Bilinear Factorization Research Articles

Clutter Removal Method for Through-Wall Radar Based on Weighted Bilinear Factorization Regularization

Clutter Removal Method for Through-Wall Radar Based on Weighted Bilinear Factorization Regularization

Exploring the pyrolytic degradation of seventeen phthalate esters using the non-targeted regions of interest-multivariate curve resolution (ROIMCR) chemometric method

The global use of phthalate esters (PAEs) in plastic production entails a need for developing effective remediation strategies to minimize exposure and health risks. In this study, pyrolysis degradation processes are evaluated for 17 different PAEs that were analyzed by high-resolution gas chromatography-mass spectrometry (Pyr-GC-Orbitrap-MS) at different temperatures (300 °C, 400 °C, 500 °C, 600 °C, 700 °C, 800 °C) both in electron ionization (EI) and positive chemical ionization (PCI) mode. All the analytical data generated have been processed with the Regions of Interest Multivariate Curve Resolution (ROIMCR) chemometrics method. A preliminary selection of the Mass Spectrometry Regions of Interest (ROIs) coupled to a bilinear factor decomposition method (MCR-ALS) allowed the identification of 4 principal components, which were used to define the thermal degradation process. ROIMCR method is a powerful tool for non-targeted analysis which allows the resolution of the elution and spectral profiles of the different constituents present in the analyzed samples, which were confirmed using PCI. Moreover, ROIMCR was used to resolve and identify the different products generated during the studied degradation processes. As a result, 10 new thermal degradation products were identified in the analysis of the different sample sets. Finally, the degradation efficiencies higher than 99.8 % were obtained for all the PAEs at 800 °C, except for benzoic acid-benzyl ester, whose removal efficiency decreased to 94.8 %. As phthalates are widespread and toxic compounds for the environment and for humans, there is a need for new remediation technologies. This study provides new knowledge to understand their elimination through thermal processes. We combine mass spectrometric data with powerful chemometric processing to determine the removal efficiency, to understand the degradation process and to identify the degradation compounds formed through thermal decomposition.

Weighted bilinear factorization of low-rank matrix with structural smoothness for image denoising

Weighted bilinear factorization of low-rank matrix with structural smoothness for image denoising

Truncated quadratic norm minimization for bilinear factorization based matrix completion

Low-rank matrix completion is an important research topic with a wide range of applications. One prevailing way for matrix recovery is based on rank minimization. Directly solving this problem is NP hard. Therefore, various rank surrogates are developed, like nuclear norm. However, nuclear norm regularization minimizes the sum of all the singular values, and hence the rank is not well approximated. We propose a new rank substitution named truncated quadratic norm that performs the corresponding truncated quadratic operation on the singular values. This function takes the square of the minor singular values and maps large singular values to one. In order to reduce computational complexity, the original target matrix is factorized into two small matrices on which the truncated quadratic norm is imposed. The resultant problem is then solved by alternating minimization. We also prove that the solution sequence is able to converge to a critical point. Experimental results on synthetic data and real-world images demonstrate the excellent performance of our method in terms of recovery accuracy.

Pattern synthesis for symmetric linear transducer array by bilinear factorization of Hankel matrices

We investigate the problem of designing an unequally spaced symmetric linear array with a minimum number of elements. For unequally spaced arrays, simultaneously tuning all the elements' positions and weights leads to a non-convex problem. Inspired by the fact that the matrix pencil method (MPM) can estimate the weights and positions of array elements from a Hankel matrix formed by samples of beampattern, we attack the design problem by finding the Hankel matrix fulfilling specifications with the minimum rank. Fortunately, the low-rank optimization can be addressed by nuclear norm relaxation. In the proposed approach, we minimize the nuclear norm of the Hankel matrix utilizing the low-rank matrix factorization-based augmented Lagrangian alternating direction method. Once the low-rank Hankel matrix is obtained, we finish the array design with the help of MPM. By finding the desired Hankel matrix with a minimum nuclear norm, the proposed approach avoids the NP-hard problem of simultaneously optimizing the weights and positions of elements. Moreover, the proposed method does not need a reference beampattern and makes no assumptions on element positions, making it more flexible in facing real-world problems. We compare the proposed approach with existing methods under different scenarios and prove its effectiveness.

