A Dynamical System-Based Framework for Dimension Reduction

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.

An Actual Survey of Dimensionality Reduction

Dimension reduction is defined as the processes of projecting high-dimensional data to a much lower-dimensional space. Dimension reduction methods variously applied in regression, classification, feature analysis and visualization. In this paper, we review in details the last and most new version of methods that extensively developed in the past decade.

A New Algorithm for Reducing Dimensionality of L1-CSVM Use Augmented Lagrange Method

Principal component analysis and generalized low rank approximation of matrices are two different dimensionality reduction methods. Two different dimensionality reduction algorithms are applied to the L1-CSVM model based on augmented Lagrange method to explore the variation of running time and accuracy of the model in dimensionality reduction space. The results show that the improved algorithm can greatly reduce the running time and improve the accuracy of the algorithm.

A frequency domain reliability analysis method for electromagnetic problems based on univariate dimension reduction method

In this paper, a class of electromagnetic field frequency domain reliability problem is first defined. The frequency domain reliability refers to the probability that an electromagnetic performance indicator can meet the intended requirements within a specific frequency band, considering the uncertainty of structural parameters and frequency-variant electromagnetic parameters.And then a frequency domain reliability analysis method based on univariate dimension reduction method is proposed, which provides an effective calculation tool for electromagnetic frequency domain reliability. In electromagnetic problems, performance indicators usually vary with frequency. The method firstly discretizes the frequency-variant performance indicator function into a series of frequency points' functions, and then transforms the frequency domain reliability problem into a series system reliability problem of discrete frequency points' functions. Secondly, the univariate dimension reduction method is introduced to solve the probability distribution functions and correlation coefficients of discrete frequency points' functions in the system. Finally, according to the above calculation results, the series system reliability can be solved to obtain the frequency domain reliability, and the cumulative distribution function of the performance indicator can also be obtained. In this study,Monte Carlo simulation is adopted to demonstrate the validity of the frequency domain reliability analysis method. Three examples are investigated to demonstrate the accuracy and efficiency of the proposed method.

Dynamic Behaviors Analysis of Reduced Rotor Models with Looseness Based on the TPOD Method

The transient proper orthogonal decomposition(TPOD) method is used to study dynamic behaviors of the reduced rotor-bearing models,and the fault-free model is compared with the models with looseness fault.A 22 degree of freedoms(DOFs) rotor model supported by bearings is established.Both one end and two ends pedestal looseness of the liquid-film bearings are studied by analyzing the time history and the frequency-spectrum curves.The effects of the initial displacement and velocity values to frequency components of the original systems and the dimension reduction efficiency are discussed.Moreover,the effects of variation of initial conditions on the efficiency of the TPOD method are studied.Reduced models can provide guidance significance from the perspectives of the theory and numerical simplification to discuss the characteristics of pedestal looseness fault.

Feature subset selection method for AdaBoost training

The feature-selection problem in training AdaBoost classifiers is addressed in this paper. A working feature subset is generated by adopting a novel feature subset selection method based on the partial least square （PLS） regression, and then trained and selected from this feature subset in Boosting. The experiments show that the proposed PLS-based feature-selection method outperforms the current feature ranking method and the random sampling method.

On Eigen-Matrix Translation Method for Classification of Biological Data

Driven by the challenge of integrating large amount of experimental data, classification technique emerges as one of the major and popular tools in computational biology and bioinformatics research. Machine learning methods, especially kernel methods with Support Vector Machines （SVMs） are very popular and effective tools. In the perspective of kernel matrix, a technique namely Eigen- matrix translation has been introduced for protein data classification. The Eigen-matrix translation strategy has a lot of nice properties which deserve more exploration. This paper investigates the major role of Eigen-matrix translation in classification. The authors propose that its importance lies in the dimension reduction of predictor attributes within the data set. This is very important when the dimension of features is huge. The authors show by numerical experiments on real biological data sets that the proposed framework is crucial and effective in improving classification accuracy. This can therefore serve as a novel perspective for future research in dimension reduction problems.

