Unified Matrix Research Articles

Two-step multi-view data classification based on dynamic Graph-ELM

This paper focuses on the classification problem of multi-view data, aiming to improve the classification accuracy of current algorithms on multi-view data. Previous multi-view classification algorithms are usually based on exploiting the complementarity of different views and fusing features from different views. A representative category is the graph-based method, which builds a graph matrix for each view, and then fuses the graph matrices of different views to obtain a unified graph. These methods have the following problems: firstly, the graph matrix is simply based on sample similarity usually; secondly, the learned graph matrix does not change dynamically; thirdly, the weight of the graph representation matrix for a single view cannot be learned in the unified graph matrix. Therefore, this paper designs a Two-step classification algorithm based on Dynamic Graph-ELM, called TSDGELM. In the TSDGELM, the dynamic Graph-ELM is used to obtain the graph representation matrix of each view to save the local neighbor information of the data, and then a joint graph learning algorithm is designed based on the GBS (Graph-Based System) mechanism to fuse the graph matrix of the single-view, and finally the united graph is input into the classifier. To evaluate the effectiveness of the proposed method in this work, we conduct a series of experiments on eight datasets, and the results demonstrate the superiority of the proposed method.

Incomplete multi-view clustering via structure exploration and missing-view inference

Incomplete multi-view clustering (IMVC) aims to boost clustering performance by capturing complementary information from incomplete multi-views, where partial data samples in one or more views are missing. Current IMVC methods mostly impute missing samples at the guidance of the global/local structure or directly learn a common representation without imputation using subspace or graph learning techniques. However, the consistent and inconsistent structures across views are often ignored during imputation, leading to the introduction of noise and biases. Additionally, lacking the handling of missing samples would mislead the learning methods and degrade clustering performance. To this end, we propose a novel approach called Structure Exploration and Missing-view Inference (SEMI) for IMVC. Specifically, SEMI explores the underlying multi-structures of data, including global, local, consistent, and inconsistent structures, by jointly modeling self-expression subspace, graph, and clustering-oriented partition learning. This enables the capture of consistent and discriminative information and fuses it into a unified coefficient matrix. The learned coefficient matrix with the explored multi-structures then guides the inference of missing views, facilitating the alleviation of the influence of existing noise and biases and the mitigation of the introduction of further noise and biases. These two components are seamlessly integrated and mutually improved through an efficient alternating optimization strategy. Experimental results demonstrate the effectiveness and superior performance of the proposed method.

A unified matrix approach to the Legendre–Sheffer and certain hybrid polynomial sequences

A unified matrix approach to the Legendre–Sheffer and certain hybrid polynomial sequences

Region-Aware Hierarchical Latent Feature Representation Learning-Guided Clustering for Hyperspectral Band Selection.

Hyperspectral band selection aims to identify an optimal subset of bands for hyperspectral images (HSIs). For most existing clustering-based band selection methods, they directly stretch each band into a single feature vector and employ the pixelwise features to address band redundancy. In this way, they do not take full consideration of the spatial information and deal with the importance of different regions in HSIs, which leads to a nonoptimal selection. To address these issues, a region-aware hierarchical latent feature representation learning-guided clustering (HLFC) method is proposed. Specifically, in order to fully preserve the spatial information of HSIs, the superpixel segmentation algorithm is adopted to segment HSIs into multiple regions first. For each segmented region, the similarity graph is constructed to reflect the bands-wise similarity, and its corresponding Laplacian matrix is generated for learning low-dimensional latent features in a hierarchical way. All latent features are then fused to form a unified feature representation of HSIs. Finally, k -means clustering is utilized on the unified feature representation matrix to generate multiple clusters from which the band with maximum information entropy is selected to form the final subset of bands. Extensive experimental results demonstrate that the proposed clustering method can achieve superior performance than the state-of-the-art representative methods on the band selection. The demo code of this work is publicly available at https://github.com/WangJun2023/HLFC.

UNMF: a unified nonnegative matrix factorization for multi-dimensional omics data.

