Optimal Estimation of High-Dimensional Covariance Matrices with Missing and Noisy Data

The estimation of covariance matrices is very important in many fields, such as statistics. In real applications, data are frequently influenced by high dimensions and noise. However, most relevant studies are based on complete data. This paper studies the optimal estimation of high-dimensional covariance matrices based on missing and noisy sample under the norm. First, the model with sub-Gaussian additive noise is presented. The generalized sample covariance is then modified to define a hard thresholding estimator , and the minimax upper bound is derived. After that, the minimax lower bound is derived, and it is concluded that the estimator presented in this article is rate-optimal. Finally, numerical simulation analysis is performed. The result shows that for missing samples with sub-Gaussian noise, if the true covariance matrix is sparse, the hard thresholding estimator outperforms the traditional estimate method.

Efficient anti-aliasing and anti-leakage Fourier transform for high-dimensional seismic data regularization using cube removal and GPU

Seismic data is commonly acquired sparsely and irregularly, which necessitates the regularization of seismic data with anti-aliasing and anti-leakage methods during seismic data processing. We propose a novel method of 4D anti-aliasing and anti-leakage Fourier transform using a cube-removal strategy to address the combination of irregular sampling and aliasing in high-dimensional seismic data. We compute a weighting function by stacking the spectrum along the radial lines, apply this function to suppress the aliasing energy, and then iteratively pick the dominant amplitude cube to construct the Fourier spectrum. The proposed method is very efficient due to a cube removal strategy for accelerating the convergence of Fourier reconstruction and a well-designed parallel architecture using CPU/GPU collaborative computing. To better fill the acquisition holes from 5D seismic data and meanwhile considering the GPU memory limitation, we developed the anti-aliasing and anti-leakage Fourier transform method in 4D with the remaining spatial dimension looped. The entire workflow is composed of three steps: data splitting, 4D regularization, and data merging. Numerical tests on both synthetic and field data examples demonstrate the high efficiency and effectiveness of our approach.

Target Controllability of Multi-Layer Networks With High-Dimensional Nodes

This paper studies the target controllability of multilayer complex networked systems,in which the nodes are highdimensional linear time invariant(LTI)dynamical systems,and the network topology is directed and weighted.The influence of inter-layer couplings on the target controllability of multi-layer networks is discussed.It is found that even if there exists a layer which is not target controllable,the entire multi-layer network can still be target controllable due to the inter-layer couplings.For the multi-layer networks with general structure,a necessary and sufficient condition for target controllability is given by establishing the relationship between uncontrollable subspace and output matrix.By the derived condition,it can be found that the system may be target controllable even if it is not state controllable.On this basis,two corollaries are derived,which clarify the relationship between target controllability,state controllability and output controllability.For the multi-layer networks where the inter-layer couplings are directed chains and directed stars,sufficient conditions for target controllability of networked systems are given,respectively.These conditions are easier to verify than the classic criterion.

Multi-Objective Equilibrium Optimizer for Feature Selection in High-Dimensional English Speech Emotion Recognition

Speech emotion recognition(SER)uses acoustic analysis to find features for emotion recognition and examines variations in voice that are caused by emotions.The number of features acquired with acoustic analysis is extremely high,so we introduce a hybrid filter-wrapper feature selection algorithm based on an improved equilibrium optimizer for constructing an emotion recognition system.The proposed algorithm implements multi-objective emotion recognition with the minimum number of selected features and maximum accuracy.First,we use the information gain and Fisher Score to sort the features extracted from signals.Then,we employ a multi-objective ranking method to evaluate these features and assign different importance to them.Features with high rankings have a large probability of being selected.Finally,we propose a repair strategy to address the problem of duplicate solutions in multi-objective feature selection,which can improve the diversity of solutions and avoid falling into local traps.Using random forest and K-nearest neighbor classifiers,four English speech emotion datasets are employed to test the proposed algorithm(MBEO)as well as other multi-objective emotion identification techniques.The results illustrate that it performs well in inverted generational distance,hypervolume,Pareto solutions,and execution time,and MBEO is appropriate for high-dimensional English SER.

