Owing to their global search capabilities and gradient-free operation,metaheuristic algorithms are widely applied to a wide range of optimization problems.However,their computational demands become prohibitive when ta...Owing to their global search capabilities and gradient-free operation,metaheuristic algorithms are widely applied to a wide range of optimization problems.However,their computational demands become prohibitive when tackling high-dimensional optimization challenges.To effectively address these challenges,this study introduces cooperative metaheuristics integrating dynamic dimension reduction(DR).Building upon particle swarm optimization(PSO)and differential evolution(DE),the proposed cooperative methods C-PSO and C-DE are developed.In the proposed methods,the modified principal components analysis(PCA)is utilized to reduce the dimension of design variables,thereby decreasing computational costs.The dynamic DR strategy implements periodic execution of modified PCA after a fixed number of iterations,resulting in the important dimensions being dynamically identified.Compared with the static one,the dynamic DR strategy can achieve precise identification of important dimensions,thereby enabling accelerated convergence toward optimal solutions.Furthermore,the influence of cumulative contribution rate thresholds on optimization problems with different dimensions is investigated.Metaheuristic algorithms(PSO,DE)and cooperative metaheuristics(C-PSO,C-DE)are examined by 15 benchmark functions and two engineering design problems(speed reducer and composite pressure vessel).Comparative results demonstrate that the cooperative methods achieve significantly superior performance compared to standard methods in both solution accuracy and computational efficiency.Compared to standard metaheuristic algorithms,cooperative metaheuristics achieve a reduction in computational cost of at least 40%.The cooperative metaheuristics can be effectively used to tackle both high-dimensional unconstrained and constrained optimization problems.展开更多
In the past decade,financial institutions have invested significant efforts in the development of accurate analytical credit scoring models.The evidence suggests that even small improvements in the accuracy of existin...In the past decade,financial institutions have invested significant efforts in the development of accurate analytical credit scoring models.The evidence suggests that even small improvements in the accuracy of existing credit-scoring models may optimize profits while effectively managing risk exposure.Despite continuing efforts,the majority of existing credit scoring models still include some judgment-based assumptions that are sometimes supported by the significant findings of previous studies but are not validated using the institution’s internal data.We argue that current studies related to the development of credit scoring models have largely ignored recent developments in statistical methods for sufficient dimension reduction.To contribute to the field of financial innovation,this study proposes a Dimension Reduction Assisted Credit Scoring(DRA-CS)method via distance covariance-based sufficient dimension reduction(DCOV-SDR)in Majorization-Minimization(MM)algorithm.First,in the presence of a large number of variables,the DRA-CS method results in greater dimension reduction and better prediction accuracy than the other methods used for dimension reduction.Second,when the DRA-CS method is employed with logistic regression,it outperforms existing methods based on different variable selection techniques.This study argues that the DRA-CS method should be used by financial institutions as a financial innovation tool to analyze high-dimensional customer datasets and improve the accuracy of existing credit scoring methods.展开更多
<strong>Purpose:</strong><span style="font-family:;" "=""><span style="font-family:Verdana;"> This study sought to review the characteristics, strengths, weak...<strong>Purpose:</strong><span style="font-family:;" "=""><span style="font-family:Verdana;"> This study sought to review the characteristics, strengths, weaknesses variants, applications areas and data types applied on the various </span><span><span style="font-family:Verdana;">Dimension Reduction techniques. </span><b><span style="font-family:Verdana;">Methodology: </span></b><span style="font-family:Verdana;">The most commonly used databases employed to search for the papers were ScienceDirect, Scopus, Google Scholar, IEEE Xplore and Mendeley. An integrative review was used for the study where </span></span></span><span style="font-family:Verdana;">341</span><span style="font-family:;" "=""><span style="font-family:Verdana;"> papers were reviewed. </span><b><span style="font-family:Verdana;">Results:</span></b><span style="font-family:Verdana;"> The linear techniques considered were Principal Component Analysis (PCA), Linear Discriminant Analysis (LDA), Singular Value Decomposition (SVD), Latent Semantic Analysis (LSA), Locality Preserving Projections (LPP), Independent Component Analysis (ICA) and Project Pursuit (PP). The non-linear techniques which were developed to work with applications that ha</span></span><span style="font-family:Verdana;">ve</span><span style="font-family:Verdana;"> complex non-linear structures considered were Kernel Principal Component Analysis (KPC</span><span style="font-family:Verdana;">A), Multi</span><span style="font-family:Verdana;">-</span><span style="font-family:;" "=""><span style="font-family:Verdana;">dimensional Scaling (MDS), Isomap, Locally Linear Embedding (LLE), Self-Organizing Map (SOM), Latent Vector Quantization (LVQ), t-Stochastic </span><span style="font-family:Verdana;">neighbor embedding (t-SNE) and Uniform Manifold Approximation and Projection (UMAP). DR techniques can further be categorized into supervised, unsupervised and more recently semi-supervised learning methods. The supervised versions are the LDA and LVQ. All the other techniques are unsupervised. Supervised variants of PCA, LPP, KPCA and MDS have </span><span style="font-family:Verdana;">been developed. Supervised and semi-supervised variants of PP and t-SNE have also been developed and a semi supervised version of the LDA has been developed. </span><b><span style="font-family:Verdana;">Conclusion:</span></b><span style="font-family:Verdana;"> The various application areas, strengths, weaknesses and variants of the DR techniques were explored. The different data types that have been applied on the various DR techniques were also explored.</span></span>展开更多
An automated method to optimize the definition of the progress variables in the flamelet-based dimension reduction is proposed. The performance of these optimized progress variables in coupling the flamelets and flow ...An automated method to optimize the definition of the progress variables in the flamelet-based dimension reduction is proposed. The performance of these optimized progress variables in coupling the flamelets and flow solver is presented. In the proposed method, the progress variables are defined according to the first two principal components （PCs） from the principal component analysis （PCA） or kernel-density-weighted PCA （KEDPCA） of a set of flamelets. These flamelets can then be mapped to these new progress variables instead of the mixture fraction/conventional progress variables. Thus, a new chemistry look-up table is constructed. A priori validation of these optimized progress variables and the new chemistry table is implemented in a CH4/N2/air lift-off flame. The reconstruction of the lift-off flame shows that the optimized progress variables perform better than the conventional ones, especially in the high temperature area. The coefficient determinations （R2 statistics） show that the KEDPCA performs slightly better than the PCA except for some minor species. The main advantage of the KEDPCA is that it is less sensitive to the database. Meanwhile, the criteria for the optimization are proposed and discussed. The constraint that the progress variables should monotonically evolve from fresh gas to burnt gas is analyzed in detail.展开更多