Factor analysis, ranging from principal component analysis to nonnegative matrix factorization, represents a foremost approach in analyzing multi-dimensional data to extract valuable patterns, and is increasingly being applied in the context of multi-dimensional omics datasets represented in tensor form. However, traditional analytical methods are heavily dependent on the format and structure of the data itself, and if these change even slightly, the analyst must change their data analysis strategy and techniques and spend a considerable amount of time on data preprocessing. Additionally, many traditional methods cannot be applied as-is in the presence of missing values in the data. We present a new statistical framework, unified nonnegative matrix factorization (UNMF), for finding informative patterns in messy biological data sets. UNMF is designed for tidy data format and structure, making data analysis easier and simplifying the development of data analysis tools. UNMF can handle a wide range of data structures and formats, and works seamlessly with tensor data including missing observations and repeated measurements. The usefulness of UNMF is demonstrated through its application to several multi-dimensional omics data, offering user-friendly and unified features for analysis and integration. Its application holds great potential for the life science community. UNMF is implemented with R and is available from GitHub (https://github.com/abikoushi/moltenNMF).

A unified density matrix functional construction of quantum baths in density matrix embedding theory beyond the mean-field approximation.

The equivalence in one-electron quantum baths between the practical implementation of density matrix embedding theory (DMET) and the more recent Householder-transformed density matrix functional embedding theory has been shown previously in the standard but special case where the reference full-size (one-electron reduced) density matrix, from which the bath is constructed, is idempotent [S. Yalouz et al., J. Chem. Phys. 157, 214112 (2022)]. We prove mathematically that the equivalence remains valid when the density matrix is not idempotent anymore, thus allowing for the construction of correlated (one-electron) quantum baths. A density-matrix functional exactification of DMET is derived within the present unified quantum embedding formalism. Numerical examples reveal that the embedding cluster can be quite sensitive to the level of density-matrix functional approximation used for computing the reference density matrix.

A DRM-SMM Framework for Wave Propagation in Layered Saturated Ground under Inclined P1-SV Waves

This paper provides a numerical framework for seismic analyses for layered saturated ground under inclined plane P1-SV waves. A unified stiffness matrix method (SMM) formula for both u-w-p and u-p formulations is first derived to obtain the dynamic response of saturated fields. Then, the domain reduction method (DRM) is extended to two-phase media to reproduce the target wavefield within the numerical models. The accuracy of the proposed SMM-DRM framework is verified by comparisons with analytical solutions and other numerical methods. Its applicability in complex boundary value problems is also proven by solving a typical SSI problem. The numerical framework is especially advantageous in the analyses of complex subdomains under obliquely incident seismic waves. With the procedure given in the paper, the framework can be implemented into existing finite element models straightforwardly.

Thermal analysis for gas storage in salt cavern based on an improved heat transfer model

Oversimplification of the heat transfer mechanism and assumption of uniform temperature and pressure in the salt cavern could cause significant errors when modeling temperature fields. This work proposed a coupled transient flow and heat transfer model for gas storage in the underground salt cavern to reflect the thermal behaviors between gas and surrounding rock, particularly the gas Joule-Thomson effect during gas operation. Then, a fully coupled numerical solution method based on a unified matrix is presented. An average error of 3.26% was observed between the model and field data quoted in literature. The case study indicates that during the gas withdrawal period, the maximum temperature difference in the salt cavern can reach 14.94 °C, while the temperature drop of the cavity wall is only about 4.07 °C, which is quite different from the traditional assumption. A special focus was given to the gas withdrawal rate, which seemed to have the most significant influence on the evolution of the temperature field in the salt cavern. Compared with the gas withdrawal rate of 35 m3/s, reducing the gas withdrawal rate to 20 m3/s can increase the minimum temperature by approximately 23.41%. This study could add further insights into the thermal performance during gas operation in the salt cavern and help to reveal the evolution of the temperature field in the cavity and surrounding rock.

Two improved assembly deviation analysis methods based on Jacobian–Torsor matrix and skin model shapes with contact deformation effort

Assembly deviation analysis methods, which have been studied and improved over the past 30 years, are necessary and effective for checking functional requirements before manufacturing. Contact deformation was not negligible and significantly affected the final assembly deviation, which prevented the application of the current assembly deviation analysis methods. Considering the contact deformation, we aimed to improve the precision of the 3D deviation analysis methods, which are based on the Jacobian-Torsor matrix and skin model shape (SMS), respectively. In this study, the contact deformation was quantified based on the Hertzian contact theory. The unified Jacobian-Torsor matrix is modified with the location points and contact deformation to increase the precision of the stack-up assembly deviation. In the SMS-based method, the assembly components are represented as non-nominal SMS models. The final posture of each component and stack-up assembly deviation were solved by iteratively mimicking the physical assembly process. The practicality of the improved deviation analysis method was successfully demonstrated through two case studies. The modified Jacobian-Torsor matrix-based method is efficient. However, the improved SMS-based method can provide more precise results by mimicking tight fitting on mating surfaces.

