Separation Matrix Research Articles

Cellwise robust regularized discriminant analysis

Quadratic and linear discriminant analysis (QDA and LDA) are the most often applied classification rules under normality. In QDA, a separate covariance matrix is estimated for each group. If there are more variables than observations in the groups, the usual estimates are singular and cannot be used anymore. Assuming homoscedasticity, as in LDA, reduces the number of parameters to estimate. This rather strong assumption is however rarely verified in practice. Regularized discriminant techniques that are computable in high dimension and cover the path between the 2 extremes QDA and LDA have been proposed in the literature. However, these procedures rely on sample covariance matrices. As such, they become inappropriate in the presence of cellwise outliers, a type of outliers that is very likely to occur in high‐dimensional datasets. In this paper, we propose cellwise robust counterparts of these regularized discriminant techniques by inserting cellwise robust covariance matrices. Our methodology results in a family of discriminant methods that (1) are robust against outlying cells, (2) cover the gap between LDA and QDA, and (3) are computable in high dimension. The good performance of the new methods is illustrated through simulated and real data examples. As a by‐product, visual tools are provided for the detection of outliers.

Fast and Robust Self-Representation Method for Hyperspectral Band Selection

In this paper, a fast and robust self-representation (FRSR) method is proposed to select a proper band subset from hyperspectral imagery (HSI). The FRSR assumes the separability structure of the HSI band set and transforms the problem of separable nonnegative matrix factorization into the robust self-representation (RSR) model. Then, the FRSR incorporates structured random projections into the RSR model to improve computational efficiency. The solution of FRSR is formulated into optimizing a convex problem and the augmented Lagrangian multipliers are adopted to estimate the proper factorization localizing matrix in the FRSR. The selected band subset is constituted with the bands corresponding to the r largest diagonal entries of the factorization localizing matrix. The experimental results show that FRSR outperforms state-of-the-art techniques in classification accuracy with lower computational cost.

Efficient preconditioning for noisy separable nonnegative matrix factorization problems by successive projection based low-rank approximations

The successive projection algorithm (SPA) can quickly solve a nonnegative matrix factorization problem under a separability assumption. Even if noise is added to the problem, SPA is robust as long as the perturbations caused by the noise are small. In particular, robustness against noise should be high when handling the problems arising from real applications. The preconditioner proposed by Gillis and Vavasis (SIAM J Optim 25(1):677–698, 2015) makes it possible to enhance the noise robustness of SPA. Meanwhile, an additional computational cost is required. The construction of the preconditioner contains a step to compute the top-k truncated singular value decomposition of an input matrix. It is known that the decomposition provides the best rank-k approximation to the input matrix; in other words, a matrix with the smallest approximation error among all matrices of rank less than k. This step is an obstacle to an efficient implementation of the preconditioned SPA. To address the cost issue, we propose a modification of the algorithm for constructing the preconditioner. Although the original algorithm uses the best rank-k approximation, instead of it, our modification uses an alternative. Ideally, this alternative should have high approximation accuracy and low computational cost. To ensure this, our modification employs a rank-k approximation produced by an SPA based algorithm. We analyze the accuracy of the approximation and evaluate the computational cost of the algorithm. We then present an empirical study revealing the actual performance of the SPA based rank-k approximation algorithm and the modified preconditioned SPA.

Perovskite hollow fiber membranes supported in a porous and catalytically active perovskite matrix for air separation

Abstract Mixed conducting perovskite membranes have attracted much research interest for use in air separation. However, the application of perovskite hollow fiber membranes is limited by their brittleness. Herein, the fiber bundling in a perovskite matrix is reported to overcome the physical weakness of the individual perovskite hollow fiber membranes. This has been achieved by binding these hollow fibers into one matrix using a porous binder made from the same membrane material, i.e., La0.6Sr0.4Co0.2Fe0.8O3−δ (LSCF) perovskite. The bending force for one individual LSCF hollow fiber is 2.18 N for a fixed length of 4 cm; in contrast, the bending forces for the LSCF bundle in the same length including 3, 5, 8, and 10 single LSCF hollow fibers are 6.80, 11.77, 23.97, and 39.02 N, respectively. The membrane bundle was evaluated for air separation using a sweep gas mode by passing the air in the shell side and argon through the fiber lumen operated from 800 to 1000 °C. The oxygen flux through the single LSCF hollow fiber at 950 °C was 0.26 mL cm−2 min−1 (standard conditions) but the bundle gave a higher flux improved by 76% up to 0.46 mL cm−2 min−1 under similar testing conditions due to the porous matrix with enhanced surface reaction kinetics. The resultant membrane bundle demonstrates exceeding performance for air separation in terms of high oxygen flux, mechanical strength, and thermal stability for an easy scale-up.