The equipment used in various fields contains an increasing number of parts with curved surfaces of increasing size.Five-axis computer numerical control(CNC)milling is the main parts machining method,while dynamics an...The equipment used in various fields contains an increasing number of parts with curved surfaces of increasing size.Five-axis computer numerical control(CNC)milling is the main parts machining method,while dynamics analysis has always been a research hotspot.The cutting conditions determined by the cutter axis,tool path,and workpiece geometry are complex and changeable,which has made dynamics research a major challenge.For this reason,this paper introduces the innovative idea of applying dimension reduction and mapping to the five-axis machining of curved surfaces,and proposes an efficient dynamics analysis model.To simplify the research object,the cutter position points along the tool path were discretized into inclined plane five-axis machining.The cutter dip angle and feed deflection angle were used to define the spatial position relationship in five-axis machining.These were then taken as the new base variables to construct an abstract two-dimensional space and establish the mapping relationship between the cutter position point and space point sets to further simplify the dimensions of the research object.Based on the in-cut cutting edge solved by the space limitation method,the dynamics of the inclined plane five-axis machining unit were studied,and the results were uniformly stored in the abstract space to produce a database.Finally,the prediction of the milling force and vibration state along the tool path became a data extraction process that significantly improved efficiency.Two experiments were also conducted which proved the accuracy and efficiency of the proposed dynamics analysis model.This study has great potential for the online synchronization of intelligent machining of large surfaces.展开更多
In the underwater waveguide,the conventional adaptive subspace detector(ASD),derived by using the generalized likelihood ratio test(GLRT)theory,suffers from a significant degradation in detection performance when the ...In the underwater waveguide,the conventional adaptive subspace detector(ASD),derived by using the generalized likelihood ratio test(GLRT)theory,suffers from a significant degradation in detection performance when the samplings of training data are deficient.This paper proposes a dimension-reduced approach to alleviate this problem.The dimension reduction includes two steps:firstly,the full array is divided into several subarrays;secondly,the test data and the training data at each subarray are transformed into the modal domain from the hydrophone domain.Then the modal-domain test data and training data at each subarray are processed to formulate the subarray statistic by using the GLRT theory.The final test statistic of the dimension-reduced ASD(DR-ASD)is obtained by summing all the subarray statistics.After the dimension reduction,the unknown parameters can be estimated more accurately so the DR-ASD achieves a better detection performance than the ASD.In order to achieve the optimal detection performance,the processing gain of the DR-ASD is deduced to choose a proper number of subarrays.Simulation experiments verify the improved detection performance of the DR-ASD compared with the ASD.展开更多
In this study,a k-nearest neighbor(kNN)method based on nonlinear directional dimension reduction is applied to gas-bearing reservoir prediction.The kNN method can select the most relevant training samples to establish...In this study,a k-nearest neighbor(kNN)method based on nonlinear directional dimension reduction is applied to gas-bearing reservoir prediction.The kNN method can select the most relevant training samples to establish a local model according to feature similarities.However,the kNN method cannot extract gas-sensitive attributes and faces dimension problems.The features important to gas-bearing reservoir prediction could not be the main features of the samples.Thus,linear dimension reduction methods,such as principal component analysis,fail to extract relevant features.We thus implemented dimension reduction using a fully connected artifi cial neural network(ANN)with proper architecture.This not only increased the separability of the samples but also maintained the samples’inherent distribution characteristics.Moreover,using the kNN to classify samples after the ANN dimension reduction is also equivalent to replacing the deep structure of the ANN,which is considered to have a linear classifi cation function.When applied to actual data,our method extracted gas-bearing sensitive features from seismic data to a certain extent.The prediction results can characterize gas-bearing reservoirs accurately in a limited scope.展开更多
We propose a novel framework for learning a low-dimensional representation of data based on nonlinear dynamical systems,which we call the dynamical dimension reduction(DDR).In the DDR model,each point is evolved via a...We propose a novel framework for learning a low-dimensional representation of data based on nonlinear dynamical systems,which we call the dynamical dimension reduction(DDR).In the DDR model,each point is evolved via a nonlinear flow towards a lower-dimensional subspace;the projection onto the subspace gives the low-dimensional embedding.Training the model involves identifying the nonlinear flow and the subspace.Following the equation discovery method,we represent the vector field that defines the flow using a linear combination of dictionary elements,where each element is a pre-specified linear/nonlinear candidate function.A regularization term for the average total kinetic energy is also introduced and motivated by the optimal transport theory.We prove that the resulting optimization problem is well-posed and establish several properties of the DDR method.We also show how the DDR method can be trained using a gradient-based optimization method,where the gradients are computed using the adjoint method from the optimal control theory.The DDR method is implemented and compared on synthetic and example data sets to other dimension reduction methods,including the PCA,t-SNE,and Umap.展开更多
Sustainable Development Capacity (SDC) is a comprehensive concept. In order to obtain a relatively objective evaluation of it, many indices of various aspects are often used in assessing index systems. However, the ov...Sustainable Development Capacity (SDC) is a comprehensive concept. In order to obtain a relatively objective evaluation of it, many indices of various aspects are often used in assessing index systems. However, the overlapping information of indices is a frequent source deviating the result from the truth. In this paper, 48 indices are selected as original variables in assessing SDC of China's coastal areas. The mathematical method of dimension reducing treatment is used for eliminating the overlapping information in 48 variables. Five new comprehensive indices are extracted bearing efficient messages of original indices. On the base of new indices values, the sequencing of 12 coastal areas SDC is gained, and five patterns of sustainable development regions are sorted. Then, the leading factors and their relations of SDC in these patterns are analyzed. The gains of research are discussed in the end.展开更多