Hybrid Physics and Data-Driven Method for Modeling and Analysis of Electricity–Heat Integrated Energy Systems

The accurate modeling and analysis of integrated energy systems (IES) can precisely obtain the system state variation trend and operation characteristics of IES, and provide the foundation and preliminary for the planning, control, and schedule of IES. However, the commonly deployed Newton–Raphson method suffers from the difficulty of initial state setting, and the differences in the operating characteristics of heterogeneous energy systems bring challenges to the modeling and analysis of IES. In this article, a hybrid physics and data-driven approach is proposed along with a thermal unified matrix model for the steady-state and transient analysis of electricity–heat IES (EH-IES). Both integrated and decomposed solution algorithms are developed to obtain the final system states. Numerical results of several EH-IESs demonstrate the effectiveness of the proposed approach, and the convergence and computational efficiency of the state analysis of EH-IES are remarkably improved.

Neutrosophic Autocratic Multi-Attribute Decision-Making Strategies for Building Material Supplier Selection

Because of the intricate nature of real-world scenarios, experts could encounter many ambiguities throughout the decision-making (DM) process. Adopting a DM strategy in conditions of indeterminacy so that the decision makers are limited to a small number of experts is always helpful in real life. Neutrosophic conception is a convenient technique for handling inconsistent, ambiguous, and uncertain values. This research presents an autocratic DM strategy based on Neutrosophic Sets (NSs) to address these ambiguities. The essential component of the suggested technique is the conversion of diverse management decision and weight matrices into a unified evaluation matrix. Supplier Selection (SS) is a multi-criteria decision-making problem where a limited number of alternative suppliers are evaluated using a limited set of criteria. The suggested methodology based on different score functions is applied to SS issues involving construction materials. The numerical illustrations indicate the success of the introduced method in selecting the best supplier with the least computational complexity. The important point obtained in this research is that adopting a suitable score function appropriate to the characteristics of the data plays an important role in the decision-making process.

Robust Discriminant Subspace Clustering With Adaptive Local Structure Embedding.

Unsupervised dimension reduction and clustering are frequently used as two separate steps to conduct clustering tasks in subspace. However, the two-step clustering methods may not necessarily reflect the cluster structure in the subspace. In addition, the existing subspace clustering methods do not consider the relationship between the low-dimensional representation and local structure in the input space. To address the above issues, we propose a robust discriminant subspace (RDS) clustering model with adaptive local structure embedding. Specifically, unlike the existing methods which incorporate dimension reduction and clustering via regularizer, thereby introducing extra parameters, RDS first integrates them into a unified matrix factorization (MF) model through theoretical proof. Furthermore, a similarity graph is constructed to learn the local structure. A constraint is imposed on the graph to guarantee that it has the same connected components with low-dimensional representation. In this spirit, the similarity graph serves as a tradeoff that adaptively balances the learning process between the low-dimensional space and the original space. Finally, RDS adopts the l2,1 -norm to measure the residual error, which enhances the robustness to noise. Using the property of the l2,1 -norm, RDS can be optimized efficiently without introducing more penalty terms. Experimental results on real-world benchmark datasets show that RDS can provide more interpretable clustering results and also outperform other state-of-the-art alternatives.

IMGC: Interactive Multiple Graph Clustering With Constrained Laplacian Rank

Numerous graph clustering methods have been proposed to explore aggregation structures across multiple graphs. In these methods, single-graph features are merely considered or multigraph features are simply weighted, which are insufficient for the construction of reasonable multiple graph clustering features, since the association information between pairwise graphs is ignored and the varied local correlations might influence the clustering preference. Thus, we propose an interactive multiple graph clustering model, iMGC, in this article, to achieve reasonable multiple graph clustering features, which cannot only express multiple relationships, but also preserve associations of nodes across multiple graphs. First, a unified graph matrix is constructed with the combination of structural differences quantified by graph representation learning, which is further optimized by minimizing the difference of structural characteristics between it and each single graph matrix. Thus, multiple relationships are well integrated and expressed, while the varied local correlations within different graphs are also balanced in the unified graph matrix. Then, a constrained Laplacian rank is applied on the unified graph matrix to generate the unified clustering result directly, which is able to preserve association features across multiple graphs. Furthermore, we provide a set of visualization and interaction interfaces, enabling users to intuitively optimize and evaluate the multiple graph clustering features, and interactively explore the multiple graphs. Case studies and quantitative comparisons based on real-world datasets have demonstrated the effectiveness of iMGC in the clustering performance from various perspectives and exploration of multiple graphs.