Bilinear model factor decomposition: A general mixture analysis tool

The analysis of mixtures is a routine task in the analytical chemistry area as well as in other research fields. The objective is to identify, quantify, and interpret the chemical components of the mixtures. Various bilinear factor decomposition methods, including MCR-ALS, NMFand BNFA, have been proposed to solve this problem. However, there is little knowledge about their comparative performance in terms of different factors, such as solution reliability, calculation speed, convergence, flexibility in constraint implementation, and ease of results interpretation.To address these issues, this work aims to compare these methods using data examples from data simulations, environmental source apportionment studies, and chromatographic analysis of chemical mixtures. Through this comparison, we hope to gain insights into the strengths and weaknesses of each method and provide recommendations for researchers working in this field. This comprehensive comparison will help researchers choose the appropriate method for their specific analysis needs, ultimately leading to more accurate and efficient analysis.

Unsupervised Learning for Salient Object Detection via Minimization of Bilinear Factor Matrix Norm

Saliency detection is an important but challenging task in the study of computer vision. In this article, we develop a new unsupervised learning approach for the saliency detection by an intrinsic regularization model, in which the Schatten-2/3 norm is integrated with the nonconvex sparse l2/3 norm. The l2/3 -norm is shown to be capable of detecting consistent values among sparse foreground by using image geometrical structure and feature similarity, while the Schatten-2/3 norm can capture the lower rank of background by matrix factorization. To improve effective performance of separation for Schatten-2/3-norm and l2/3 -norm, a Laplacian regularization is adopted to the foreground for the smoothness. The proposed model essentially converts the required nonconvex optimization problem into the convex one, conducted by splitting the objective function based on singular value decomposition on one much smaller factor matrix and then optimized by using the alternating direction method of the multiplier. The convergence of the proposed algorithm is discussed in detail. Extensive experiments on three benchmark datasets demonstrate that our unsupervised learning approach is very competitive and appears to be more consistent across various salient objects than the current existing approaches.

Structured controller synthesis through block-diagonal factorization and parameter space optimization

Constraints on the feedback structure arise in many control systems due to implementing cost, hardware limitations and operational reliability. The parameter space method aims to solve the robust structured controller design problems based on a convex reformulation technique. Despite its attractiveness, the structural constraints are limited to be either decentralized or linear dependence among entries within the same row or column in the current literature. And the global optimal solution is yet to be guaranteed, since a non-convex constraint is introduced in the parameter space after reformulating it as the output feedback synthesis problem. In this paper, we extend the parameter space method to a more generalized structured optimal control problem, such that the linear dependence can occur among its arbitrary entries. A bilinear factorization to the feedback gain matrix is proposed by a special Kronecker product decomposition. Subsequently, an equivalent transformation is proposed to convert this structured control design problem to a controller synthesis problem under decentralized full-state feedback. Thereby, the prior non-convex constraint in the parameter space is removed and the globally optimal structured controller is synthesized by convex programming. Examples such as integrated design and formation control demonstrate its practical appeals.

Low-rank matrix factorization with nonconvex regularization and bilinear decomposition

Low-rank matrix factorization (LRMF) is a powerful approach that can recover useful information with low-rank features from corrupted data and has been broadly applied in various scenarios such as computer vision and statistics. Existing convex relaxation-based LRMF models' performance and solutions are often limited by unsatisfied recovery accuracy and prolonged execution time due to excessive relaxation bias and heavy computational burden. In this paper, we first explore one class of parameterized non-convex penalty function and generalize it as a non-convex relaxation substitution term for the original rank function in the LRMF, which can effectively enhance the recovery capability for low-rank data. In order to reduce the computational burden of the nuclear-norm-based optimization scheme and make LRMF applicable to large-scale data. We propose to perform bilinear decomposition on the low-rank matrix and derive the bilinear factorization formula under the parameterized non-convex alternative. With the above considering, a low-rank matrix recovery model via bilinear decomposition and non-convex regularization, denoted as NCBF, is formulated. Further, the optimal solution algorithm for the NCBF model is developed in the framework of the block coordinate descent, combining simultaneously three strategies of decoupling, proximal gradient descent, and block prox-linear. Also, the convergence condition for the proposed algorithm has been given. We perform extensive experiments using synthetic data and real-world image datasets. The synthetic data test results demonstrate the dual superiority of the bilinear decomposition scheme in terms of operation time and estimation accuracy. Application of denoising to both generic and CT image datasets, experimental results show that NCBF outperforms several existing methods under both subjective and objective metrics evaluations.

