Discriminant Matrix Research Articles

Locality-Constrained Discriminative Matrix Regression for Robust Face Identification.

Regression-based methods have been widely applied in face identification, which attempts to approximately represent a query sample as a linear combination of all training samples. Recently, a matrix regression model based on nuclear norm has been proposed and shown strong robustness to structural noises. However, it may ignore two important issues: the label information and local relationship of data. In this article, a novel robust representation method called locality-constrained discriminative matrix regression (LDMR) is proposed, which takes label information and locality structure into account. Instead of focusing on the representation coefficients, LDMR directly imposes constraints on representation components by fully considering the label information, which has a closer connection to identification process. The locality structure characterized by subspace distances is used to learn class weights, and the correct class is forced to make more contribution to representation. Furthermore, the class weights are also incorporated into a competitive constraint on the representation components, which reduces the pairwise correlations between different classes and enhances the competitive relationships among all classes. An iterative optimization algorithm is presented to solve LDMR. Experiments on several benchmark data sets demonstrate that LDMR outperforms some state-of-the-art regression-based methods.

Electronic Performance-Oriented Mold Sharing Method and Application in QTT 110 m Large Radio Telescope

The reflector surface of a large reflector antenna may even consist of thousands of panels, and if the panel molds with high-precision requirements are fabricated uniquely for each ring, the overall cost will be very high. Therefore, from a perspective of reducing the cost, the mold sharing design is of particular significance. In order to obtain the minimum number of molds satisfying the given electronic performance index, the electronic performance-oriented mold sharing design is suggested, in which the effective surface accuracy is used to evaluate electrical performance. The smaller the combined effective root-mean-square (rms) error value introduced after sharing the mold, the more preferential these rings should share the mold to reduce the number of molds. Based on such idea, a fast mold reduction process is presented, which can give the minimum number of molds quickly according to the electrical performance requirements. During this process, a combined effective rms value matrix and a mold sharing discriminant matrix are defined and used. To construct these two matrices, the panel normal error induced by mold sharing is derived, and the optimal mold position is determined first. As a test problem, application of the proposed method to mold reduction of a 110 m radio telescope is presented, and the discussions of the results are given.

Blockchain For Intelligent Transport System

ABSTRACT Intelligent Transportation System (ITS) is gaining attention but at the same time, road accidents, congestion, delays, etc. have also increased. Relative information about such events is vital. Such information can be presented in legal processes as digital proof. Availability of the information is not a problem as multidimensional data have been recorded all the time by ITS. Recording all the information in ITS arises the problem of fetching relevant information and removing other facts and figure that are not required to describe certain situations such as an accident. To address this issue, we analyze road accident data and reduce various dimensions with Principal Component Analysis (PCA), Linear Discriminant Analysis (LDA) and Non-negative Matrix Factorization (NMF). We conduct comparative analysis with three datasets where error rate for PCA is 32% with Dataset1. Likewise, error rate for LDA and NMF are 36% and 35%, receptively. While keeping in mind that such reduced data is helpful in many legal processes, we introduce Blockchain in the framework. Blockchain can make data immutable thus can be considered as digital proof. Blockchain also requires a smart contract in this situation between insurance companies to collect data in case of any uncertain situation. Such analysis can offer a different point of views and trends in data. Information can be more explainable to define the situation and helps to develop a friendly environment for day-to-day customers. The proposed framework provides dimensionality reduction of data that eventually reduce the data dimension to store in Blockchain.