Comparison of dimension reduction methods for DEA under big data via Monte Carlo simulation

Data with large dimensions will bring various problems to the application of data envelopment analysis(DEA).In this study,we focus on a“big data”problem related to the considerably large dimensions of the input-output data.The four most widely used approaches to guide dimension reduction in DEA are compared via Monte Carlo simulation,including principal component analysis(PCA-DEA),which is based on the idea of aggregating input and output,efficiency contribution measurement(ECM),average efficiency measure(AEC),and regression-based detection(RB),which is based on the idea of variable selection.We compare the performance of these methods under different scenarios and a brand-new comparison benchmark for the simulation test.In addition,we discuss the effect of initial variable selection in RB for the first time.Based on the results,we offer guidelines that are more reliable on how to choose an appropriate method.

Motion Planning for Robots with Topological Dimension Reduction Method

This paper explores the realization of robotic motion planning, especially Findpath problem, which is a basic motion planning problem that arises in the development of robotics. Findpath means: Give the initial and desired final configurations of a robotic arm in 3-dimensionnl space, and give descriptions of the obstacles in the space, determine whether there is a continuous collision-free motion of the robotic arm from one configure- tion to the other and find such a motion if it exists. There are several branches of approach in motion planning area, but in reality the important things are feasibility, efficiency and accuracy of the method. In this paper ac- cording to the concepts of Configuration Space (C-Space) and Rotation Mapping Graph (RMG) discussed in [1], a topological method named Dimension Reduction Method (DRM) for investigating the connectivity of the RMG (or the topologic structure of the RMG )is presented by using topologic technique. Based on this ap- proach the Findpath problem is thus transformed to that of finding a connected way in a finite Characteristic Network (CN). The method has shown great potentiality in practice. Here a simulation system is designed to embody DRM and it is in sight that DRM can he adopted in the first overall planning of real robot sys- tem in the near future.

An Intrusion Detection Approach Based on Particle Method

In recent years,the network continues to enter people’s lives,followed by network security issues that continue to appear,causing substantial economic losses to the world.As an effective method to tackle the network security issues,intrusion detection system has been widely used and studied.In this paper,the NSL-KDD data set is used to reduce the dimension of data features,remove the features of low correlation and high interference,and improve the computational efficiency.To improve the detection rate and accuracy of intrusion detection,this paper introduces the particle method for the first time that we call it intrusion detection with particle(IDP).To illustrate the effectiveness of this method,experiments are carried out on three kinds of data-before dimension reduction,after dimension reduction and importing particle method based on dimension reduction.By comparing the results of DT,NN,SVM,K-NN,and NB,it is proved that the particle method can effectively improve the intrusion detection rate.

轴向流作用下均布非线性弹簧支承二维壁板的复杂响应

考虑刚性导流段和尾流段对流场的影响,建立轴向流作用下二维板的非线性流固耦合运动控制方程,用有限差分法对控制方程进行离散。为了克服差分网格较多时带来的计算规模较大的问题,对控制方程用主模态缩减法缩减自由度,然后对离散方程进行数值积分,得到系统的复杂响应,分析其分岔和混沌特性。计算结果表明,以来流流速幅值和阻尼参数为可变参数时,系统具有极其复杂的动态响应,通过分岔图、相图和庞加莱截面图等方法判断了系统多种形式的周期、拟周期和混沌运动,在以来流流速幅值为可变参数时,系统一开始经由周期倍化分岔的方式进入混沌;在以阻尼系数为可变参数时,经由倒周期倍化分岔的方式从混沌运动退回到周期振动。

二维复杂弹性空腔的边光滑有限元建模及分析

在弹性空腔结构上敷设被动约束层阻尼(passive constraint layer damping, PCLD)可达到减振降噪的效果,针对这类复杂结构建立了二维复合弹性空腔的边光滑有限元耦合动力学模型。其中,PCLD结构采用两节点四自由度的PCLD梁单元,声场采用边光滑有限元模型。以二维全敷设复合矩形空腔模型为数值算例,以精细网格下的有限元法结果作为参考解,对比研究了在相同背景网格下,边光滑有限元法和有限元法的频响结果,发现前者更接近参考解,说明同样的计算成本下,边光滑有限元法具有更高的精确性,特别是在中频计算中。最后,分析了PCLD结构对某汽车驾驶舱的降噪效果,以及黏弹层和约束层厚度参数的影响规律,发现黏弹层厚度增大,可一定程度上降低空腔噪声,而约束层厚度增大,并不能在整个频段得到很好的降噪效果。