Characterization of Foveal Development in Treatment-Naïve Extremely Preterm Infants.

ObjectiveTo characterize and quantify foveal development in treatment-naïve extremely preterm infants using optical coherence tomography.MethodsIn this cross-sectional study, eyes treated for retinopathy of prematurity before imaging were excluded. Inner retinal thickness and outer retina thickness at foveal center and foveal rim were assessed. Extremely preterm (EPT, <28 weeks gestational age) eyes were compared with infants more than 28 weeks of gestation using a multivariable dimension reduction analysis (principal component analysis) and a bilinear factor mode analysis (partial least square discriminant analysis) to determine group intervariability. Further analyses were performed to investigate the effects of gestation on foveal development.ResultsTwenty-six infants born at gestational ages ranging from 22 to 39 weeks were imaged between 32 and 80 weeks postmenstrual age. A principal component analysis and partial least squares discriminant analysis revealed that the foveal inner retina thickness was the main difference between EPT infants and non-EPT infants. This difference was reflected by comparing their inner retinal thickness over time (32–80 weeks postmenstrual age), which revealed a sustained thicker foveal inner retina for EPT infants when compared with non-EPT infants. The foveal pit seemed to be shallower in EPT infants when compared with non-EPT infants.ConclusionsTwenty-eight weeks of gestation seems to be a critical timepoint for foveal development; EPT infants had altered foveal inner retinal development throughout early postnatal development, which led to a thicker foveal inner retina and a shallower foveal pit soon after birth.Translational RelevanceMeasuring untreated foveal parameters informs about the effects of prematurity on the fovea and provides a baseline when comparing with post-treatment foveal development.

Reweighted Low-Rank Factorization With Deep Prior for Image Restoration

The low-rank recovery is a powerful tool to restore images from incomplete and corrupted observations. Conventional low-rank recovery techniques employ the reweighted nuclear norm minimization, which requires performing the full singular value decomposition and thus is computationally expensive. Using the scheme of bilinear factorization, we propose the Reweighted Low-rank Matrix Factorization (RLMF) method for single channel image restoration. The RLMF method can not only inherit the computational efficiency of bilinear factorization, but also incorporate the empirical distribution of the singular values in natural images. Then, considering the correlation between image channels, we generalize the reweighted nuclear norm from matrices to tensors, and develop the Reweighted Low-rank Tensor Factorization (RLTF) method for multichannel image restoration. Moreover, we enhance the RLMF and RLTF methods by introducing the deep image prior information, which is capable of capturing the implicit image structure through the neural network architecture to improve restoration accuracy. Experimental results show the computational efficiency of the proposed low-rank factorization scheme, and the superior restoration accuracy of the proposed methods compared with the state-of-the-art methods.

Drug\u2013target interaction prediction using unifying of graph regularized nuclear norm with bilinear factorization

BackgroundWet-lab experiments for identification of interactions between drugs and target proteins are time-consuming, costly and labor-intensive. The use of computational prediction of drug–target interactions (DTIs), which is one of the significant points in drug discovery, has been considered by many researchers in recent years. It also reduces the search space of interactions by proposing potential interaction candidates.ResultsIn this paper, a new approach based on unifying matrix factorization and nuclear norm minimization is proposed to find a low-rank interaction. In this combined method, to solve the low-rank matrix approximation, the terms in the DTI problem are used in such a way that the nuclear norm regularized problem is optimized by a bilinear factorization based on Rank-Restricted Soft Singular Value Decomposition (RRSSVD). In the proposed method, adjacencies between drugs and targets are encoded by graphs. Drug–target interaction, drug-drug similarity, target-target, and combination of similarities have also been used as input.ConclusionsThe proposed method is evaluated on four benchmark datasets known as Enzymes (E), Ion channels (ICs), G protein-coupled receptors (GPCRs) and nuclear receptors (NRs) based on AUC, AUPR, and time measure. The results show an improvement in the performance of the proposed method compared to the state-of-the-art techniques.