The performance of the traditional Voice Activity Detection （VAD） algorithms declines sharply in lower Signal-to-Noise Ratio （SNR） environments. In this paper, a feature weighting likelihood method is proposed for...The performance of the traditional Voice Activity Detection （VAD） algorithms declines sharply in lower Signal-to-Noise Ratio （SNR） environments. In this paper, a feature weighting likelihood method is proposed for noise-robust VAD. The contribution of dynamic features to likelihood score can be increased via the method, which improves consequently the noise robustness of VAD. Divergence based dimension reduction method is proposed for saving computation, which reduces these feature dimensions with smaller divergence value at the cost of degrading the performance a little. Experimental results on Aurora Ⅱ database show that the detection performance in noise environments can remarkably be improved by the proposed method when the model trained in clean data is used to detect speech endpoints. Using weighting likelihood on the dimension-reduced features obtains comparable, even better, performance compared to original full-dimensional feature.展开更多
The precision of the kernel independent component analysis( KICA) algorithm depends on the type and parameter values of kernel function. Therefore,it's of great significance to study the choice method of KICA'...The precision of the kernel independent component analysis( KICA) algorithm depends on the type and parameter values of kernel function. Therefore,it's of great significance to study the choice method of KICA's kernel parameters for improving its feature dimension reduction result. In this paper, a fitness function was established by use of the ideal of Fisher discrimination function firstly. Then the global optimal solution of fitness function was searched by particle swarm optimization( PSO) algorithm and a multi-state information dimension reduction algorithm based on PSO-KICA was established. Finally,the validity of this algorithm to enhance the precision of feature dimension reduction has been proven.展开更多
In our previous work, we have given an algorithm for segmenting a simplex in the n-dimensional space into rt n＋ 1 polyhedrons and provided map F which maps the n-dimensional unit cube to these polyhedrons. In this pa...In our previous work, we have given an algorithm for segmenting a simplex in the n-dimensional space into rt n＋ 1 polyhedrons and provided map F which maps the n-dimensional unit cube to these polyhedrons. In this paper, we prove that the map F is a one to one correspondence at least in lower dimensional spaces （n _〈 3）. Moreover, we propose the approximating subdivision and the interpolatory subdivision schemes and the estimation of computational complexity for triangular Bézier patches on a 2-dimensional space. Finally, we compare our schemes with Goldman＇s in computational complexity and speed.展开更多
Federated learning has become a popular tool in the big data era nowadays.It trains a centralized model based on data from different clients while keeping data decentralized.In this paper,we propose a federated sparse...Federated learning has become a popular tool in the big data era nowadays.It trains a centralized model based on data from different clients while keeping data decentralized.In this paper,we propose a federated sparse sliced inverse regression algorithm for the first time.Our method can simultaneously estimate the central dimension reduction subspace and perform variable selection in a federated setting.We transform this federated high-dimensional sparse sliced inverse regression problem into a convex optimization problem by constructing the covariance matrix safely and losslessly.We then use a linearized alternating direction method of multipliers algorithm to estimate the central subspace.We also give approaches of Bayesian information criterion and holdout validation to ascertain the dimension of the central subspace and the hyperparameter of the algorithm.We establish an upper bound of the statistical error rate of our estimator under the heterogeneous setting.We demonstrate the effectiveness of our method through simulations and real world applications.展开更多
The inversion of large sparse matrices poses a major challenge in geophysics,particularly in Bayesian seismic inversion,significantly limiting computational efficiency and practical applicability to largescale dataset...The inversion of large sparse matrices poses a major challenge in geophysics,particularly in Bayesian seismic inversion,significantly limiting computational efficiency and practical applicability to largescale datasets.Existing dimensionality reduction methods have achieved partial success in addressing this issue.However,they remain limited in terms of the achievable degree of dimensionality reduction.An incremental deep dimensionality reduction approach is proposed herein to significantly reduce matrix size and is applied to Bayesian linearized inversion(BLI),a stochastic seismic inversion approach that heavily depends on large sparse matrices inversion.The proposed method first employs a linear transformation based on the discrete cosine transform(DCT)to extract the matrix's essential information and eliminate redundant components,forming the foundation of the dimensionality reduction framework.Subsequently,an innovative iterative DCT-based dimensionality reduction process is applied,where the reduction magnitude is carefully calibrated at each iteration to incrementally reduce dimensionality,thereby effectively eliminating matrix redundancy in depth.This process is referred to as the incremental discrete cosine transform(IDCT).Ultimately,a linear IDCT-based reduction operator is constructed and applied to the kernel matrix inversion in BLI,resulting in a more efficient BLI framework.The proposed method was evaluated through synthetic and field data tests and compared with conventional dimensionality reduction methods.The IDCT approach significantly improves the dimensionality reduction efficiency of the core inversion matrix while preserving inversion accuracy,demonstrating prominent advantages in solving Bayesian inverse problems more efficiently.展开更多
Gas turbine rotors are complex dynamic systems with high-dimensional,discrete,and multi-source nonlinear coupling characteristics.Significant amounts of resources and time are spent during the process of solving dynam...Gas turbine rotors are complex dynamic systems with high-dimensional,discrete,and multi-source nonlinear coupling characteristics.Significant amounts of resources and time are spent during the process of solving dynamic characteristics.Therefore,it is necessary to design a lowdimensional model that can well reflect the dynamic characteristics of high-dimensional system.To build such a low-dimensional model,this study developed a dimensionality reduction method considering global order energy distribution by modifying the proper orthogonal decomposition theory.First,sensitivity analysis of key dimensionality reduction parameters to the energy distribution was conducted.Then a high-dimensional rotor-bearing system considering the nonlinear stiffness and oil film force was reduced,and the accuracy and the reusability of the low-dimensional model under different operating conditions were examined.Finally,the response results of a multi-disk rotor-bearing test bench were reduced using the proposed method,and spectrum results were then compared experimentally.Numerical and experimental results demonstrate that,during the dimensionality reduction process,the solution period of dynamic response results has the most significant influence on the accuracy of energy preservation.The transient signal in the transformation matrix mainly affects the high-order energy distribution of the rotor system.The larger the proportion of steady-state signals is,the closer the energy tends to accumulate towards lower orders.The low-dimensional rotor model accurately reflects the frequency response characteristics of the original high-dimensional system with an accuracy of up to 98%.The proposed dimensionality reduction method exhibits significant application potential in the dynamic analysis of highdimensional systems coupled with strong nonlinearities under variable operating conditions.展开更多