基于最优近邻的局部保持投影方法

局部保持投影(LPP)方法是机器学习领域中一种经典的降维方法。然而LPP方法以及部分改进方法在构建数据的局部结构时简单地使用k最近邻(k-NN)分类算法寻找样本的近邻点,容易受到参数k、噪声和异常值的影响。为了解决上述问题,提出一种基于最优近邻的LPP方法。该方法使用寻找最优近邻算法,在找到样本近邻点后,进一步选择与样本有一定数量的共同近邻点的近邻样本作为最优近邻,通过共同近邻点的限定来选择与样本最相似的近邻,增强近邻样本间的相关性,避免了传统LPP方法受参数k影响大等问题。在选择出足够的样本最优近邻后,构建数据局部结构,以便准确地反映数据的本质结构特征,使降维后的数据能最大程度保留样本的有效信息,提升后续机器学习模型的性能。公共图像数据集上的对比实验结果表明,该方法具有较好的数据降维效果,有效地提高了图像识别准确率。

高层建筑深基坑支护结构位移动态监测方法

针对高层建筑深基坑支护结构位移监测时,位移轨迹、位移速率以及位移时间变化监测准确性较差问题,本文研究了高层建筑深基坑支护结构位移动态监测方法。对支护结构位移影响因素进行具体分析,生成了影响指标;再对基坑数据进行采集,建立数据集并进行降维处理;计算获取目标函数,结合影响指标建立时间序列模型,依据对模型的计算建立动态变量矩阵;通过对矩阵的计算获取动态监测数据的统计量,完成支护结构的动态监测。研究结果表明:运用该方法进行监测时,位移移动轨迹监测误差为0.1,位移速率保持在0.9 mm/d以下,且与实际位移速率基本一致,纵向位移量达到202 mm,且与实际沉降量一致。本文方法能够有效应用于高层建筑深基坑支护结构的位移动态监测,为保障高层建筑的稳定性和安全性提供重要的技术支持。

多因子降维法分析MTHFR C677T基因多态性-Hcy交互作用对高血压合并冠心病的影响

目的:基于多因子降维法(GMDR)分析亚甲基四氢叶酸还原酶(MTHFR)C677T基因多态性-Hcy交互作用对高血压合并冠心病的影响。方法:选取2021年3月至2022年10月我院收治的150例高血压患者作为研究对象,根据冠脉造影结果分为单纯高血压组(n=51)、高血压合并冠心病组(n=99),比较两组一般资料、Hcy水平、MTHFR C677T基因多态性分布,采用Logistic回归方程分析高血压合并冠心病影响因素,采用GMDR分析MTHFR C677T基因多态性与Hcy交互作用。结果:两组MTHFR C677T基因型频率实测值与理论值比较差异无统计学意义(P>0.05);高血压病程、Hcy、LDL-C、MTHFR C677T基因型-TT及等位基因T是高血压合并冠心病影响因素(P<0.05);GMDR结果显示,MTHFR C677T基因型-TT与Hcy交互模型为高血压合并冠心病风险的最优模型,其交叉检验一致性为10/10,检验准确度为75.00%,符合检验值为0.011。结论:MTHFR C677T基因多态性、Hcy交互作用可能增加冠心病发生风险,临床应动态监测上述指标变化情况,及时采取有效治疗措施,减少冠心病发生。

基于特征工程的S-FCN火灾图像检测方法

针对复杂背景下火灾图像检测深度学习算法存在的计算复杂度高、检测实时性差等问题,提出一种基于特征工程的单隐层全连接网络(S-FCN)火灾图像检测方法。首先,从图像中提取多色彩空间颜色特征,并使用互信息量进行多色彩空间颜色特征降维;其次,简化深度学习模型的网络结构,将单隐层全连接网络作为其主干网络,其中,多色彩空间下的颜色特征能够更好地表征火灾烟雾与火焰,多色彩空间颜色特征降维能够有效降低输入特征的冗余度,单隐层全连接网络能够有效减少模型在传递过程中的参数数量;最后,将该方法在真实的复杂背景火灾图像数据集上进行试验评估。结果表明:所提方法取得的检测精度为93.83%,取得的检测实时性帧率为10869帧/s,能够实现复杂场景下高精度、高速度的火灾图像检测。