Small-angle perturbation method for moving platform orientation to avoid singularity of asymmetrical 3-RRR planner parallel manipulator

To overcome the weakness of the present methods of singularity avoidance for 3-RRR planar parallel manipulator (PPM), a new method of avoiding singular points on planed paths in workspace via orientation perturbation to moving platforms is proposed. First, an inverse kinematics model of 3-RRR PPM is built. A discriminant matrix of type II singularity is specified and the mapping between determinant values of the matrix and points in workspace of 3-RRR PPM is defined as a singularity surface. Then, the planned path is regarded as a directrix and intersecting line between cylindrical surfaces (its generating line is parallel to the z-axis) and the singularity surface is defined as a singularity curve corresponding to a planned path. By determining the critical perturbation value of the moving platform’s orientation angle, the maximum value of the singularity curve corresponding to the planned path is no larger than 0 or its minimum value is no smaller than 0. Therefore, singular points on the planned path are avoided by changing the moving platform’s orientation angle without changing the planned path. Moreover, a numerical realization method is given; example and experiment verification indicates that singular points in the planned path can be avoided when perturbation to the moving platform’s orientation angle is no larger than 0.1745 rad. Therefore, the proposed method lays a solid foundation for singularity-free kinematics control based on inverse solutions.

Toward Efficient Image Representation: Sparse Concept Discriminant Matrix Factorization

The key ingredients of matrix factorization lie in basic learning and coefficient representation. To enhance the discriminant ability of the learned basis, discriminant graph embedding is usually introduced in the matrix factorization model. However, the existing matrix factorization methods based on graph embedding generally conduct discriminant analysis via a single type of adjacency graph, either similarity-based graphs (e.g., Laplacian eigenmaps graph) or reconstruction-based graphs (e.g., ${L}_{1}$ -graph), while ignoring the cooperation of the different types of adjacency graphs that can better depict the discriminant structure of original data. To address the above issue, we propose a novel Fisher-like criterion, based on graph embedding, to extract sufficient discriminant information via two different types of adjacency graphs. One graph preserves the reconstruction relationships of neighboring samples in the same category, and the other suppresses the similarity relationships of neighboring samples from different categories. Moreover, we also leverage the sparse coding to promote the sparsity of the coefficients. By virtue of the proposed Fisher-like criterion and sparse coding, a new matrix factorization framework called Sparse concept Discriminant Matrix Factorization (SDMF) is proposed for efficient image representation. Furthermore, we extend the Fisher-like criterion to an unsupervised context, thus yielding an unsupervised version of SDMF. Experimental results on seven benchmark datasets demonstrate the effectiveness and efficiency of the proposed SDMFs on both image classification and clustering tasks.

Eigenbasis of the evolution operator of 2-tessellable quantum walks

Staggered quantum walks on graphs are based on the concept of graph tessellation and generalize some well-known discrete-time quantum walk models. In this work, we address the class of 2-tessellable quantum walks with the goal of obtaining an eigenbasis of the evolution operator. By interpreting the evolution operator as a quantum Markov chain on an underlying multigraph, we define the concept of quantum detailed balance, which helps to obtain the eigenbasis. A subset of the eigenvectors is obtained from the eigenvectors of the double discriminant matrix of the quantum Markov chain. To obtain the remaining eigenvectors, we have to use the quantum detailed balance conditions. If the quantum Markov chain has a quantum detailed balance, there is an eigenvector for each fundamental cycle of the underlying multigraph. If the quantum Markov chain does not have a quantum detailed balance, we have to use two fundamental cycles linked by a path in order to find the remaining eigenvectors. We exemplify the process of obtaining the eigenbasis of the evolution operator using the kagome lattice (the line graph of the hexagonal lattice), which has symmetry properties that help in the calculation process.

Establishment of comprehensive quality evaluation model of fresh instant rice.