In order to accurately identify speech emotion information, the discriminant-cascading effect in dimensionality reduction of speech emotion recognition is investigated. Based on the existing locality preserving projec...In order to accurately identify speech emotion information, the discriminant-cascading effect in dimensionality reduction of speech emotion recognition is investigated. Based on the existing locality preserving projections and graph embedding framework, a novel discriminant-cascading dimensionality reduction method is proposed, which is named discriminant-cascading locality preserving projections （DCLPP）. The proposed method specifically utilizes supervised embedding graphs and it keeps the original space for the inner products of samples to maintain enough information for speech emotion recognition. Then, the kernel DCLPP （KDCLPP） is also proposed to extend the mapping form. Validated by the experiments on the corpus of EMO-DB and eNTERFACE＇05, the proposed method can clearly outperform the existing common dimensionality reduction methods, such as principal component analysis （PCA）, linear discriminant analysis （LDA）, locality preserving projections （LPP）, local discriminant embedding （LDE）, graph-based Fisher analysis （GbFA） and so on, with different categories of classifiers.展开更多
Single-cell RNA sequencing(scRNA-seq) is a powerful technique to analyze the transcriptomic heterogeneities at the single cell level. It is an important step for studying cell subpopulations and lineages, with an effe...Single-cell RNA sequencing(scRNA-seq) is a powerful technique to analyze the transcriptomic heterogeneities at the single cell level. It is an important step for studying cell subpopulations and lineages, with an effective low-dimensional representation and visualization of the original scRNA-Seq data. At the single cell level, the transcriptional fluctuations are much larger than the average of a cell population, and the low amount of RNA transcripts will increase the rate of technical dropout events. Therefore, scRNA-seq data are much noisier than traditional bulk RNA-seq data. In this study, we proposed the deep variational autoencoder for scRNA-seq data(VASC), a deep multi-layer generative model, for the unsupervised dimension reduction and visualization of scRNA-seq data. VASC can explicitly model the dropout events and find the nonlinear hierarchical feature representations of the original data. Tested on over 20 datasets, VASC shows superior performances in most cases and exhibits broader dataset compatibility compared to four state-of-the-art dimension reduction and visualization methods. In addition, VASC provides better representations for very rare cell populations in the 2D visualization. As a case study, VASC successfully re-establishes the cell dynamics in pre-implantation embryos and identifies several candidate marker genes associated with early embryo development. Moreover, VASC also performs well on a 10× Genomics dataset with more cells and higher dropout rate.展开更多
In this paper, a low-dimensional multiple-input and multiple-output （MIMO） model predictive control （MPC） configuration is presented for partial differential equation （PDE） unknown spatially-distributed systems ...In this paper, a low-dimensional multiple-input and multiple-output （MIMO） model predictive control （MPC） configuration is presented for partial differential equation （PDE） unknown spatially-distributed systems （SDSs）. First, the dimension reduction with principal component analysis （PCA） is used to transform the high-dimensional spatio-temporal data into a low-dimensional time domain. The MPC strategy is proposed based on the online correction low-dimensional models, where the state of the system at a previous time is used to correct the output of low-dimensional models. Sufficient conditions for closed-loop stability are presented and proven. Simulations demonstrate the accuracy and efficiency of the proposed methodologies.展开更多
Large-scale cooling energy system has developed well in the past decade.However,its optimization is still a problem to be tackled due to the nonlinearity and large scale of existing systems.Reducing the scale of probl...Large-scale cooling energy system has developed well in the past decade.However,its optimization is still a problem to be tackled due to the nonlinearity and large scale of existing systems.Reducing the scale of problems without oversimplifying the actual system model is a big challenge nowadays.This paper proposes a dimension reduction-based many-objective optimization(DRMO)method to solve an accurate nonlinear model of a practical large-scale cooling energy system.In the first stage,many-objective and many-variable of the large system are pre-processed to reduce the overall scale of the optimization problem.The relationships between many objectives are analyzed to find a few representative objectives.Key control variables are extracted to reduce the dimension of variables and the number of equality constraints.In the second stage,the manyobjective group search optimization(GSO)method is used to solve the low-dimensional nonlinear model,and a Pareto-front is obtained.In the final stage,candidate solutions along the Paretofront are graded on many-objective levels of system operators.The candidate solution with the highest average utility value is selected as the best running mode.Simulations are carried out on a 619-node-614-branch cooling system,and results show the ability of the proposed method in solving large-scale system operation problems.展开更多
We are concerned with partial dimension reduction for the conditional mean function in the presence of controlling variables.We suggest a profile least squares approach to perform partial dimension reduction for a gen...We are concerned with partial dimension reduction for the conditional mean function in the presence of controlling variables.We suggest a profile least squares approach to perform partial dimension reduction for a general class of semi-parametric models.The asymptotic properties of the resulting estimates for the central partial mean subspace and the mean function are provided.In addition,a Wald-type test is proposed to evaluate a linear hypothesis of the central partial mean subspace,and a generalized likelihood ratio test is constructed to check whether the nonparametric mean function has a specific parametric form.These tests can be used to evaluate whether there exist interactions between the covariates and the controlling variables,and if any,in what form.A Bayesian information criterion(BIC)-type criterion is applied to determine the structural dimension of the central partial mean subspace.Its consistency is also established.Numerical studies through simulations and real data examples are conducted to demonstrate the power and utility of the proposed semi-parametric approaches.展开更多
基金funded by National Natural Science Foundation of China(Nos.12402142,11832013 and 11572134)Natural Science Foundation of Hubei Province(No.2024AFB235)+1 种基金Hubei Provincial Department of Education Science and Technology Research Project(No.Q20221714)the Opening Foundation of Hubei Key Laboratory of Digital Textile Equipment(Nos.DTL2023019 and DTL2022012).