An Efficient Reliability-Based Optimization Method Utilizing High-Dimensional Model Representation and Weight-Point Estimation Method

The objective of reliability-based design optimization(RBDO)is to minimize the optimization objective while satisfying the corresponding reliability requirements.However,the nested loop characteristic reduces the efficiency of RBDO algorithm,which hinders their application to high-dimensional engineering problems.To address these issues,this paper proposes an efficient decoupled RBDO method combining high dimensional model representation(HDMR)and the weight-point estimation method(WPEM).First,we decouple the RBDO model using HDMR and WPEM.Second,Lagrange interpolation is used to approximate a univariate function.Finally,based on the results of the first two steps,the original nested loop reliability optimization model is completely transformed into a deterministic design optimization model that can be solved by a series of mature constrained optimization methods without any additional calculations.Two numerical examples of a planar 10-bar structure and an aviation hydraulic piping system with 28 design variables are analyzed to illustrate the performance and practicability of the proposed method.

Censored Composite Conditional Quantile Screening for High-Dimensional Survival Data

In this paper,we introduce the censored composite conditional quantile coefficient(cC-CQC)to rank the relative importance of each predictor in high-dimensional censored regression.The cCCQC takes advantage of all useful information across quantiles and can detect nonlinear effects including interactions and heterogeneity,effectively.Furthermore,the proposed screening method based on cCCQC is robust to the existence of outliers and enjoys the sure screening property.Simulation results demonstrate that the proposed method performs competitively on survival datasets of high-dimensional predictors,particularly when the variables are highly correlated.

A State-Migration Particle Swarm Optimizer for Adaptive Latent Factor Analysis of High-Dimensional and Incomplete Data

High-dimensional and incomplete(HDI) matrices are primarily generated in all kinds of big-data-related practical applications. A latent factor analysis(LFA) model is capable of conducting efficient representation learning to an HDI matrix,whose hyper-parameter adaptation can be implemented through a particle swarm optimizer(PSO) to meet scalable requirements.However, conventional PSO is limited by its premature issues,which leads to the accuracy loss of a resultant LFA model. To address this thorny issue, this study merges the information of each particle's state migration into its evolution process following the principle of a generalized momentum method for improving its search ability, thereby building a state-migration particle swarm optimizer(SPSO), whose theoretical convergence is rigorously proved in this study. It is then incorporated into an LFA model for implementing efficient hyper-parameter adaptation without accuracy loss. Experiments on six HDI matrices indicate that an SPSO-incorporated LFA model outperforms state-of-the-art LFA models in terms of prediction accuracy for missing data of an HDI matrix with competitive computational efficiency.Hence, SPSO's use ensures efficient and reliable hyper-parameter adaptation in an LFA model, thus ensuring practicality and accurate representation learning for HDI matrices.

Guaranteed Cost Consensus for High-dimensional Multi-agent Systems With Time-varying Delays

Guaranteed cost consensus analysis and design problems for high-dimensional multi-agent systems with time varying delays are investigated. The idea of guaranteed cost con trol is introduced into consensus problems for high-dimensiona multi-agent systems with time-varying delays, where a cos function is defined based on state errors among neighboring agents and control inputs of all the agents. By the state space decomposition approach and the linear matrix inequality(LMI)sufficient conditions for guaranteed cost consensus and consensu alization are given. Moreover, a guaranteed cost upper bound o the cost function is determined. It should be mentioned that these LMI criteria are dependent on the change rate of time delays and the maximum time delay, the guaranteed cost upper bound is only dependent on the maximum time delay but independen of the Laplacian matrix. Finally, numerical simulations are given to demonstrate theoretical results.

Random Subspace Learning Approach to High-Dimensional Outliers Detection

We introduce and develop a novel approach to outlier detection based on adaptation of random subspace learning. Our proposed method handles both high-dimension low-sample size and traditional low-dimensional high-sample size datasets. Essentially, we avoid the computational bottleneck of techniques like Minimum Covariance Determinant (MCD) by computing the needed determinants and associated measures in much lower dimensional subspaces. Both theoretical and computational development of our approach reveal that it is computationally more efficient than the regularized methods in high-dimensional low-sample size, and often competes favorably with existing methods as far as the percentage of correct outlier detection are concerned.