Bilinear factorizations subject to monomial equality constraints via tensor decompositions

The Canonical Polyadic Decomposition (CPD), which decomposes a tensor into a sum of rank one terms, plays an important role in signal processing and machine learning. In this paper we extend the CPD framework to the more general case of bilinear factorizations subject to monomial equality constraints. This includes extensions of multilinear algebraic uniqueness conditions originally developed for the CPD. We obtain a deterministic uniqueness condition that admits a constructive interpretation. Computationally, we reduce the bilinear factorization problem into a CPD problem, which can be solved via a matrix EigenValue Decomposition (EVD). Under the given conditions, the discussed EVD-based algorithms are guaranteed to return the exact bilinear factorization. Finally, we make a connection between bilinear factorizations subject to monomial equality constraints and the coupled block term decomposition, which allows us to translate monomial structures into low-rank structures.

When algorithm selection meets Bi-linear Learning to Rank: accuracy and inference time trade off with candidates expansion

Algorithm selection (AS) tasks are dedicated to find the optimal algorithm for an unseen problem instance. With the knowledge of problem instances’ meta-features and algorithms’ landmark performances, Machine Learning (ML) approaches are applied to solve AS problems. However, the standard training process of benchmark ML approaches in AS either needs to train the models specifically for every algorithm or relies on the sparse one-hot encoding as the algorithms’ representation. To escape these intermediate steps and form the mapping function directly, we borrow the learning to rank framework from Recommender System (RS) and embed the bi-linear factorization to model the algorithms’ performances in AS. This Bi-linear Learning to Rank (BLR) has proven to work with competence in some AS scenarios and thus is also proposed as a benchmark approach. Thinking from the evaluation perspective in the modern AS challenges, precisely predicting the performance is usually the measuring goal. Though approaches’ inference time also needs to be counted for the running time cost calculation, it’s always overlooked in the evaluation process. The multi-objective evaluation metric Adjusted Ratio of Root Ratios (A3R) is therefore advocated in this paper to balance the trade-off between the accuracy and inference time in AS. Concerning A3R, BLR outperforms other benchmarks when expanding the candidates range to TOP3. The better effect of this candidates expansion results from the cumulative optimum performance during the AS process. We take the further step in the experimentation to represent the advantage of such TOPK expansion, and illustrate that such expansion can be considered as the supplement for the convention of TOP1 selection during the evaluation process.

Robust low rank representation via feature and sample scaling

Low-rank representation (LRR) is a very competitive technique in various real-world applications for its powerful capability in discovering latent structure of noisy or corrupted data set. However, traditional low-rank models treat each data point and feature equally so that noisy data cannot be detected and suppressed effectively and have obvious deterioration in performance, especially in heavy noisy scenario. In this paper, to address this problem, we develop a method of feature and sample scaling for low rank representation. The importance of data points and their features in both feature and sample spaces are considered, as such, clean data points and noisy data points and their features can be distinguished. In addition, based on the observation that noisy data points are usually deviated far away from the principal projection of the data set, a cosine similarity metric between data vector and the principal projection vector is developed to measure the importance of each sample. Applying our method into two classical low rank models such as Low Rank Representation (LRR) and Bilinear Factorization (BF), we can learn better low-rank structure of clean data, while the outliers or missing data being suppressed. Extensive experimental results on ORL, COIL20 and video surveillance, demonstrate that our proposed method can outperform state-of-the-art low rank methods in image clustering tasks with various levels of corruptions, especially in a heavy noisy scenario.

Hyperspectral image denoising by total variation-regularized bilinear factorization

Hyperspectral image (HSI) denoising is a prevalent research topic in the remote sensing area. In general, HSIs are inevitably impaired by different types of noise during the data acquisition. To fully characterize the underlying structures of clean HSI and remove mixed noises, we introduce a novel HSI denoising method named total variation-regularized bilinear factorization (BFTV) model. Specifically, we first utilize the bilinear factorization term to explore the globally low-rank structure of the clean HSI and suppress a certain degree of Gaussian noise, so as to make BFTV free to the singular value decomposition. Then the l1-norm is applied to detect and separate the mixed sparse noise including impulse noise, deadlines, and stripes. Besides, the TV regularization is introduced to describe the locally piecewise smoothness property of the clean HSI both in spatial and spectral domains. To solve this optimization problem, we devise an effective algorithm based on the augmented Lagrange multiplier method. Numerical experiments on five different kinds of mixed noise scenarios and one real world data have tested and demonstrated the superior denoising power of the proposed BFTV model compared with three state-of-the-art low-rank-based approaches.