BackgroundAlthough the rice processing characteristics and processing quality evaluation technologies have been studied for many years in China, there have been few reports on the evaluation index system and evaluation method of fresh instant rice processing quality.ObjectiveThe aim of this study was to establish a comprehensive quality evaluation model of fresh instant rice to achieve the effective quantitative quality analysis.MethodsA total of 108 japonica rice varieties were selected as the test samples, followed by the production of fresh instant rice. The color value, physicochemical quality, texture characteristic, and sensory quality of fresh instant rice were systematically analyzed. Difference analysis, correlation analysis, factor analysis, and cluster analysis were used to determine the representative quality indexes of fresh instant rice. Through initialization, forward, and normalization, the standardized indexes (0≤ Xi ≤1) were obtained. The discriminant matrix of the analytic hierarchy process (AHP) was used to confirm the weight (Wi) of each representative quality index, establishing the comprehensive quality evaluation model.ResultsThe variable coefficients of 12 out of 17 quality indexes were more than 10%. There were 136 correlation coefficients, including 15 cases with a significant difference at the level of α = 0.05 and 52 cases with a significant difference at the level of α = 0.01. Five representative quality indexes of fresh instant rice were selected by factor analysis and cluster analysis, including palatability, adhesiveness, b* value, resilience, and iodine color value. And the comprehensive quality evaluation model of fresh instant rice integrating representative indexes was obtained: Y = 0.5650 × palatability + 0.2294 × adhesiveness + 0.0328 × resilience + 0.1175 × b* value + 0.0533 × iodine color value.ConclusionThe AHP combined with factor analysis and cluster analysis can convert a number of quality indexes into a comprehensive quality index, and thus establish the comprehensive quality evaluation model of fresh instant rice, effectively performing the quantitative quality analysis. This model not only provided a scientific basis for the accurate evaluation of fresh instant rice quality, but also laid the foundation for the formulation of fresh instant rice standards in the future.

Improved Design of Risk Assessment Model for PPP Project under the Development of Marine Architecture

Liu, Y.; Hao, Y., and Lu, Y. 2018. Improved design of risk assessment model for PPP project under the development of marine architecture. In: Liu, Z.L. and Mi, C. (eds.), Advances in Sustainable Port and Ocean Engineering. Journal of Coastal Research, Special Issue No. 83, pp. 74–80. Coconut Creek (Florida), ISSN 0749-0208.The current risk assessment model of marine architecture project is mainly processed by analyzing the risk factor of the PPP project, quantifying and sorting them, and achieving assessment through the sorting results. In the current model, the weight of risk decision cannot be calculated accurately, and the accuracy of risk assessment is low. To address this problem, a risk assessment model of PPP project under the development of marine architecture based on grey system theory is proposed in this paper. Some experts are invited to compare of PPP project risk index to establish risk discriminant matrix. The empirical value of expert weight is obtained by analytic hierarchy process. According to the empirical values given by the experts, the weight of the risk index is determined by the improved grey relational degree, and the project risk assessment model is built. Ex perimental results show that the improved model has a high accuracy of risk assessment and is more practical.

Quantum fast-forwarding: Markov chains and graph property testing

We introduce a new tool for quantum algorithms called quantum fast-forwarding (QFF). The tool uses quantum walks as a means to quadratically fast-forward a reversible Markov chain. More specifically, with P the Markov chain transition matrix and D = \sqrt{P\circ P^T} its discriminant matrix (D=P if P is symmetric), we construct a quantum walk algorithm that for any quantum state |v> and integer t returns a quantum state \epsilon-close to the state D^t|v>/\|D^t|v>. The algorithm uses O(|D^t|v>|^{-1}\sqrt{t\log(\epsilon\|D^t|v>})^{-1}}) expected quantum walk steps and O(\|D^t|v>|^{-1}) expected reflections around |v>. This shows that quantum walks can accelerate the transient dynamics of Markov chains, complementing the line of results that proves the acceleration of their limit behavior. We show that this tool leads to speedups on random walk algorithms in a very natural way. Specifically we consider random walk algorithms for testing the graph expansion and clusterability, and show that we can quadratically improve the dependency of the classical property testers on the random walk runtime. Moreover, our quantum algorithm exponentially improves the space complexity of the classical tester to logarithmic. As a subroutine of independent interest, we use QFF for determining whether a given pair of nodes lies in the same cluster or in separate clusters. This solves a robust version of s-t connectivity, relevant in a learning context for classifying objects among a set of examples. The different algorithms crucially rely on the quantum speedup of the transient behavior of random walks.

