Projection pursuit cluster model and its application in water quality assessment

One of the difficulties frequently encountered in water quality assessment is that there are many factors and they cannot be assessed according to one factor, all the effect factors associated with water quality must be used. In order to overcome this issues the projection pursuit principle is introduced into water quality assessment, and projection pursuit cluster(PPC) model is developed in this study. The PPC model makes the transition from high dimension to one-dimension. In other words, based on the PPC model, multifactor problem can be converted to one factor problem. The application of PPC model can be divided into four parts: (1) to estimate projection index function Q(); (2) to find the right projection direction ; (3) to calculate projection characteristic value of the i th sample z-i, and (4) to draw comprehensive analysis on the basis of z-i. On the other hand, the empirical formula of cutoff radius R is developed, which is benefit for the model to be used in practice. Finally, a case study of water quality assessment is proposed in this paper. The results showed that the PPC model is reasonable, and it is more objective and less subjective in water quality assessment. It is a new method for multivariate problem comprehensive analysis.

Application of Projection Pursuit Evaluation Model Based on Real-Coded Accelerating Genetic Algorithm in Evaluating Wetland Soil Quality Variations in the Sanjiang Plain, China

A new technique of dimension reduction named projection pursuit is applied to model and evaluatewetland soil quality variations in the Sanjiang Plain, Helongjiang Province, China. By adopting the im-proved real-coded accelerating genetic algorithm (RAGA), the projection direction is optimized and multi-dimensional indexes are converted into low-dimensional space. Classification of wetland soils and evaluationof wetland soil quality variations are realized by pursuing optimum projection direction and projection func-tion value. Therefore, by adopting this new method, any possible human interference can be avoided andsound results can be achieved in researching quality changes and classification of wetland soils.

Projection Pursuit Dynamic Cluster Model and its Application to Water Resources Carrying Capacity Evaluation

The research shows that projection pursuit cluster (PPC) model is able to form a suitable index for overcom-ing the difficulties in comprehensive evaluation, which can be used to analyze complex multivariate prob-lems. The PPC model is widely used in multifactor cluster and evaluation analysis, but there are a few prob-lems needed to be solved in practice, such as cutoff radius parameter calibration. In this study, a new model-projection pursuit dynamic cluster (PPDC) model-based on projection pursuit principle is developed and used in water resources carrying capacity evaluation in China for the first time. In the PPDC model, there are two improvements compared with the PPC model, 1) a new projection index is constructed based on dynamic cluster principle, which avoids the problem of parameter calibration in the PPC model success-fully;2) the cluster results can be outputted directly according to the PPDC model, but the cluster results can be got based on the scatter points of projected characteristic values or the re-analysis for projected character-istic values in the PPC model. The results show that the PPDC model is a very effective and powerful tool in multifactor data exploratory analysis. It is a new method for water resources carrying capacity evaluation. The PPDC model and its application to water resources carrying capacity evaluation are introduced in detail in this paper.

The application of projection pursuit classification in the process of strategy selection and evaluation based on the real coded accelerating genetic algorithm

During the process of enterprises＇ strategy evaluation and selection, there are many evaluating indicators, and among them there are some potential correlations and conflicts. Thus it poses the problems to the decision-makers how to conduct correct evaluation on a business and how to make strategy adjustment and selection according to the evaluation. Based on the qualitative and quantitative method, the paper introduces the Projection Pursuit Classification （PPC） model based on the Real-coded Accelerating Genetic Algorithm （RAGA） into the process of enterprises＇ strategy evaluation and selection. The characteristic of PPC model is that it ultimately overcomes the influence of the proportion of subjectivity and avoids precocious convergence, thus providing a new objective method for strategy evaluation and selection by pursuing the most objective strategy evaluation to make the relatively sensible strategy portfolio and action.

Approach to Weighted Geometric Evaluation Based on Projection Pursuit

Weighted geometric evaluation approach based on Projection pursuit (PP) model is presented in this paper to optimize the choice of schemes. By using PP model, the multi-dimension evaluation index values of schemes can be synthesized into projection value with one dimension. The scheme with a bigger projection value is much better, so the schemes sample can be an optimized choice according to the projection value of each scheme. The modeling of PP based on accelerating genetic algorithm can predigest the realized process of projection pursuit technique, can overcome the shortcomings of large computation amount and the difficulty of computer programming in traditional projection pursuit methods, and can give a new method for application of projection pursuit technique to optimize choice of schemes by using weighted geometric evaluation. The analysis of an applied sample shows that applying PP model driven directly by samples data to optimize choice of schemes is both simple and feasible, that its projection values are relatively decentralized and profit decision-making, that its applicability and maneuverability are high. It can avoid the shortcoming of subjective weighing method, and its results are scientific and objective.

