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 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.

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.

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.

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.

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.

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.

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.

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.

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).

A Projection Pursuit Dynamic Cluster Model Based on a Memetic Algorithm

A Projection Pursuit Dynamic Cluster(PPDC) model optimized by Memetic Algorithm(MA) was proposed to solve the practical problems of nonlinearity and high dimensions of sample data, which appear in the context of evaluation or prediction in complex systems. Projection pursuit theory was used to determine the optimal projection direction; then dynamic clusters and minimal total distance within clusters(min TDc) were used to build a PPDC model. 17 agronomic traits of 19 tomato varieties were evaluated by a PPDC model. The projection direction was optimized by Simulated Annealing(SA) algorithm, Particle Swarm Optimization(PSO), and MA. A PPDC model,based on an MA, avoids the problem of parameter calibration in Projection Pursuit Cluster(PPC) models. Its final results can be output directly, making the cluster results objective and definite. The calculation results show that a PPDC model based on an MA can solve the practical difficulties of nonlinearity and high dimensionality of sample data.

PROJECTION PURSUIT PRINCIPAL COMPONENT ANALYSIS AND ITS APPLICATION TO METEOROLOGY

Projection Pursuit (PP) Principal Component Analysis (PCA) method is herein introduced and applied to the field of meteorology for the first time. Some problems relevant to meteorological application are dis- cussed in detail and comparisons with EOF method are made with the emphasis on robustness.

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.

Protection efficiency assessment and quality of coastal shelterbelt for Dongshan Island at the coastal section scale

The coastal shelter forest in China is under threat of destruction and degradation because of the impact of human activities. Protection efficiency assessment of the coastal shelterbelt is an important component of shelterforest remediation planning and sustainable management. In this study, a protection efficiency index （PEI） model was established using the projection pursuit method to assess the protective quality of the coastal shelter forest at the coastal section scale of Dongshan Island, China. Three criteria were used, including forest stand structure, forest belt structure, and windbreak effect; each criterion further comprised multiple factors. Based on survey data of 31 plots in the coastal shelter forest of Dongshan Island, we calculated PEI values using a projection of a pursuit model. The result showed 64.5 % of the PEIs fell at or below the middle level, which can indicate the status of the coastal shelterbelt is unsatisfactory. To further explore whether the different bays and land use types create significant differences in PEIs and evaluation indices, we used an ANOVA to test the influence of various bays and forms of land use on coastal shelterbelts. The results showed that PEI and most of the indices differed significantly by bay; mean tree height, mean DBH, mean crown width, stand density, vegetation coverage, and wind velocity reduction differed significantly by land use. Therefore, relevant measures for different locations, bays and surrounding land use can be proposed to improve the existing conditions of the coastal shelterbelt. The results of this study provide a theoretical and technical framework for future changes and sustainable management of coastal shelterbelt on Dongshan Island.

Comprehensive Evaluation of Water Quality of Rivers in Binzhou Based on RAGA-PPCE Model

The water quality of main rivers in Binzhou City,Shandong Province was comprehensively evaluated based on RAGA-PPCE model. Six main factors such as ammonia nitrogen(NH-N),total phosphorus(TP),total nitrogen(TN),chemical oxygen demand(COD),dissolved oxygen(DO) and p H were used to establish the evaluation and classification standards of water quality. The results show that the evaluation results of water quality by RAGA-PPCE model and the fuzzy comprehensive evaluation method are basically the same. The evaluation results of RAGA-PPCE model are objective and reasonable and can be applied to the comprehensive evaluation of water quality.

PROJECTION-PURSUIT BASED PRINCIPAL COMPONENT ANALYSIS:A LARGE SAMPLE THEORY

The principal component analysis （PCA） is one of the most celebrated methods in analysing multivariate data. An effort of extending PCA is projection pursuit （PP）, a more general class of dimension-reduction techniques. However, the application of this extended procedure is often hampered by its complexity in computation and by lack of some appropriate theory. In this paper, by use of the empirical processes we established a large sample theory for the robust PP estimators of the principal components and dispersion matrix.

BOOTSTRAPPING GENERALIZED U－PROCESSES AND V－PROCESSES AND THEIR APPLICATIONS IN PROJECTION PURSUIT

In this paper, we study bootstrap approximation for generalized U-processes (GUP) indexedby a class of functions. Under mild conditions we obtain that the asymptotic distributions ofbootstrapping generalized U-processes (BGUP) are the same as those of GUP almost surely. Asa result, the asymptotic properties of bootstrap approximation for PP generalized U-processes(BPPGUP) are obtained. In addition we have derived bootstrap approximation for generalizedV-processes (GVP). Thus, we can use BGUP or bootstrapping GVP (BGVP) to simulate GUPand GVP.

ON SOME TESTS FOR ELLIPTICAL SYMMETRY

In this paper, some test statistics of Kolmogorov type and Cramer-von Mises type based on projection pursuit technique are proposed for testing the sphericity problem of a high-dimensional distribution. The limiting distributions of the test statistics are derived under the null hypothesis and any fixed alternative. The asymptotic properties of Bootstrap approximation are investigated.Furthermore, for computational reasons, an approximation for the statistics, based on number theoretic method, is suggested.

Application of PPE Model in Land Adaptability Appraisal in Small Basin Based on RAGA

The paper applies multi-dimension to lower technology-projection pursuit evaluation model in the conservation of water and soil discipline domain, optimizes the projection direction using the improved acceleration genetic algorithms, transforms the multi-dimensional data target to lower sub-space, and values soil adaptability of Dongdagou basin in Keshan County by searching the optimal projection direction and the projection function data. The paper provides a new notion and method for the conservation of water and soil in small basin.