Observable Degree Analysis for Multi-Sensor Fusion System.

Multi-sensor fusion system has many advantages, such as reduce error and improve filtering accuracy. The observability of the system state is an important index to test the convergence accuracy and speed of the designed Kalman filter. In this paper, we evaluate different multi-sensor fusion systems from the perspective of observability. To adjust and optimize the filter performance before filtering, in this paper, we derive the expression form of estimation error covariance of three different fusion methods and discussed both observable degree of fusion center and local filter of fusion step. Based on the ODAEPM, we obtained their discriminant matrix of observable degree and the relationship among different fusion methods is given by mathematical proof. To confirm mathematical conclusion, the simulation analysis is done for multi-sensor CV model. The result demonstrates our theory and verifies the advantage of information fusion system.

New class separability measure for radar signals

AbstractWe propose a novel class separability measure for radar signals. To evaluate the discriminatory power of the radar signals, the proposed method first either calculates the correlation coefficients between two radar cross sections (RCSs), linearly shifts one‐dimensional (1‐D) high‐resolution‐range profiles (HRRPs), or rotates two 2‐D inverse synthetic aperture radar (ISAR) images. Then, it uses the correlation coefficient when the two radar signals are best aligned. Next, the proposed method obtains new correlation‐ based discriminant matrices (CDMs) using the correlation coefficients. The mean value of the CDMs precisely represents the discriminatory power of the radar signal. Our experimental results show that the proposed method can accurately measure target separability.

Robust visual tracking via nonlocal regularized multi-view sparse representation

The multi-view sparse representation based visual tracking has attracted increasing attention because the sparse representations of different object features can complement with each other. Since the robustness of different object features is actually not the same in challenging video sequences, it may contain unreliable features (the features with low robustness) in multi-view sparse representation. In this case, how to highlight the useful information of unreliable features for proper multi-feature fusion has become a tough work. To solve this problem, we propose a multi-view discriminant sparse representation method for robust visual tracking, in which we firstly divide the multi-view observations into different groups, and then estimate the sparse representations of multi-view group projections for calculating the observation likelihood. The advantages of the proposed sparse representation method are two-folds: 1) It can properly fuse the observation groups with reliable and unreliable features by using an online updated discriminant matrix to explore the group similarity in multi-feature space. 2) It introduces a nonlocal regularizer to enforce the spatial smoothness among the sparse representations of different group projections, which can enhance the robustness of multi-view sparse representation. Experimental results show that our method can achieve a better tracking performance than state-of-the-art tracking methods do.

On discriminant matrices

This paper considers the usual compound matrix, the additive compound matrix, and the discriminant matrix. An investigation of the Jordan structure of discriminant matrices is initiated. The primary objective of the paper is the determination of the Jordan form of the discriminant of one Jordan block. This Jordan form has a very simple pattern. A number of related results are obtained. The main results are facilitated by the new precedence relation ordering and the block-persymmetric property of the matrices. Examples of the discriminant matrices and Jordan forms are provided.

Non-negative enhanced discriminant matrix factorization method with sparsity regularization

Efficient low-rank representation of data plays a significant role in the field of computer vision and pattern recognition. In order to obtain a more discriminant and sparse low-dimensional representation, a novel non-negative enhanced discriminant matrix factorization method with sparsity regularization is proposed in this paper. Firstly, the local invariance and discriminant information of the low-dimensional representation are incorporated into the objective function to construct a new within-class encouragement constraint term, and the weighted coefficients are introduced to further enhance the compactness between the samples that belong to the same class in the new base space. Secondly, a new between-class penalty term is constructed to maximize the difference between different classes of samples, and meanwhile, the weighted coefficients are introduced to further enhance the discreteness and discriminativeness between classes. Finally, to learn the part-based representation of data better, the sparse constraint term is further introduced, and consequently, the sparseness of data representation, the local invariance, and the discriminativeness are integrated into a unified framework. Moreover, the optimization solution and the convergence proof of objective function are given. The extensive experiments demonstrate the strong robustness of the proposed method to face recognition and image classification under occlusions.