Adaptive quantile low-rank matrix factorization

Low-rank matrix factorization (LRMF) has received much popularity owing to its successful applications in both computer vision and data mining. By assuming noise to come from a Gaussian, Laplace or mixture of Gaussian distributions, significant efforts have been made on optimizing the (weighted) L1 or L2-norm loss between an observed matrix and its bilinear factorization. However, the type of noise distribution is generally unknown in real applications and inappropriate assumptions will inevitably deteriorate the behavior of LRMF. On the other hand, real data are often corrupted by skew rather than symmetric noise. To tackle this problem, this paper presents a novel LRMF model called AQ-LRMF by modeling noise with a mixture of asymmetric Laplace distributions. An efficient algorithm based on the expectation-maximization (EM) algorithm is also offered to estimate the parameters involved in AQ-LRMF. The AQ-LRMF model possesses the advantage that it can approximate noise well no matter whether the real noise is symmetric or skew. The core idea of AQ-LRMF lies in solving a weighted L1 problem with weights being learned from data. The experiments conducted on synthetic and real data sets show that AQ-LRMF outperforms several state-of-the-art techniques. Furthermore, AQ-LRMF also has the superiority over the other algorithms in terms of capturing local structural information contained in real images.

Bilinear Image Translation for Temporal Analysis of Photo Collections.

We propose an approach for analyzing unpaired visual data annotated with time stamps by generating how images would have looked like if they were from different times. To isolate and transfer time dependent appearance variations, we introduce a new trainable bilinear factor separation module. We analyze its relation to classical factored representations [1] and concatenation-based auto-encoders [2] . We demonstrate this new module has clear advantages compared to standard concatenation when used in a bottleneck encoder-decoder convolutional neural network architecture. We also show that it can be inserted in a recent adversarial image translation architecture [3] , enabling the image transformation to multiple different target time periods using a single network. We apply our model to a challenging collection of more than 13,000 cars manufactured between 1920 and 2000 [4] and a dataset of high school yearbook portraits from 1930 to 2009 [5] . This allows us, for a given new input image, to generate a "history-lapse video" revealing changes over time by simply varying the target year. We show that by analyzing the generated history-lapse videos we can identify object deformations across time, extracting interesting changes in visual style over decades.

Constrained bilinear factorization multi-view subspace clustering

Multi-view clustering is an important and fundamental problem. Many multi-view subspace clustering methods have been proposed, and most of them assume that all views share a same coefficient matrix. However, the underlying information of multi-view data are not fully exploited under this assumption, since the coefficient matrices of different views should have the same clustering properties rather than be uniform among multiple views. To this end, this paper proposes a novel Constrained Bilinear Factorization Multi-view Subspace Clustering (CBF-MSC) method. Specifically, the bilinear factorization with an orthonormality constraint and a low-rank constraint is imposed for all coefficient matrices to make them have the same trace-norm instead of being equivalent, so as to explore the consensus information of multi-view data more fully. Finally, an Augmented Lagrangian Multiplier (ALM) based algorithm is designed to optimize the objective function. Comprehensive experiments tested on nine benchmark datasets validate the effectiveness and competitiveness of the proposed approach compared with several state-of-the-arts.

Multi-Set Low-Rank Factorizations With Shared and Unshared Components

Low-rank matrix/tensor factorizations play a significant role in science and engineering. An important example is the canonical polyadic decomposition (CPD). There is also a growing interest in multi-set extensions of low-rank matrix/tensor factorizations in which the associated factor matrices are partially shared. In this paper we propose a more unified framework for multi-set matrix/tensor factorizations. In particular, we propose a multi-set extension of bilinear factorizations subject to monomial equality constraints to the case of shared and unshared factors. The presented framework encompasses (generalized) canonical correlation analysis (CCA) and (coupled) CPD models as special cases. CPD, CCA and hybrid models between them feature interesting uniqueness properties. We derive uniqueness conditions for CCA and multi-set low-rank factorization with partially shared entities. Computationally, we reduce multi-set low-rank factorizations with shared and unshared components into a special CPD problem, which can be solved via a matrix eigenvalue decomposition. Finally, numerical experiments demonstrate the importance of taking the coupling between multi-set low-rank factorizations into account in the actual computation.