文摘Owing to their global search capabilities and gradient-free operation,metaheuristic algorithms are widely applied to a wide range of optimization problems.However,their computational demands become prohibitive when tackling high-dimensional optimization challenges.To effectively address these challenges,this study introduces cooperative metaheuristics integrating dynamic dimension reduction(DR).Building upon particle swarm optimization(PSO)and differential evolution(DE),the proposed cooperative methods C-PSO and C-DE are developed.In the proposed methods,the modified principal components analysis(PCA)is utilized to reduce the dimension of design variables,thereby decreasing computational costs.The dynamic DR strategy implements periodic execution of modified PCA after a fixed number of iterations,resulting in the important dimensions being dynamically identified.Compared with the static one,the dynamic DR strategy can achieve precise identification of important dimensions,thereby enabling accelerated convergence toward optimal solutions.Furthermore,the influence of cumulative contribution rate thresholds on optimization problems with different dimensions is investigated.Metaheuristic algorithms(PSO,DE)and cooperative metaheuristics(C-PSO,C-DE)are examined by 15 benchmark functions and two engineering design problems(speed reducer and composite pressure vessel).Comparative results demonstrate that the cooperative methods achieve significantly superior performance compared to standard methods in both solution accuracy and computational efficiency.Compared to standard metaheuristic algorithms,cooperative metaheuristics achieve a reduction in computational cost of at least 40%.The cooperative metaheuristics can be effectively used to tackle both high-dimensional unconstrained and constrained optimization problems.
文摘In the past decade,financial institutions have invested significant efforts in the development of accurate analytical credit scoring models.The evidence suggests that even small improvements in the accuracy of existing credit-scoring models may optimize profits while effectively managing risk exposure.Despite continuing efforts,the majority of existing credit scoring models still include some judgment-based assumptions that are sometimes supported by the significant findings of previous studies but are not validated using the institution’s internal data.We argue that current studies related to the development of credit scoring models have largely ignored recent developments in statistical methods for sufficient dimension reduction.To contribute to the field of financial innovation,this study proposes a Dimension Reduction Assisted Credit Scoring(DRA-CS)method via distance covariance-based sufficient dimension reduction(DCOV-SDR)in Majorization-Minimization(MM)algorithm.First,in the presence of a large number of variables,the DRA-CS method results in greater dimension reduction and better prediction accuracy than the other methods used for dimension reduction.Second,when the DRA-CS method is employed with logistic regression,it outperforms existing methods based on different variable selection techniques.This study argues that the DRA-CS method should be used by financial institutions as a financial innovation tool to analyze high-dimensional customer datasets and improve the accuracy of existing credit scoring methods.
文摘<strong>Purpose:</strong><span style="font-family:;" "=""><span style="font-family:Verdana;"> This study sought to review the characteristics, strengths, weaknesses variants, applications areas and data types applied on the various </span><span><span style="font-family:Verdana;">Dimension Reduction techniques. </span><b><span style="font-family:Verdana;">Methodology: </span></b><span style="font-family:Verdana;">The most commonly used databases employed to search for the papers were ScienceDirect, Scopus, Google Scholar, IEEE Xplore and Mendeley. An integrative review was used for the study where </span></span></span><span style="font-family:Verdana;">341</span><span style="font-family:;" "=""><span style="font-family:Verdana;"> papers were reviewed. </span><b><span style="font-family:Verdana;">Results:</span></b><span style="font-family:Verdana;"> The linear techniques considered were Principal Component Analysis (PCA), Linear Discriminant Analysis (LDA), Singular Value Decomposition (SVD), Latent Semantic Analysis (LSA), Locality Preserving Projections (LPP), Independent Component Analysis (ICA) and Project Pursuit (PP). The non-linear techniques which were developed to work with applications that ha</span></span><span style="font-family:Verdana;">ve</span><span style="font-family:Verdana;"> complex non-linear structures considered were Kernel Principal Component Analysis (KPC</span><span style="font-family:Verdana;">A), Multi</span><span style="font-family:Verdana;">-</span><span style="font-family:;" "=""><span style="font-family:Verdana;">dimensional Scaling (MDS), Isomap, Locally Linear Embedding (LLE), Self-Organizing Map (SOM), Latent Vector Quantization (LVQ), t-Stochastic </span><span style="font-family:Verdana;">neighbor embedding (t-SNE) and Uniform Manifold Approximation and Projection (UMAP). DR techniques can further be categorized into supervised, unsupervised and more recently semi-supervised learning methods. The supervised versions are the LDA and LVQ. All the other techniques are unsupervised. Supervised variants of PCA, LPP, KPCA and MDS have </span><span style="font-family:Verdana;">been developed. Supervised and semi-supervised variants of PP and t-SNE have also been developed and a semi supervised version of the LDA has been developed. </span><b><span style="font-family:Verdana;">Conclusion:</span></b><span style="font-family:Verdana;"> The various application areas, strengths, weaknesses and variants of the DR techniques were explored. The different data types that have been applied on the various DR techniques were also explored.</span></span>
基金Project supported by the National Natural Science Foundation of China(Nos.50936005,51576182,and 11172296)
文摘An automated method to optimize the definition of the progress variables in the flamelet-based dimension reduction is proposed. The performance of these optimized progress variables in coupling the flamelets and flow solver is presented. In the proposed method, the progress variables are defined according to the first two principal components （PCs） from the principal component analysis （PCA） or kernel-density-weighted PCA （KEDPCA） of a set of flamelets. These flamelets can then be mapped to these new progress variables instead of the mixture fraction/conventional progress variables. Thus, a new chemistry look-up table is constructed. A priori validation of these optimized progress variables and the new chemistry table is implemented in a CH4/N2/air lift-off flame. The reconstruction of the lift-off flame shows that the optimized progress variables perform better than the conventional ones, especially in the high temperature area. The coefficient determinations （R2 statistics） show that the KEDPCA performs slightly better than the PCA except for some minor species. The main advantage of the KEDPCA is that it is less sensitive to the database. Meanwhile, the criteria for the optimization are proposed and discussed. The constraint that the progress variables should monotonically evolve from fresh gas to burnt gas is analyzed in detail.