A NEW APPROACH FOR UNSUPERVISED RESTORING IMAGES BASED ON WAVELET-DOMAIN PROJECTION PURSUIT LEARNING NETWORK

The Wavelet-Domain Projection Pursuit Learning Network (WDPPLN) is proposedfor restoring degraded image. The new network combines the advantages of both projectionpursuit and wavelet shrinkage. Restoring image is very difficult when little is known about apriori knowledge for multisource degraded factors. WDPPLN successfully resolves this problemby separately processing wavelet coefficients and scale coefficients. Parameters in WDPPLN,which are used to simulate degraded factors, are estimated via WDPPLN training, using scalecoefficients. Also, WDPPLN uses soft-threshold of wavelet shrinkage technique to suppress noisein three high frequency subbands. The new method is compared with the traditional methodsand the Projection Pursuit Learning Network (PPLN) method. Experimental results demonstratethat it is an effective method for unsupervised restoring degraded image.

基于Projection Pursuit-RAGA-NK-GERT的质量绩效提升路径优化——以组织质量特异性免疫和产品生命周期为主导逻辑的解释框架

依据组织免疫和组织质量特异性免疫的相关理论,引入情境变量产品生命周期,构建基于组织质量监视、组织质量防御软要素、组织质量防御硬要素和组织质量记忆的质量绩效提升路径理论框架。使用基于RAGA的投影寻踪模型、适应度景观和NK模型对产品生命周期不同阶段的质量绩效提升路径进行实证分析,实证结果表明:产品生命周期不同阶段有不同的质量绩效提升路径,产品导入期遵循的质量绩效提升路径为组织质量监视→组织质量防御→组织质量记忆,产品成长期遵循的质量绩效提升路径为组织质量防御软要素→组织质量防御硬要素→组织质量监视→组织质量记忆,产品成熟期遵循的质量绩效提升路径为组织质量防御硬要素→组织质量防御软要素→组织质量监视→组织质量记忆,产品衰退期遵循的质量绩效提升路径为组织质量记忆→组织质量监视→组织质量防御。并建立产品生命周期不同阶段质量绩效提升路径优化的GERT网络,优化产品生命周期不同阶段的质量绩效提升路径。

Regional partitioning of agricultural non-point source pollution in China using a projection pursuit cluster model

A projection pursuit cluster（PPC） model was used to analyze the regional partitioning of agricultural non-point source pollution in China.The environmental factors impacting the agricultural non-point source pollution were compiled into a projection index to set up the projection index function.A novel optimization algorithm called Free search（FS） was introduced to optimize the projection direction of the PPC model.By making the appropriate improvements as we explored the use of the algorithm,it became simpler,and developed better exploration abilities.Thus,the multi-factor problem was converted into a single-factor cluster,according to the projection,which successfully avoided subjective disturbance and produced objective results.The cluster results of the PPC model mirror the actual regional partitioning of the agricultural non-point source pollution in China,indicating that the PPC model is a powerful tool in multi-factor cluster analysis,and could be a new method for the regional partitioning of agricultural non-point source pollution.

Projection Pursuit Flood Disaster Classification Assessment Method Based on Multi-Swarm Cooperative Particle Swarm Optimization

The indicators of flood damage assessment in the flood classification are often incompatible, and it is very difficult to use those indicators value directly for classification assessment. Projection pursuit technology can project higher dimensional incompatible data into lower dimensional sub-space, and find the projection values for optimal projection index function to get the higher dimensional data structure features, which has been improved to be reasonable and effective for flood disaster classification assessment. However, it is a bit difficult to optimize the parameters of projection index functions, as a result, that limits the applications of this method. As an emerging heuristic global optimization algorithm based on swarm intelligence, particle swarm optimization algorithm has the ability of solving complex optimization problem, but it still be easily convergent early, and can not search the global optimal solution. In this paper, a flood disaster classification assessment method based on multi-swarm cooperative particle swarm optimization is proposed, which adopts a tri-parameter Logistic curve to construct the flood disaster projection pursuit model, and uses mul-ti-swarm system particle swarm optimization method to optimize the parameters of the projection index functions. The typical test function experiment shows that this optimization method can solve the early convergence commonly found in standard particle swarm optimization algorithm, which global optimized ability is improved greatly. Applied in flood disaster assessment in HeNan Province, the results using this method comparing with others indicates that it can assess effectively the flood disaster, and has better assessment accuracy and disaster resolution.