Incorporating Gene Annotation into Genomic Prediction of Complex Phenotypes.

Today, genomic prediction (GP) is an established technology in plant and animal breeding programs. Current standard methods are purely based on statistical considerations but do not make use of the abundant biological knowledge, which is easily available from public databases. Major questions that have to be answered before biological prior information can be used routinely in GP approaches are which types of information can be used, and at which points they can be incorporated into prediction methods. In this study, we propose a novel strategy to incorporate gene annotation into GP of complex phenotypes by defining haploblocks according to gene positions. Haplotype effects are then modeled as categorical or as numerical allele dosage variables. The underlying concept of this approach is to build the statistical model on variables representing the biologically functional units. We evaluate the new methods with data from a heterogeneous stock mouse population, the Drosophila Genetic Reference Panel (DGRP), and a rice breeding population from the Rice Diversity Panel. Our results show that using gene annotation to define haploblocks often leads to a comparable, but for some traits to a higher, predictive ability compared to SNP-based models or to haplotype models that do not use gene annotation information. Modeling gene interaction effects can further improve predictive ability. We also illustrate that the additional use of markers that have not been mapped to any gene in a second separate relatedness matrix does in many cases not lead to a relevant additional increase in predictive ability when the first matrix is based on haploblocks defined with gene annotation data, suggesting that intergenic markers only provide redundant information on the considered data sets. Therefore, gene annotation information seems to be appropriate to perceive the importance of DNA segments. Finally, we discuss the effects of gene annotation quality, marker density, and linkage disequilibrium on the performance of the new methods. To our knowledge, this is the first work that incorporates epistatic interaction or gene annotation into haplotype-based prediction approaches.

Independent Component Analysis Method Based on Genetic Algorithm in Compound Fault Separation

Compound faults often exist in roller bearing, which increase the difficulty for the fault diagnosis. In order to extract the characteristics of compound fault signals, independent component analysis (ICA) method was used toseparate fault signals. However, the selection of initial weight about ICA will affect the number of iterations and astringency. Therefore, a novel ICA method based on improved genetic algorithm was proposed. The kurtosis ofsignal was used as the optimization function, and then genetic algorithm was applied to find the separation matrix according to the maximum of the kurtosis. This method avoids the problem of redundant iteration and convergence, which is caused by randomness of initial weight vector. Finally, the proposed method was used to separate source signal from the mixed signals and achieve the roller bearings fault identification and separation. The results show that the proposed method is superior to traditional ICA method, and the compound fault can be separated based on the proposed method.

An Improved FastICA Algorithm Based on Modified-M Estimate Function

In order to improve the detection rate of ship information, fast independent component analysis (FastICA) algorithm is adopted to separate satellite-based automatic identification system (AIS) mixed signals. FastICA algorithm has the advantages of fast convergence rate and simple form. However, it is sensitive to the initialization of the separation matrix and the robust performance is poor. Aimed at the problem, an improved FastICA algorithm is proposed. This new algorithm is based on constant model of AIS signal and chooses Modified-M estimation function as nonlinear function so as to improve the robustness of algorithm. The improved algorithm also modifies Newton iterative algorithm. The experimental simulation results indicate that the proposed method reduces the iteration times and the accuracy has been improved.