基金Supported by National Natural Science Foundation of China(Grant Nos.52005078,U1908231,52075076).
文摘The equipment used in various fields contains an increasing number of parts with curved surfaces of increasing size.Five-axis computer numerical control(CNC)milling is the main parts machining method,while dynamics analysis has always been a research hotspot.The cutting conditions determined by the cutter axis,tool path,and workpiece geometry are complex and changeable,which has made dynamics research a major challenge.For this reason,this paper introduces the innovative idea of applying dimension reduction and mapping to the five-axis machining of curved surfaces,and proposes an efficient dynamics analysis model.To simplify the research object,the cutter position points along the tool path were discretized into inclined plane five-axis machining.The cutter dip angle and feed deflection angle were used to define the spatial position relationship in five-axis machining.These were then taken as the new base variables to construct an abstract two-dimensional space and establish the mapping relationship between the cutter position point and space point sets to further simplify the dimensions of the research object.Based on the in-cut cutting edge solved by the space limitation method,the dynamics of the inclined plane five-axis machining unit were studied,and the results were uniformly stored in the abstract space to produce a database.Finally,the prediction of the milling force and vibration state along the tool path became a data extraction process that significantly improved efficiency.Two experiments were also conducted which proved the accuracy and efficiency of the proposed dynamics analysis model.This study has great potential for the online synchronization of intelligent machining of large surfaces.
基金the National Natural Science Foundation of China (Grant No. 11534009, 11974285) to provide fund for conducting this research
文摘In the underwater waveguide,the conventional adaptive subspace detector(ASD),derived by using the generalized likelihood ratio test(GLRT)theory,suffers from a significant degradation in detection performance when the samplings of training data are deficient.This paper proposes a dimension-reduced approach to alleviate this problem.The dimension reduction includes two steps:firstly,the full array is divided into several subarrays;secondly,the test data and the training data at each subarray are transformed into the modal domain from the hydrophone domain.Then the modal-domain test data and training data at each subarray are processed to formulate the subarray statistic by using the GLRT theory.The final test statistic of the dimension-reduced ASD(DR-ASD)is obtained by summing all the subarray statistics.After the dimension reduction,the unknown parameters can be estimated more accurately so the DR-ASD achieves a better detection performance than the ASD.In order to achieve the optimal detection performance,the processing gain of the DR-ASD is deduced to choose a proper number of subarrays.Simulation experiments verify the improved detection performance of the DR-ASD compared with the ASD.
基金supported by the National Key R&D Program of China(No.2018YFA0702504)the National Natural Science Foundation of China(No.42174152 and No.41974140)the Strategic Cooperation Technology Projects of CNPC and CUPB(No.ZLZX2020-03).
文摘In this study,a k-nearest neighbor(kNN)method based on nonlinear directional dimension reduction is applied to gas-bearing reservoir prediction.The kNN method can select the most relevant training samples to establish a local model according to feature similarities.However,the kNN method cannot extract gas-sensitive attributes and faces dimension problems.The features important to gas-bearing reservoir prediction could not be the main features of the samples.Thus,linear dimension reduction methods,such as principal component analysis,fail to extract relevant features.We thus implemented dimension reduction using a fully connected artifi cial neural network(ANN)with proper architecture.This not only increased the separability of the samples but also maintained the samples’inherent distribution characteristics.Moreover,using the kNN to classify samples after the ANN dimension reduction is also equivalent to replacing the deep structure of the ANN,which is considered to have a linear classifi cation function.When applied to actual data,our method extracted gas-bearing sensitive features from seismic data to a certain extent.The prediction results can characterize gas-bearing reservoirs accurately in a limited scope.
文摘We propose a novel framework for learning a low-dimensional representation of data based on nonlinear dynamical systems,which we call the dynamical dimension reduction(DDR).In the DDR model,each point is evolved via a nonlinear flow towards a lower-dimensional subspace;the projection onto the subspace gives the low-dimensional embedding.Training the model involves identifying the nonlinear flow and the subspace.Following the equation discovery method,we represent the vector field that defines the flow using a linear combination of dictionary elements,where each element is a pre-specified linear/nonlinear candidate function.A regularization term for the average total kinetic energy is also introduced and motivated by the optimal transport theory.We prove that the resulting optimization problem is well-posed and establish several properties of the DDR method.We also show how the DDR method can be trained using a gradient-based optimization method,where the gradients are computed using the adjoint method from the optimal control theory.The DDR method is implemented and compared on synthetic and example data sets to other dimension reduction methods,including the PCA,t-SNE,and Umap.
基金Knowledge Innovation Project of Chinese Academy of Sciences (KZCX2-307-05) Knowledge Innovation Project of Institute of Geograp
文摘Sustainable Development Capacity (SDC) is a comprehensive concept. In order to obtain a relatively objective evaluation of it, many indices of various aspects are often used in assessing index systems. However, the overlapping information of indices is a frequent source deviating the result from the truth. In this paper, 48 indices are selected as original variables in assessing SDC of China's coastal areas. The mathematical method of dimension reducing treatment is used for eliminating the overlapping information in 48 variables. Five new comprehensive indices are extracted bearing efficient messages of original indices. On the base of new indices values, the sequencing of 12 coastal areas SDC is gained, and five patterns of sustainable development regions are sorted. Then, the leading factors and their relations of SDC in these patterns are analyzed. The gains of research are discussed in the end.