On grey relation projection model based on projection pursuit

Multidimensional grey relation projection value can be synthesized as one-dimensional projection value by using projection pursuit model. The larger the projection value is,the better the model. Thus,according to the projection value,the best one can be chosen from the model aggregation. Because projection pursuit modeling based on accelerating genetic algorithm can simplify the implementation procedure of the projection pursuit technique and overcome its complex calculation as well as the difficulty in implementing its program,a new method can be obtained for choosing the best grey relation projection model based on the projection pursuit technique.

A Genetic Fuzzy Analytical Hierarchy Process Based Projection Pursuit Method for Selecting Schemes of Water Transportation Projects

The optimal selection of schemes of water transportation projects is a process of choosing a relatively optimal scheme from a number of schemes of water transportation programming and management projects, which is of importance in both theory and practice in water resource systems engineering. In order to achieve consistency and eliminate the dimensions of fuzzy qualitative and fuzzy quantitative evaluation indexes, to determine the weights of the indexes objectively, and to increase the differences among the comprehensive evaluation index values of water transportation project schemes, a projection pursuit method, named FPRM-PP for short, was developed in this work for selecting the optimal water transportation project scheme based on the fuzzy preference relation matrix. The research results show that FPRM-PP is intuitive and practical, the correction range of the fuzzy rained is both stable and accurate; preference relation matrix A it produces is relatively small, and the result obtherefore FPRM-PP can be widely used in the optimal selection of different multi-factor decision-making schemes.

A Case Retrieval Projection Pursuit Model for Configuration Design of a Product Family

The paper studies on case-based reasoning of uncertain product attributes in configuration design of a product family. Interval numbers characterize uncertain product attributes. By interpolating a number of certain values randomly to replace interval numbers and making projection pursuit analysis on source cases and target cases of expanded numbers, we can get a projection value in the optimal projection direction. Based on projection value, we can construct a case retrieval model of projection pursuit that can handle coexisting certain and uncertain product attributes. The application examples of chainsaw configuration design show that case retrieval is highly sensitive to reliable results.

CLUSTERING VIA DIMENSIONAL REDUCTION METHOD FOR THE PROJECTION PURSUIT BASED ON THE ICSA

The performance of the classical clustering algorithm is not always satisfied with the high-dimensional datasets, which make clustering method limited in many application. To solve this problem, clustering method with Projection Pursuit dimension reduction based on Immune Clonal Selection Algorithm (ICSA-PP) is proposed in this paper. Projection pursuit strategy can maintain consistent Euclidean distances between points in the low-dimensional embeddings where the ICSA is used to search optimizing projection direction. The proposed algorithm can converge quickly with less iteration to reduce dimension of some high-dimensional datasets, and in which space, K-mean clustering algorithm is used to partition the reduced data. The experiment results on UCI data show that the presented method can search quicker to optimize projection direction than Genetic Algorithm (GA) and it has better clustering results compared with traditional linear dimension reduction method for Principle Component Analysis (PCA).

Benefit Evaluation Model of Small Watershed Control Based on Projection Pursuit

A projection pursuit model is presented in this paper for comprehensive evaluation of benefits of small watershed control.By using the model,small watershed control samples with many benefit evaluation indexes can be synthesized projective values with one dimension.The samples can be naturally evaluated according to the projective values.The parameters of the model is optimized by using real coding beased accelerating genetic aglrothm,which overcomes the shortcomings of large computation amount and difficulty of computer programming in traditional projection prusuit methods,and provides a new way for wide applications of projection pursuit technique to different evaluation problems in agricultural systems engineering.

Projection pursuit model of vehicle emission on air pollution at intersections based on the improved bat algorithm

The projection pursuit model is used to study the assessment of air pollution caused by vehicle emissions at intersections. Based on the analysis of the characteristics and regularities of vehicle emissions at intersections, a vehicle emission model based on projection pursuit is established, and the bat algorithm is used to solve the optimization function. The research results show that the projection pursuit model can not only measure the air pollution of vehicle emissions at intersections, but also effectively evaluate the level of vehicle exhaust emissions at intersections. Taking the air pollution caused by vehicle emissions at intersections as the research object and considering the influence factors of vehicle emissions on air pollution comprehensively, the evaluation index system of vehicle emissions at intersections on air pollution is constructed. Based on large data analysis, a prediction model of air pollution caused by vehicle emissions at intersections is constructed, and an improved bat algorithm is used to realize the assessment process. The application results show that the prediction model of vehicle emissions at intersections can define the degree of air pollution caused by vehicle emissions, and it has good guiding significance and practical value for solving the problem of air pollution caused by vehicle emissions.

