discriminator. Deep multi-task network learns the aesthetic attributes and score simultaneously to capture their dependencies and extract better feature representations. Specifically, we use ranking constraint in the label space, similarity constraint and prior probabilities loss in the privileged information space to make the output of multi-task network converge to that of ground truth. Adversarial loss is used to identify and distinguish the predicted privileged information of a deep multi-task network from the ground truth PI distribution. Experimental results on two benchmark databases demonstrate the superiority of the proposed method to state-of-the-art.

Learning interpretable shared space via rank constraint for multi-view clustering

Learning interpretable shared space via rank constraint for multi-view clustering

An optimality-theoretic account of the acquisition of English tenses: The case of Moroccan EFL learners

The study intends to describe the acquisition of the English tenses among Moroccan EFL learners. The analysis investigates each tense, employing the constraint demotion algorithm (CDA). The belief here is that errors emerging at the initial learning stages are indicators of L1 transfer. Based on the L1 properties, CDA rearranges the constraints to establish a constraint ranking, identical to that of English, based on the hierarchy detected through universal grammar (UG). Two hundred and twenty students, belonging to three different academic levels, participated in the study. The questionnaire they answered tested tenses through three different tasks. The output stemming from the analysis was that students’ mother tongue plays an important role in the acquisition of the tenses of English. The article concludes that the learners reach an intermediate phase in the interlanguage before eventually learning the correct tense form.

Analyzing the Constraints as Perceived by the Board of Directors in the Initial Development Phase of the Farmer Producer Organizations

Farmer Producer Organizations (FPOs) are the group of organization which is formed to solve marketing and value addition constraints of small and marginal farmers, minimize involvement of middlemen, empower farmers and to make farming more profi table. But FPOs are facing various constraints especially in initial stages of development.The objective of this study was framed to fi nd out and rank constraints perceived by Board of Directors (BODs) of FPO in Jharkhand. One BOD member from each selected 45 FPOs was interviewed for data collection. Constraints were identifi ed and ranked using Garrett Ranking Technique. Less knowledge of how to strengthen FPO; less facility of storage of produce; members are not willing to contribute for FPO; only few members of BOD are active and advance payment is required for getting inputs were perceived most severe constraints among technical, marketing, fi nancial, governance and input supply respectively.

Research on Talent Evaluation Technology Based on Systematic Co-Reaction Force Method

In the multi-method and multi-model collaborative matrix model clustering calculation analysis, the talent evaluation sample data itself is used as a dictionary to re-represent each sample data, and the sample-based collaborative data reconstruction is carried out, and the talent evaluation reconstruction coefficient matrix is sparse, Low rank and smooth constraints greatly improve the reliability and validity of enterprise talent evaluation samples[1]. The main purpose of this paper is to design and construct a multi-model and multi-view collaborative similarity matrix for enterprise talent assessment, to mine the relationship between talent assessment samples, and to achieve clustering and collaboration of assessment samples.