Chip-Based High-Dimensional Optical Neural Network

Parallel multi-thread processing in advanced intelligent processors is the core to realize high-speed and high-capacity signal processing systems.Optical neural network(ONN)has the native advantages of high parallelization,large bandwidth,and low power consumption to meet the demand of big data.Here,we demonstrate the dual-layer ONN with Mach-Zehnder interferometer(MZI)network and nonlinear layer,while the nonlinear activation function is achieved by optical-electronic signal conversion.Two frequency components from the microcomb source carrying digit datasets are simultaneously imposed and intelligently recognized through the ONN.We successfully achieve the digit classification of different frequency components by demultiplexing the output signal and testing power distribution.Efficient parallelization feasibility with wavelength division multiplexing is demonstrated in our high-dimensional ONN.This work provides a high-performance architecture for future parallel high-capacity optical analog computing.

A Sequence Image Matching Method Based on Improved High-Dimensional Combined Features

Image matching technology is theoretically significant and practically promising in the field of autonomous navigation.Addressing shortcomings of existing image matching navigation technologies,the concept of high-dimensional combined feature is presented based on sequence image matching navigation.To balance between the distribution of high-dimensional combined features and the shortcomings of the only use of geometric relations,we propose a method based on Delaunay triangulation to improve the feature,and add the regional characteristics of the features together with their geometric characteristics.Finally,k-nearest neighbor(KNN)algorithm is adopted to optimize searching process.Simulation results show that the matching can be realized at the rotation angle of-8°to 8°and the scale factor of 0.9 to 1.1,and when the image size is 160 pixel×160 pixel,the matching time is less than 0.5 s.Therefore,the proposed algorithm can substantially reduce computational complexity,improve the matching speed,and exhibit robustness to the rotation and scale changes.

Perfect Transfer of Many-Particle Quantum State via High-Dimensional Systems with Spectrum-Matched Symmetry

The quantum state transmission through the medium of high-dimensional many-particle system （boson or spinless fermion） is generally studied with a symmetry analysis. We discover that, if the spectrum of a Hamiltonian matches the symmetry of a fermion or boson system in a certain fashion, a perfect quantum state transfer can be implemented without any operation on the medium with pre-engineered nearest neighbor （NN）. We also study a simple but realistic near half-filled tight-bindlng fermion system wlth uniform NN hopping integral. We show that an arbitrary many-particle state near the fermi surface can be perfectly transferred to its translational counterpart.

Randomized Latent Factor Model for High-dimensional and Sparse Matrices from Industrial Applications

Latent factor(LF) models are highly effective in extracting useful knowledge from High-Dimensional and Sparse(HiDS) matrices which are commonly seen in various industrial applications. An LF model usually adopts iterative optimizers,which may consume many iterations to achieve a local optima,resulting in considerable time cost. Hence, determining how to accelerate the training process for LF models has become a significant issue. To address this, this work proposes a randomized latent factor(RLF) model. It incorporates the principle of randomized learning techniques from neural networks into the LF analysis of HiDS matrices, thereby greatly alleviating computational burden. It also extends a standard learning process for randomized neural networks in context of LF analysis to make the resulting model represent an HiDS matrix correctly.Experimental results on three HiDS matrices from industrial applications demonstrate that compared with state-of-the-art LF models, RLF is able to achieve significantly higher computational efficiency and comparable prediction accuracy for missing data.I provides an important alternative approach to LF analysis of HiDS matrices, which is especially desired for industrial applications demanding highly efficient models.

Similarity measurement method of high-dimensional data based on normalized net lattice subspace

The performance of conventional similarity measurement methods is affected seriously by the curse of dimensionality of high-dimensional data.The reason is that data difference between sparse and noisy dimensionalities occupies a large proportion of the similarity,leading to the dissimilarities between any results.A similarity measurement method of high-dimensional data based on normalized net lattice subspace is proposed.The data range of each dimension is divided into several intervals,and the components in different dimensions are mapped onto the corresponding interval.Only the component in the same or adjacent interval is used to calculate the similarity.To validate this method,three data types are used,and seven common similarity measurement methods are compared.The experimental result indicates that the relative difference of the method is increasing with the dimensionality and is approximately two or three orders of magnitude higher than the conventional method.In addition,the similarity range of this method in different dimensions is [0,1],which is fit for similarity analysis after dimensionality reduction.