Recognizing geochemical patterns related to mineralization using a self-organizing map

The recognition of geochemical patterns, including the spatial association of geochemical patterns, geochemical element associations, and geochemical anomalies related to mineralization, requires different methods to meet the corresponding requirements. In this study, a self-organizing map (SOM), an unsupervised learning technique, was employed to realize the whole processes of geochemical pattern recognition in southeastern Hubei Province, China. First, the clustering ability of SOM was adopted to reveal the spatial association of geochemical patterns; then, geochemical elemental associations were adopted according to the association between variables and clusters derived from the correlation analysis between the unified distance matrix (U-matrix) and SOM maps, and finally the quantification error (QE) of the SOM was adopted as an anomalous index to detect multivariate geochemical anomalies related to mineralization. The obtained results show that two of the clusters are spatially closely related to ore-forming geological bodies, that is Precambrian strata and Yanshanian intrusive rocks. The associations of Au–As–Ba–Cd–Sb–V and Au–Ag–Pb–Zn–Bi–Cu–Mo–Na2O–P–Sr–W are responsible for the characterization of the two clusters, and their combination was further used for multivariate geochemical anomaly detection. The extracted multivariate geochemical anomalies are closely spatially correlated with known gold polymetallic deposits. Both the receiver operating characteristic (ROC) and success-rate curves suggest a satisfactory anomaly detection results, which can provide guidance for further mineral exploration. The results of this study also suggest that SOM is an effective and interpretable tool for a better recognition of geochemical patterns related to mineralization.

A Lattice-Reduction-Aided Sphere Decoder for Underwater Acoustic FBMC/OQAM Communications

Because of the inherent interference, it is difficult for filter-bank multi-carrier (FBMC) with the offset-quadrature amplitude modulation (OQAM) systems to achieve high-performance symbol detection, especially over the underwater acoustic (UWA) channels. This letter explores a novel receiver approach to solve this problem by establishing a unified transmission matrix (UTM) model and proposing a lattice-reduction-aided sphere decoder (LRA-SD). The simulation and sea trial results indicate that in the UWA FBMC/OQAM communication systems, the UTM-based LRA-SD outperforms the linear detectors and is more computationally efficient than the maximum likelihood (ML) detector.

Reweighted multi-view clustering with tissue-like P system.

Multi-view clustering has received substantial research because of its ability to discover heterogeneous information in the data. The weight distribution of each view of data has always been difficult problem in multi-view clustering. In order to solve this problem and improve computational efficiency at the same time, in this paper, Reweighted multi-view clustering with tissue-like P system (RMVCP) algorithm is proposed. RMVCP performs a two-step operation on data. Firstly, each similarity matrix is constructed by self-representation method, and each view is fused to obtain a unified similarity matrix and the updated similarity matrix of each view. Subsequently, the updated similarity matrix of each view obtained in the first step is taken as the input, and then the view fusion operation is carried out to obtain the final similarity matrix. At the same time, Constrained Laplacian Rank (CLR) is applied to the final matrix, so that the clustering result is directly obtained without additional clustering steps. In addition, in order to improve the computational efficiency of the RMVCP algorithm, the algorithm is embedded in the framework of the tissue-like P system, and the computational efficiency can be improved through the computational parallelism of the tissue-like P system. Finally, experiments verify that the effectiveness of the RMVCP algorithm is better than existing state-of-the-art algorithms.

Self-Weighted Graph-Based Framework for Multi-View Clustering

Multiple perspectives can be used to explore rich and complex datasets that are widely used in many applications. However, in real-world applications, the multi-view data are often noisy because of various environmental factors. The key challenge of graph-based multi-view clustering is obtaining a consistent clustering structure. Most graph-based methods learn independently in one view how similar the data points in each view are to one another. However, the consistency of information in a multi-view dataset is easily overlooked, causing an unsatisfactory unified graph matrix. To address this problem, this study proposes a novel self-weighted graph-based framework for multi-view clustering (SGMF). This framework integrates these initial similar graph matrices into a unified graph matrix by assigning different weights to the initial graphs of each view. This algorithm’s goal is to effectively learn a unified graph matrix and eliminate noise or irrelevant information from the dataset. This is the first time a generalized multi-view framework based on the L1-norm has been proposed. L1-norm can be used to improve the robustness of the algorithm. Particularly, SGMF can automatically weigh each view’s initial similar graph matrix to solve the noise problem and obtain a consistent data structure. Simultaneously, a rank constraint is imposed on the graph Laplacian matrix of the final unified matrix, which helps to automatically divide the data points into the appropriate number of clusters. The experimental results on synthetic and real datasets verify the effectiveness and superiority of the proposed method over the latest baseline.