Nonnegative Discriminant Matrix Factorization

Nonnegative matrix factorization (NMF), which aims at obtaining the nonnegative low-dimensional representation of data, has received wide attention. To obtain more effective nonnegative discriminant bases from the original NMF, in this paper, a novel method called nonnegative discriminant matrix factorization (NDMF) is proposed for image classification. NDMF integrates the nonnegative constraint, orthogonality, and discriminant information in the objective function. NDMF considers the incoherent information of both factors in standard NMF and is proposed to enhance the discriminant ability of the learned base matrix. NDMF projects the low-dimensional representation of the subspace of the base matrix to regularize the NMF for discriminant subspace learning. Based on the Euclidean distance metric and the generalized Kullback-Leibler (KL) divergence, two kinds of iterative algorithms are presented to solve the optimization problem. The between- and within-class scatter matrices are divided into positive and negative parts for the update rules and the proofs of the convergence are also presented. Extensive experimental results demonstrate the effectiveness of the proposed method in comparison with the state-of-the-art discriminant NMF algorithms.

Monitoring Key Points Analysis of Livestock Products Safety Regulation

As the improvement of people's living standard, livestock products including meat, eggs, milk and other animal foods have become the main source of public nutrition intake, and the proportion in food consumption is more and more high. Livestock products consumption is regarded as one of important signs of a country’s or region's economic development and the progress of society. As a kind of fresh products, livestock products have natural characteristics of putrescibility and not easy to save (Li Yang, An Yufa, Gu Chuan 2013) [1], therefore it is prone to problems in the sectors of production, processing, transportation, storage, consumption. Besides, the quality problems of livestock products have been common such as “Water-injected meat”, “quick chicken” and “magdala red” eggs and even some large food enterprises have serious quality problems of products. Therefore, ensuring food safety of livestock products should become the focus of the work of food safety and the research field of Chinese food safety. Wang Panpan (2010) defines the food supply chain for the order of link and operation from primary production to consumers, involving production, processing, distribution, storage and consumption of food and accessories. She thinks there are risk of food safety problems in the link of source, processing, distribution and consumption of food supply chain and should strengthen supervision on the key control points in above links [2]. M. F. Stringer (2007) divided the food supply chain into 27 unit steps and found out 21 essential reasons causing food safety problems, and based on which M. F. Stringer defined the key control points of food safety problems [3]. Bian Linlin (2010) studied game relation among supermarkets, suppliers, consumers and regulators with game theory and got the result that supermarkets play a role in promoting the establishment and development of China's food quality control system and supermarkets should strengthen the supervision and control on supplier and internal staff [4]. Through the researches of agricultural leading enterprises in Hunan Province, combined with the principle of the HACCP, Xie Jingwen (2012) proposed that we should position the key points of supply chain, which is helpful to the whole process monitoring of food supply chain and the establishment of the traceability system for monitoring food [5]. Liu Chang (2012) constructed the food quality and safety SC-RC discriminant and location matrix based on 1460 food safety cases, and analysed the weak links and key control points of food safety in our country with empirical analysis [6]. In summary, domestic and foreign scholars have been carried out on the key control points of food safety and made a lot of research results. But most studies take all food as research object, but location of different food the key control points should also be different and this study intends to analyze the livestock products.

Object tracking by features and particles selection in multiple subspace

The existing appearance models and motions researches for object tracking are usually restricted to a single space, and thus the appearance models are not abundant enough for the object representation. In addition, the particles' accuracies are not good enough to provide the candidate object positions after particle filtration. Herein, we propose an object tracking algorithm based on selection of features and particles in multiple subspaces. First of all, discriminative subspace matrix of the object was built according to discriminative subspaces. To get the discriminative features of the subspaces, PCA was proposed. Thus, discriminative subspace and colour matrix for the object was successfully represented. Furthermore, in motion researching, the particles are selected based on the features' similarity and the spatial coherence in multiple discriminative subspaces. Based on the appearance model and those selected effective particles, the algorithm determines the final position. Experimental results show that the proposed algorithm outperforms the state-of-the-art schemes, especially for the illumination changes, rotations, scaling and fast motion.