Acoustic Scattering for Rotational and Translational Symmetric Structures in Nonuniform Potential Flow

An efficient approach is proposed to predict acoustic scattering with nonuniform potential flow effects for structures with rotational and translational symmetries. The convected wave equation is transformed to Helmholtz and Laplace equations using a time transformation. The boundary-element method is used to formulate scattering by rotationally symmetric structures as two separate block circulant matrix equations and, similarly, as two separate block Toeplitz matrix equations for structures with translational symmetry. Discrete Fourier transform is employed to solve the block circulant systems. The block Toeplitz systems are solved using the generalized minimal residual method along with the discrete Fourier transform. Solving the convected wave equation using structured matrices significantly reduces computational time and storage requirements. To demonstrate the application of the formulation, two exterior acoustic case studies are considered. The first case study examines acoustic scattering from a sphere submerged in potential flow under monopole source excitation. Directivity plots obtained using the proposed technique are compared with analytical results. The second case study examines flow-induced noise generated by a rigid cylinder immersed in low-Mach-number flow, with the effect of mean flow on the scattered acoustic field taken into account using nonuniform potential flow. The fluctuating flowfield is obtained using an incompressible computational fluid dynamics solver. Acoustic sources based on Lighthill’s analogy are extracted from the flowfield data using a high-order reconstruction scheme. Results from the hybrid computational fluid dynamics– boundary-element method technique are presented for turbulent flow past the cylinder, with Reynolds number based on cylinder diameter of and Mach number . The aeroacoustic results are compared with data from literature.

Thermally rearranged mixed matrix membranes for CO2 separation: An aging study

In this work, the aging behavior of a thermally rearranged polybenzoxazole-co-imide (TR-PBOI) mixed matrix membrane loaded with 0.5wt.% of oxidized multi-wall carbon nanotubes (MWCNT) was evaluated and then compared to a pure TR polymeric membrane prepared from the same precursor. To the best of authors knowledge, this is the first report of a mixed matrix membrane being prepared through the dispersion of MWCNTs within a thermally rearranged polymer matrix for CO2 separation. Microporous structures were created in both membranes when thermally rearranged at 375°C, facilitating fast mass transfer ideal for membrane gas separation. The TR mixed matrix membrane with oxidized CNTs demonstrated improved separation properties with regard to both permeability and selectivity compared to the pure TR polymeric membrane due to a greater degree of thermal rearrangement (11.3%) than what was exhibited by the TR membrane (6.7%). Moreover, the high CO2 solubility typical of TR polymers coupled with diffusivity enhancements improved the CO2/N2 selectivity. The addition of oxidized CNTs to the TR-PBOI polymer did not significantly influence the aging behavior of the mixed matrix membrane. Both pure TR-PBOI and mixed matrix membranes exhibited an increase in CO2 selectivity due to physical aging. The improved separation properties in conjunction with an unchanged membrane stability over time suggested that the addition of CNTs to pure TR membranes could be an excellent approach toward improving the performance of thermally rearranged membranes applied toward gas separation.

Associative Memory Model-Based Linear Filtering and Its Application to Tandem Connectionist Blind Source Separation

We propose a blind source separation method that yields high-quality speech with low distortion. Time-frequency (TF) masking can effectively reduce interference, but it produces nonlinear distortion. By contrast, linear filtering using a separation matrix such as independent vector analysis (IVA) can avoid nonlinear distortion, but the separation performance is reduced under reverberant conditions. The tandem connectionist approach combines several separation methods and it has been used frequently to compensate for the disadvantages of these methods. In this study, we propose associative memory model (AMM)-based linear filtering and a tandem connectionist framework, which applies TF masking followed by linear filtering. By using AMM trained with speech spectra to optimize the separation matrix, the proposed linear filtering method considers the properties of speech that are not considered explicitly in IVA, such as the harmonic components of spectra. TF masking is applied in the proposed tandem connectionist framework to reduce unwanted components that hinder the optimization of the separation matrix, and it is approximated by using a linear separation matrix to reduce nonlinear distortion. The results obtained in simultaneous speech separation experiments demonstrate that although the proposed linear filtering method can increase the signal-to-distortion ratio (SDR) and signal-to-interference ratio (SIR) compared with IVA, the proposed tandem connectionist framework can obtain greater increases in SDR and SIR, and it reduces the phoneme error rate more than the proposed linear filtering method.