Seismic comprehensive forecast based on modified project pursuit regression

In the research of projection pursuit for seismic comprehensive forecast, the algorithm of projection pursuit regression （PPR） is one of most applicable methods. But generally, the algorithm structure of the PPR is very complicated. By partial smooth regressions for many times, it has a large amount of calculation and complicated extrapolation, so it is easily trapped in partial solution. On the basis of the algorithm features of the PPR method, some solutions are given as below to aim at some shortcomings in the PPR calculation： to optimize project direction by using particle swarm optimization instead of Gauss-Newton algorithm, to simplify the optimal process with fitting ridge function by using Hermitian polynomial instead of piecewise linear regression. The overall optimal ridge function can be obtained without grouping the parameter optimization. The modeling capability and calculating accuracy of projection pursuit method are tested by means of numerical emulation technique on the basis of particle swarm optimization and Hermitian polynomial, and then applied to the seismic comprehensive forecasting models of poly-dimensional seismic time series and general disorder seismic samples. The calculation and analysis show that the projection pursuit model in this paper is characterized by simplicity, celerity and effectiveness. And this model is approved to have satisfactory effects in the real seismic comprehensive forecasting, which can be regarded as a comprehensive analysis method in seismic comprehensive forecast.

Accelerated Matrix Recovery via Random Projection Based on Inexact Augmented Lagrange Multiplier Method

In this paper, a unified matrix recovery model was proposed for diverse corrupted matrices. Resulting from the separable structure of the proposed model, the convex optimization problem can be solved efficiently by adopting an inexact augmented Lagrange multiplier (IALM) method. Additionally, a random projection accelerated technique (IALM+RP) was adopted to improve the success rate. From the preliminary numerical comparisons, it was indicated that for the standard robust principal component analysis (PCA) problem, IALM+RP was at least two to six times faster than IALM with an insignificant reduction in accuracy; and for the outlier pursuit (OP) problem, IALM+RP was at least 6.9 times faster, even up to 8.3 times faster when the size of matrix was 2 000×2 000.

基于FA-ISSA-PPR模型的旋风分离器分离效率预测

旋风分离器是气田开发中常用的气固分离设备,准确预测旋风分离器的分离效率对于指导其结构设计和方法优化具有重要意义。在对数据集进行相关性分析的基础上,采用因子分析(factor analysis, FA)简化变量,降低预测模型的复杂程度,利用改进的樽海鞘群算法(improved salp swarm algorithm, ISSA)对投影寻踪(projection pursuit regression, PPR)的模型参数进行优化,形成FA-ISSA-PPR组合模型。结果表明,利用FA模型,原数据集的10个变量可以简化合并为4个公因子,分别代表尺寸参数、颗粒沉降特性、粒子运行轨迹和等效分割粒径对分离效率的影响;与半经验模型和其余机器学习模型相比,组合模型在预测精度和训练时间上具有一定的优越性,在测试样本上的平均绝对误差(MAE)为0.005 91,R^(2)可达0.995,证明了其在小样本、非线性数据分析上的准确性、鲁棒性和泛化性。

基于WTD-PPAR的中国碳排放预测研究

碳排放预测对我国的碳排放规划和政策颁布具有一定的参考价值。使用小波阈值去噪模型对碳排放数据建模能够有效缓解其存在的非线性和波动性问题,筛选得到数据的有效增长趋势。在此基础上,利用碳排放数据的时间序列特征建立其投影寻踪自回归(PPAR)模型,从而对碳排放进行预测分析。将该模型与未进行去噪的PPAR、BP、LSSVM、SVR、LSTM模型进行对比,发现WTD-PPAR模型的预测精度更高,预测结果更准确。分析结果显示,我国碳排放将在2029年达到峰值,约为1081.89 mt,能够实现碳达峰的目标。

基于博弈论原理的PP-AHP权重优化模型在河流健康评价中的应用

为了解决传统层次分析法在指标权重赋值中主观意识影响过大导致河流健康评价结果具有较强主观随意性的问题,本文利用客观性较强的投影寻踪法来改进层次分析法,综合考虑主客观影响,通过博弈论原理对指标权重进行优化,并运用优化模型权重对扬州市城区三条城市河流进行了丰枯期健康评价。结果表明:优化后的权重能综合主、客观权重的特点,使评价结果更加合理;在进行权重优化的过程中,得到最优加权系数分别为0.5435、0.4565。为了简化权重处理步骤,同时选取0.5、0.5作为加权系数进行等权处理,该处理对评价结果影响较小,可为今后河流建康评价中的主客观权重耦合提供一定的参考。