基金Supported by the National Basic Research Program of China (973 Program) (No.2007CB311104)
文摘The performance of the traditional Voice Activity Detection （VAD） algorithms declines sharply in lower Signal-to-Noise Ratio （SNR） environments. In this paper, a feature weighting likelihood method is proposed for noise-robust VAD. The contribution of dynamic features to likelihood score can be increased via the method, which improves consequently the noise robustness of VAD. Divergence based dimension reduction method is proposed for saving computation, which reduces these feature dimensions with smaller divergence value at the cost of degrading the performance a little. Experimental results on Aurora Ⅱ database show that the detection performance in noise environments can remarkably be improved by the proposed method when the model trained in clean data is used to detect speech endpoints. Using weighting likelihood on the dimension-reduced features obtains comparable, even better, performance compared to original full-dimensional feature.
文摘The precision of the kernel independent component analysis( KICA) algorithm depends on the type and parameter values of kernel function. Therefore,it's of great significance to study the choice method of KICA's kernel parameters for improving its feature dimension reduction result. In this paper, a fitness function was established by use of the ideal of Fisher discrimination function firstly. Then the global optimal solution of fitness function was searched by particle swarm optimization( PSO) algorithm and a multi-state information dimension reduction algorithm based on PSO-KICA was established. Finally,the validity of this algorithm to enhance the precision of feature dimension reduction has been proven.
文摘In our previous work, we have given an algorithm for segmenting a simplex in the n-dimensional space into rt n＋ 1 polyhedrons and provided map F which maps the n-dimensional unit cube to these polyhedrons. In this paper, we prove that the map F is a one to one correspondence at least in lower dimensional spaces （n _〈 3）. Moreover, we propose the approximating subdivision and the interpolatory subdivision schemes and the estimation of computational complexity for triangular Bézier patches on a 2-dimensional space. Finally, we compare our schemes with Goldman＇s in computational complexity and speed.
文摘Federated learning has become a popular tool in the big data era nowadays.It trains a centralized model based on data from different clients while keeping data decentralized.In this paper,we propose a federated sparse sliced inverse regression algorithm for the first time.Our method can simultaneously estimate the central dimension reduction subspace and perform variable selection in a federated setting.We transform this federated high-dimensional sparse sliced inverse regression problem into a convex optimization problem by constructing the covariance matrix safely and losslessly.We then use a linearized alternating direction method of multipliers algorithm to estimate the central subspace.We also give approaches of Bayesian information criterion and holdout validation to ascertain the dimension of the central subspace and the hyperparameter of the algorithm.We establish an upper bound of the statistical error rate of our estimator under the heterogeneous setting.We demonstrate the effectiveness of our method through simulations and real world applications.
基金partly supported by Hainan Provincial Joint Project of Sanya Yazhou Bay Science and Technology City(2021JJLH0052)National Natural Science Foundation of China(42274154,42304116)+2 种基金Natural Science Foundation of Heilongjiang Province,China(LH2024D013)Heilongjiang Postdoctoral Fund(LBHZ23103)Hainan Yazhou Bay Science and Technology City Jingying Talent Project(SKJC-JYRC-2024-05)。
文摘The inversion of large sparse matrices poses a major challenge in geophysics,particularly in Bayesian seismic inversion,significantly limiting computational efficiency and practical applicability to largescale datasets.Existing dimensionality reduction methods have achieved partial success in addressing this issue.However,they remain limited in terms of the achievable degree of dimensionality reduction.An incremental deep dimensionality reduction approach is proposed herein to significantly reduce matrix size and is applied to Bayesian linearized inversion(BLI),a stochastic seismic inversion approach that heavily depends on large sparse matrices inversion.The proposed method first employs a linear transformation based on the discrete cosine transform(DCT)to extract the matrix's essential information and eliminate redundant components,forming the foundation of the dimensionality reduction framework.Subsequently,an innovative iterative DCT-based dimensionality reduction process is applied,where the reduction magnitude is carefully calibrated at each iteration to incrementally reduce dimensionality,thereby effectively eliminating matrix redundancy in depth.This process is referred to as the incremental discrete cosine transform(IDCT).Ultimately,a linear IDCT-based reduction operator is constructed and applied to the kernel matrix inversion in BLI,resulting in a more efficient BLI framework.The proposed method was evaluated through synthetic and field data tests and compared with conventional dimensionality reduction methods.The IDCT approach significantly improves the dimensionality reduction efficiency of the core inversion matrix while preserving inversion accuracy,demonstrating prominent advantages in solving Bayesian inverse problems more efficiently.
基金supported by the China Postdoctoral Science Foundation(No.2024M764171)the Postdoctoral Research Start-up Funds,China(No.AUGA5710027424)+1 种基金the National Natural Science Foundation of China(No.U2341237)the Development and construction funds for the School of Mechatronics Engineering of HIT,China(No.CBQQ8880103624)。
文摘Gas turbine rotors are complex dynamic systems with high-dimensional,discrete,and multi-source nonlinear coupling characteristics.Significant amounts of resources and time are spent during the process of solving dynamic characteristics.Therefore,it is necessary to design a lowdimensional model that can well reflect the dynamic characteristics of high-dimensional system.To build such a low-dimensional model,this study developed a dimensionality reduction method considering global order energy distribution by modifying the proper orthogonal decomposition theory.First,sensitivity analysis of key dimensionality reduction parameters to the energy distribution was conducted.Then a high-dimensional rotor-bearing system considering the nonlinear stiffness and oil film force was reduced,and the accuracy and the reusability of the low-dimensional model under different operating conditions were examined.Finally,the response results of a multi-disk rotor-bearing test bench were reduced using the proposed method,and spectrum results were then compared experimentally.Numerical and experimental results demonstrate that,during the dimensionality reduction process,the solution period of dynamic response results has the most significant influence on the accuracy of energy preservation.The transient signal in the transformation matrix mainly affects the high-order energy distribution of the rotor system.The larger the proportion of steady-state signals is,the closer the energy tends to accumulate towards lower orders.The low-dimensional rotor model accurately reflects the frequency response characteristics of the original high-dimensional system with an accuracy of up to 98%.The proposed dimensionality reduction method exhibits significant application potential in the dynamic analysis of highdimensional systems coupled with strong nonlinearities under variable operating conditions.