Searching all truncated impossible differentials in SPN

This study concentrates on finding all truncated impossible differentials in substitution-permutation networks (SPNs) ciphers. Instead of using the miss-in-the-middle approach, the authors propose a mathematical description of the truncated impossible differentials. First, they prove that all truncated impossible differentials in an r + 1 rounds SPN cipher could be obtained by searching entry `0' in D ( P ) r , where D ( P ) denotes the differential pattern matrix (DPM) of P -layer, thus the length of impossible differentials of an SPN cipher is upper bounded by the minimum integer r such that there is no entry `0' in D ( P ) r . Second, they provide two efficient algorithms to compute the DPMs for both bit-shuffles and matrices over GF(2 n ). Using these tools they prove that the longest truncated impossible differentials in SPN structure is 2-round, if the P -layer is designed as an maximum distance separable (MDS) matrix. Finally, all truncated impossible differentials of advanced encryption standard (AES), ARIA, AES-MDS, PRESENT, MAYA and Puffin are obtained.

A two-stage dual-matrix method of blind signal separation

In this paper, we propose a dual-matrix method (DMM) that uses constrained terms to reflect the numerical relation between a mixing matrix and a separating matrix. Thus, some undesired solutions are excluded, the search region is reduced, and the convergent efficiency of the algorithm is ultimately improved. Moreover, DMM is proven to converge in a separable matrix only if its cost function converges to zero. Computer simulations indicate that the algorithm excellently performs blind signal separation; moreover, theoretical analysis matches the simulated results. On the other hand, two-separating system is proposed in the separating stage, and a new performance index (PI) is presented as well. Further, the theoretical properties of the new PI are proven, and the simulations indicate that the new PI is more practical than the commonly used one. Two numerical simulations were performed in the current study to illustrate the efficiency of the proposed method.

Devising a method for maintaining manageability at multidimensional automated control of tethered underwater vehicle

Automated control of spatial motion of remotely operated underwater vehicle (ROV) is a known scientific problem since as an object of control it is essentially nonlinear. Operational control of ROV is a multi-dimensional problem. The synthesis of regulators separately for each degree of freedom is complicated by mutual influence of kinematic parameters of ROV. Nonlinearity of the restrictions type, typical for ROV, leads to the occurrence of strong and degrees of freedom. This degrades the quality of automated control system (SAC) as a whole. We obtained a matrix notation of the basic law of dynamics of marine movable object as a solid body. Own and added masses and moments of inertia of the body and the fluid are brought into a separate matrix. This makes it possible to apply the resulting equation without structural changes to study the dynamics of spatial motion of ROV with different parameters. The equation is used in direct form to model the motion of ROV and in the inverse form for the synthesis of SAC over its spatial motion. An inverse regulator (IR) of ROV with six degrees of freedom is synthesized based on the method of inverse dynamics and decomposition of the reference model. We simulated the work of inverse controller IR of ROV and demonstrated a loss of manageability by the weak rotating degrees of freedom. The fundamentals of the method for maintaining manageability with automated control of a multidimensional object are formulated. The essence of the method is in driving the contours of SAC out of the modes of saturation by scaling control errors. We designed SAC of spatial motion of ROV based on the synthesized IR and the unit for maintaining manageability. It provides controlled motion of ROV by six degrees of freedom without losing manageability. A simulation of the developed SAC of spatial motion of ROV is performed. The simulation results revealed that the unit for maintaining manageability provides for the operation of SAC on the verge of saturation of its contours. This enables the ROV motion by six degrees of freedom without losing manageability.

Camera identification based on very low bit rate videos with overall noise pattern having time varying statistics

This paper proposes a method for performing the camera identification based on very low bit rate videos with the overall noise patterns having time varying statistics. First, the overall noise pattern of each frame of each video is converted to a vector. Then, the odd order statistic moments of these vectors are computed. By performing the principal component analysis, only the most major component of each statistic moment vector is attained. These components of all the frames form a feature vector for each video. To minimize the intraclass separation and maximize the interclass separation, the linear discriminant analysis is performed. As many eigenvalues of the interclass separation matrix are close to zero, the column vectors which span the null spaces of the corresponding matrices are found and the feature vector of each video is projected to these columns and forms a new vector. It is found that these new vectors are pairwisely linear separable. Hence, a bank of perceptrons can be applied to perform the camera identification. Computer numerical simulations show that our proposed method significantly outperforms the conventional correlation based method and the conventional support vector machine based method.