Robust Latent Factor Analysis for Precise Representation of High-Dimensional and Sparse Data

High-dimensional and sparse(HiDS)matrices commonly arise in various industrial applications,e.g.,recommender systems(RSs),social networks,and wireless sensor networks.Since they contain rich information,how to accurately represent them is of great significance.A latent factor(LF)model is one of the most popular and successful ways to address this issue.Current LF models mostly adopt L2-norm-oriented Loss to represent an HiDS matrix,i.e.,they sum the errors between observed data and predicted ones with L2-norm.Yet L2-norm is sensitive to outlier data.Unfortunately,outlier data usually exist in such matrices.For example,an HiDS matrix from RSs commonly contains many outlier ratings due to some heedless/malicious users.To address this issue,this work proposes a smooth L1-norm-oriented latent factor(SL-LF)model.Its main idea is to adopt smooth L1-norm rather than L2-norm to form its Loss,making it have both strong robustness and high accuracy in predicting the missing data of an HiDS matrix.Experimental results on eight HiDS matrices generated by industrial applications verify that the proposed SL-LF model not only is robust to the outlier data but also has significantly higher prediction accuracy than state-of-the-art models when they are used to predict the missing data of HiDS matrices.

High-Dimensional Schwarzian Derivatives and Painlevé Integrable Models

Because all the known integrable models possess Schwarzian forms with Mobious transformation invariance,it may be one of the best ways to find new integrable models starting from some suitable Mobious transformation invariant equations. In this paper, we study the Painlevé integrability of some special (3+1)-dimensional Schwarzian models.

Computation of the Rational Representation for Solutions of High-dimensional Systems

This paper deals with the representation of the solutions of a polynomial system, and concentrates on the high-dimensional case. Based on the rational univari- ate representation of zero-dimensional polynomial systems, we give a new description called rational representation for the solutions of a high-dimensional polynomial sys- tem and propose an algorithm for computing it. By this way all the solutions of any high-dimensional polynomial system can be represented by a set of so-called rational- representation sets.

New semi-quantum key agreement protocol based on high-dimensional single-particle states

A new efficient two-party semi-quantum key agreement protocol is proposed with high-dimensional single-particle states.Different from the previous semi-quantum key agreement protocols based on the two-level quantum system,the propounded protocol makes use of the advantage of the high-dimensional quantum system,which possesses higher efficiency and better robustness against eavesdropping.Besides,the protocol allows the classical participant to encode the secret key with qudit shifting operations without involving any quantum measurement abilities.The designed semi-quantum key agreement protocol could resist both participant attacks and outsider attacks.Meanwhile,the conjoint analysis of security and efficiency provides an appropriate choice for reference on the dimension of single-particle states and the number of decoy states.

CSFW-SC: Cuckoo Search Fuzzy-Weighting Algorithm for Subspace Clustering Applying to High-Dimensional Clustering

Aimed at the issue that traditional clustering methods are not appropriate to high-dimensional data, a cuckoo search fuzzy-weighting algorithm for subspace clustering is presented on the basis of the exited soft subspace clustering algorithm. In the proposed algorithm, a novel objective function is firstly designed by considering the fuzzy weighting within-cluster compactness and the between-cluster separation, and loosening the constraints of dimension weight matrix. Then gradual membership and improved Cuckoo search, a global search strategy, are introduced to optimize the objective function and search subspace clusters, giving novel learning rules for clustering. At last, the performance of the proposed algorithm on the clustering analysis of various low and high dimensional datasets is experimentally compared with that of several competitive subspace clustering algorithms. Experimental studies demonstrate that the proposed algorithm can obtain better performance than most of the existing soft subspace clustering algorithms.

Finite-key analysis of practical time-bin high-dimensional quantum key distribution with afterpulse effect

High-dimensional quantum resources provide the ability to encode several bits of information on a single photon,which can particularly increase the secret key rate rate of quantum key distribution(QKD) systems. Recently, a practical four-dimensional QKD scheme based on time-bin quantum photonic state, only with two single-photon avalanche detectors as measurement setup, has been proven to have a superior performance than the qubit-based one. In this paper, we extend the results to our proposed eight-dimensional scheme. Then, we consider two main practical factors to improve its secret key bound. Concretely, we take the afterpulse effect into account and apply a finite-key analysis with the intensity fluctuations.Our secret bounds give consideration to both the intensity fluctuations and the afterpulse effect for the high-dimensional QKD systems. Numerical simulations show the bound of eight-dimensional QKD scheme is more robust to the intensity fluctuations but more sensitive to the afterpulse effect than the four-dimensional one.