Characterizing the solutions to scattering equations that support tree-level N k MHV gauge/gravity amplitudes

In this paper we define, independent of theories, two discriminant matrices involving a solution to the scattering equations in four dimensions, the ranks of which are used to divide the solution set into a disjoint union of subsets. We further demonstrate, {entirely within the Cachazo-He-Yuan formalism,} that each subset of solutions gives nonzero contribution to tree-level $\text{N}^{k}\text{MHV}$ gauge/gravity amplitudes only for a specific value of $k$. Thus the solutions can be characterized by the rank of their discriminant matrices, which in turn determines the value of $k$ of the $\text{N}^{k} \text{MHV}$ amplitudes a solution can support. As another application of the technique developed, we show analytically that in Einstein-Yang-Mills theory, if all gluons have the same helicity, the tree-level single-trace amplitudes must vanish.

3D human pose regression via robust sparse tensor subspace learning

In this paper, we present a novel algorithm called robust sparse tensor subspace learning (RSTSL) for 3D human pose regression, and it further extends the latest presented tensor learning to a sparse case. A set of interrelated sparse discriminant projection matrices for feature extraction can be obtained by introducing k-mode optimization and elastic-net algorithm into the objective function of RSTSL and each non-zero element in each discriminant projection matrix is selected from the most typical variables. Thus, the most important low-dimensional tensor feature (LDTF) that corresponds to a test image (i.e., high-order tensor) is extracted through sparse projection transformation. Moreover, we present a novel regression model called optimal-order support tensor regression (OOSTR) to build a finest mapping function between LDTF and 3D human pose configuration. Extensive simulations are conducted on two human motion databases, HumanEva and Brown databases, experimental results show that our proposed RSTSL can not only weaken the sensitivity to incoherent human motions caused by transient occlusion of cameras, sudden change in human velocity and low-frame rate but also strengthen the robustness to silhouette ambiguity, obstacle occlusion and random noise. All the results have confirmed that our tracking system achieves the most significant performance against the compared the state-of-the-art approaches, especially in the complicated human motion databases with different clustered backgrounds, human movements, clothing-style, illumination and subjects like HumanEva database.

A Unique Approach to Epilepsy Classification from EEG Signals Using Dimensionality Reduction and Neural Networks

Characterized by recurrent and rapid seizures, epilepsy is a great threat to the livelihood of the human beings. Abnormal transient behaviour of neurons in the cortical regions of the brain leads to a seizure which characterizes epilepsy. The physical and mental activities of the patient are totally dampened with this epileptic seizure. A significant clinical tool for the study, analysis and diagnosis of the epilepsy is electroencephalogram (EEG). To detect such seizures, EEG signals aids greatly to the clinical experts and it is used as an important tool for the analysis of brain disorders, especially epilepsy. In this paper, the high dimensional EEG data are reduced to a low dimension by incorporating techniques such as Fuzzy Mutual Information (FMI), Independent Component Analysis (ICA), Linear Graph Embedding (LGE), Linear Discriminant Analysis (LDA) and Variational Bayesian Matrix Factorization (VBMF). After employing them as dimensionality reduction techniques, the Neural Networks (NN) such as Cascaded Feed Forward Neural Network (CFFNN), Time Delay Neural Network (TDNN) and Generalized Regression Neural Network (GRNN) are used as Post Classifiers for the Classification of Epilepsy Risk Levels from EEG signals. The bench mark parameters used here are Performance Index (PI), Quality Values (QV), Time Delay, Accuracy, Specificity and Sensitivity.