Hypergraphs and hypermatrices with symmetric spectrum

It is well known that a graph is bipartite if and only if the spectrum of its adjacency matrix is symmetric. In the present paper, this assertion is dissected into three separate matrix results of wider scope, which are extended to hypermatrices. To this end, the concept of bipartiteness is generalized by a new monotone property of cubical hypermatrices, called odd-colorable matrices. It is shown that a nonnegative symmetric r-matrix A has a symmetric spectrum if and only if r is even and A is odd-colorable. This result also solves a problem of Pearson and Zhang about hypergraphs with symmetric spectrum and disproves a conjecture of Zhou, Sun, Wang, and Bu.Separately, similar results are obtained for the H-spectrum of hypermatrices.

Cellwise Robust Regularized Discriminant Analysis

Quadratic and Linear Discriminant Analysis (QDA/LDA) are the most often applied classification rules under normality. In QDA, a separate covariance matrix is estimated for each group. If there are more variables than observations in the groups, the usual estimates are singular and cannot be used anymore. Assuming homoscedasticity, as in LDA, reduces the number of parameters to estimate. This rather strong assumption is however rarely verified in practice. Regularized discriminant techniques that are computable in high-dimension and cover the path between the two extremes QDA and LDA have been proposed in the literature. However, these procedures rely on sample covariance matrices. As such, they become inappropriate in presence of cellwise outliers, a type of outliers that is very likely to occur in high-dimensional datasets. In this paper, we propose cellwise robust counterparts of these regularized discriminant techniques by inserting cellwise robust covariance matrices. Our methodology results in a family of discriminant methods that (i) are robust against outlying cells, (ii) cover the gap between LDA and QDA and (iii) are computable in high-dimension. The good performance of the new methods is illustrated through simulated and real data examples. As a by-product, visual tools are provided for the detection of outliers.

Transform-based coding method for remote sensing hyperspectral data compression

A version of the transform-based coding compression method for remote sensing hyperspectral data is proposed. New version is based on the calculation of a separate quantization matrix for each image and the preliminary removal of low-frequency components in the input data. Larger compression ratios are shown in comparison with the layered JPEG algorithm with the same mean square recovery error.

Stationary Points of a Kurtosis Maximization Criterion for Noisy Blind Source Extraction

Blind source extraction (BSE) is often posed as the maximization of a statistical criterion under a unitary constraint. This paper addresses the convergence problem of a kurtosis-based criterion in the presence of noise. We present the stationary points of such criterion, and show that these extrema are simplified as the minimum mean square error (MMSE) solutions with some approximations. Moreover, we introduce a robust preprocessing approach, which allows one to find the MMSE separation matrix up to an orthogonal factor. The excellent performance of the BSE algorithm based on this preprocessing approach shows that the analysis of the stationary point is reliable.

An ionic coordination hybrid hydrogel for bioseparation.

An ionic coordination hybrid hydrogel is formed with ionic and covalent crosslinked networks via one-step copolymation. It is demonstrated that the hybrid crosslinker gel is used as a separation matrix for bioseparation, showing high separation efficiency, in contrast to traditional polyacrylamide gels. The hydrogel might serve as a novel matrix for bioseparation.

Spatial Panel Data Model with Error Dependence: A Bayesian Separable Covariance Approach

A hierarchical Bayesian model for spatial panel data is proposed. The idea behind the proposed method is to analyze spatially dependent panel data by means of a separable covariance matrix. Let us indicate the observations as yit, in i=1,…,N regions and at t=1,…,T times, and suppose the covariance matrix of y, given a set of regressors, is written as a Kronecker product of a purely spatial and a purely temporal covariance. On the one hand, the structure of separable covariances dramatically reduces the number of parameters, while on the other hand, the lack of a structured pattern for spatial and temporal covariances permits capturing possible unknown dependencies (both in time and space). The use of the Bayesian approach allows one to overcome some of the difficulties of the classical (MLE or GMM based) approach. We present two illustrative examples: the estimation of cigarette price elasticity and of the determinants of the house price in 120 municipalities in the Province of Rome.