基金The National Natural Science Foundation of China(No.61231002,61273266)the Ph.D.Program Foundation of Ministry of Education of China(No.20110092130004)China Postdoctoral Science Foundation(No.2015M571637)
文摘In order to accurately identify speech emotion information, the discriminant-cascading effect in dimensionality reduction of speech emotion recognition is investigated. Based on the existing locality preserving projections and graph embedding framework, a novel discriminant-cascading dimensionality reduction method is proposed, which is named discriminant-cascading locality preserving projections （DCLPP）. The proposed method specifically utilizes supervised embedding graphs and it keeps the original space for the inner products of samples to maintain enough information for speech emotion recognition. Then, the kernel DCLPP （KDCLPP） is also proposed to extend the mapping form. Validated by the experiments on the corpus of EMO-DB and eNTERFACE＇05, the proposed method can clearly outperform the existing common dimensionality reduction methods, such as principal component analysis （PCA）, linear discriminant analysis （LDA）, locality preserving projections （LPP）, local discriminant embedding （LDE）, graph-based Fisher analysis （GbFA） and so on, with different categories of classifiers.
基金supported by the National Natural Science Foundation of China (Grant Nos.61370035 and 31361163004)Tsinghua University Initiative Scientific Research Program
文摘Single-cell RNA sequencing(scRNA-seq) is a powerful technique to analyze the transcriptomic heterogeneities at the single cell level. It is an important step for studying cell subpopulations and lineages, with an effective low-dimensional representation and visualization of the original scRNA-Seq data. At the single cell level, the transcriptional fluctuations are much larger than the average of a cell population, and the low amount of RNA transcripts will increase the rate of technical dropout events. Therefore, scRNA-seq data are much noisier than traditional bulk RNA-seq data. In this study, we proposed the deep variational autoencoder for scRNA-seq data(VASC), a deep multi-layer generative model, for the unsupervised dimension reduction and visualization of scRNA-seq data. VASC can explicitly model the dropout events and find the nonlinear hierarchical feature representations of the original data. Tested on over 20 datasets, VASC shows superior performances in most cases and exhibits broader dataset compatibility compared to four state-of-the-art dimension reduction and visualization methods. In addition, VASC provides better representations for very rare cell populations in the 2D visualization. As a case study, VASC successfully re-establishes the cell dynamics in pre-implantation embryos and identifies several candidate marker genes associated with early embryo development. Moreover, VASC also performs well on a 10× Genomics dataset with more cells and higher dropout rate.
基金supported by National High Technology Research and Development Program of China (863 Program)(No. 2009AA04Z162)National Nature Science Foundation of China(No. 60825302, No. 60934007, No. 61074061)+1 种基金Program of Shanghai Subject Chief Scientist,"Shu Guang" project supported by Shang-hai Municipal Education Commission and Shanghai Education Development FoundationKey Project of Shanghai Science and Technology Commission, China (No. 10JC1403400)
文摘In this paper, a low-dimensional multiple-input and multiple-output （MIMO） model predictive control （MPC） configuration is presented for partial differential equation （PDE） unknown spatially-distributed systems （SDSs）. First, the dimension reduction with principal component analysis （PCA） is used to transform the high-dimensional spatio-temporal data into a low-dimensional time domain. The MPC strategy is proposed based on the online correction low-dimensional models, where the state of the system at a previous time is used to correct the output of low-dimensional models. Sufficient conditions for closed-loop stability are presented and proven. Simulations demonstrate the accuracy and efficiency of the proposed methodologies.
基金supported by the Key-Area Research and Development Program of Guangdong Province(2020B010166004)Natural Science Foundation of China(52007066).
文摘Large-scale cooling energy system has developed well in the past decade.However,its optimization is still a problem to be tackled due to the nonlinearity and large scale of existing systems.Reducing the scale of problems without oversimplifying the actual system model is a big challenge nowadays.This paper proposes a dimension reduction-based many-objective optimization(DRMO)method to solve an accurate nonlinear model of a practical large-scale cooling energy system.In the first stage,many-objective and many-variable of the large system are pre-processed to reduce the overall scale of the optimization problem.The relationships between many objectives are analyzed to find a few representative objectives.Key control variables are extracted to reduce the dimension of variables and the number of equality constraints.In the second stage,the manyobjective group search optimization(GSO)method is used to solve the low-dimensional nonlinear model,and a Pareto-front is obtained.In the final stage,candidate solutions along the Paretofront are graded on many-objective levels of system operators.The candidate solution with the highest average utility value is selected as the best running mode.Simulations are carried out on a 619-node-614-branch cooling system,and results show the ability of the proposed method in solving large-scale system operation problems.
基金supported by Humanities and Social Science Foundation of Ministry of Education(Grant No.20YJC910003)Natural Science Foundation of Shanghai(Grant No.20ZR1423000)+1 种基金supported by Natural Science Foundation of Beijing(Grant No.Z19J0002)National Natural Science Foundation of China(Grant Nos.11731011 and 11931014)。
文摘We are concerned with partial dimension reduction for the conditional mean function in the presence of controlling variables.We suggest a profile least squares approach to perform partial dimension reduction for a general class of semi-parametric models.The asymptotic properties of the resulting estimates for the central partial mean subspace and the mean function are provided.In addition,a Wald-type test is proposed to evaluate a linear hypothesis of the central partial mean subspace,and a generalized likelihood ratio test is constructed to check whether the nonparametric mean function has a specific parametric form.These tests can be used to evaluate whether there exist interactions between the covariates and the controlling variables,and if any,in what form.A Bayesian information criterion(BIC)-type criterion is applied to determine the structural dimension of the central partial mean subspace.Its consistency is also established.Numerical studies through simulations and real data examples are conducted to demonstrate the power and utility of the proposed semi-parametric approaches.