基于改进ID3算法的非结构化大数据分类优化方法

针对非结构化大数据在分类过程中,由于其数据中存在大量的冗余数据,若不能及时清洗大数据中的冗余数据,会降低数据分类精度的问题,提出一种基于改进ID3(Iterative Dichotomiser 3)算法的非结构化大数据分类优化方法。该方法针对非结构化大数据集合中冗余数据多以及维度繁杂的问题,对数据进行清洗处理,并结合有监督辨识矩阵完成数据降维;根据数据降维结果,采用改进ID3算法建立用于数据分类的决策树分类模型,通过该模型对非结构化大数据进行分类处理,从而实现数据的精准分类。实验结果表明,使用该方法对非结构化大数据分类时,分类效果好,精度高。

面向联合作战运用的探索性实验方法

针对联合作战背景下运用作战实验方法开展方案评估可能出现“维数灾难”的问题,以有人/无人机协同作战中的编组方案研究为切入点,提出一种基于空间降维与模糊综合评估的探索性实验方法,以快速高效确定所研究问题的优选方案。结合空中力量联合抗击对方海空兵力应用场景,利用探索性实验方法,分析有人/无人机编组优选方案,验证了该方法的有效性。

A novel order reduction method for nonlinear dynamical system under external periodic excitations

The concept of approximate inertial manifold (AIM) is extended to develop a kind of nonlinear order reduction technique for non-autonomous nonlinear systems in second-order form in this paper.Using the modal transformation,a large nonlinear dynamical system is split into a 'master' subsystem,a 'slave' subsystem,and a 'negligible' subsystem.Accordingly,a novel order reduction method (Method I) is developed to construct a low order subsystem by neglecting the 'negligible' subsystem and slaving the 'slave' subsystem into the 'master' subsystem using the extended AIM.As a comparison,Method II accounting for the effects of both 'slave' subsystem and the 'negligible' subsystem is also applied to obtain the reduced order subsystem.Then,a typical 5-degree-of-freedom nonlinear dynamical system is given to compare the accuracy and efficiency of the traditional Galerkin truncation (ignoring the contributions of the slave and negligible subsystems),Method I and Method II.It is shown that Method I gives a considerable increase in accuracy for little computational cost in comparison with the standard Galerkin method,and produces almost the same accuracy as Method II.Finally,a 3-degree-of-freedom nonlinear dynamical system is analyzed by using the analytic method for showing predominance and convenience of Method I to obtain the analytically reduced order system.

混积型碳酸盐岩储层特征及关键参数计算——以四川盆地蓬莱气区寒武系沧浪铺组为例

四川盆地川中地区乐山-龙女寺古隆起北斜坡蓬莱气区下寒武统沧浪铺组一段为清水浅水陆棚和混积浅水陆棚交替沉积,硅质碎屑岩和碳酸盐岩沉积物在纵向上互层或平面上交替沉积,发育泥质、硅质、方解石、白云石和黄铁矿等多种矿物,组成岩石类型多样。储层岩性纵横向变化快,且低孔低渗,不同岩性的孔渗关系迥异,传统的双矿物计算模型难以满足混积岩复杂矿物成分计算要求,相应的孔隙度计算精度也无法保证。为解决混积型碳酸盐岩储层复杂矿物含量和孔隙度两个关键参数计算问题开展研究,通过应用大量的全岩X衍射、物性、压汞实验分析数据和岩化分析、岩性扫描测井标定的常规测井信息,形成降维法、神经网络分析法、元素反演矿物组分法和最优化处理法4种计算沧浪铺组复杂岩石矿物组分方法。研究结果表明:4种方法的计算结果与全岩分析和岩性扫描均具有一致性,其中最优化处理结果最佳,降维法可操作性最强;在获得准确矿物组分含量基础上,建立基于三孔隙度曲线的变骨架参数孔隙度计算模型,用于混积型碳酸盐岩储层测井评价,具有重要意义。