Deep Image Registration With Depth-Aware Homography Estimation

Image registration is a basic task in computer vision, for its wide potential applications in image stitching, stereo vision, motion estimation, and etc. Most current methods achieve image registration by estimating a global homography matrix between candidate images with point-feature-based matching or direct prediction. However, as real-world 3D scenes have point-variant photograph distances (depth), a unified homography matrix is not sufficient to depict the specific pixel-wise relations between two images. Some researchers try to alleviate this problem by predicting multiple homography matrixes for different patches or segmentation areas in images; in this letter, we tackle this problem with further refinement, i.e. matching images with pixel-wise, depth-aware homography estimation. Firstly, we construct an efficient convolutional network, the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">DPH-Net</i> , to predict the essential parameters causing image deviation, the rotation ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$R$</tex-math></inline-formula> ) and translation ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$T$</tex-math></inline-formula> ) of cameras. Then, we feed-in an image depth map for the calculation of initial pixel-wise homography matrixes, which are refined with an online optimization scheme. Finally, with the estimated pixel-specific homography parameters, pixel correspondences between candidate images can be easily computed for registration. Compared with state-of-the-art image registration algorithms, the proposed <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">DPH-Net</i> has the highest performance of 0.912 EPE and 0.977 SSIM, demonstrating the effectiveness of adding depth information and estimating pixel-wise homography into the image registration process.

DSPU: An Efficient Deep Learning-Based Dense RGB-D Data Acquisition With Sensor Fusion and 3-D Perception SoC

3-D red, green, blue, and depth (RGB-D) and 3-D perception are essential information for 3-D applications such as autonomous driving and augmented reality (AR)/virtual reality (VR) systems. However, battery- and resource-limited mobile devices face difficulties in obtaining dense RGB-D data and 3-D perception information in low-power (LP) and real-time. Specifically, an RGB-D sensor is used to acquire 3-D RGB-D data, but it consumes high power and produces sparse depth data. Moreover, preprocessing for RGB-D data requires a long execution time. Previous 3-D perception accelerators also have limited reconfigurability, making them incapable of executing diverse 3-D perception tasks. In this article, an LP and real-time depth signal processing system-on-chip (SoC), depth signal processing unit (DSPU), is presented. The DSPU produces accurate dense RGB-D data using a convolutional neural network (CNN)-based monocular depth estimation (MDE) and a sensor fusion with an LP ToF sensor. Then, the DSPU performs 3-D perception inferring a point cloud-based neural network (PNN). The DSPU executes the depth signal processing system with the following features: 1) a unified point processing unit (UPPU) with a flexible window based-search algorithm for simplifying the complexity of point processing algorithms and saving the arithmetic units and buffers; 2) a unified matrix processing unit (UMPU) with bit-slice-level sparsity exploitation to accelerate various matrix processing algorithms; 3) a band matrix encoder and decoder to decrease the data transactions in the conjugate-gradient (C-Grad) method; and 4) a point feature (PF) reuse method with a pipelined architecture for low-latency and LP PNN inference. Finally, the DSPU achieves real-time implementation with 281.6 mW of the end-to-end 3-D B-box extraction system.

High-Resolution Continuous-Scan Beamforming

The paper adapts the delay-and-sum beamforming method and related deconvolution techniques for microphone phased arrays comprising fixed and continuously scanning sensors. Processing of the nonstationary signals introduced by the scanning sensors requires division of all the signals into quasi-stationary blocks and application of a frequency-dependent window within each block. Three distinct approaches are developed: application of delay and sum to each block of the divided signals, followed by assembly of the outputs of the blocks; a cross-spectral matrix completion process; and a partial fields decomposition method. The last two approaches result in a unified cross-spectral matrix that facilitates deconvolution of the array output. The methodologies are applied to a synthetic noise source and to a supersonic underexpanded jet that presented the phenomenon of screech. Introduction of a single scanning sensor to a far-field array comprising 13 fixed sensors significantly improves the fidelity of beamforming. The deconvolved images of the jet noise source resolve fine shock-cell features for which the dimensions are similar to those imaged by optical techniques in past investigations.