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.

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.

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.

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.

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.

A PROJECTION NT-TYPE TEST OF ELLIPTICAL SYMMETRY BASED ON THE SKEWNESS AND KURTOSIS MEASURES

In this paper, we propose a new approach to the test of elliptical symmetry based on theprojection pursuit (P.P.) technique, the number-theoretic method, skewness and kurtosis. Thelimiting null distributions of the new statistics are derived. The powers of the tests against sixalternatives are calculated by simulation, which shows that the new t.st's are acceptable.

PP Multivariate Random Weighting Method

According to the Projection Pursuit (PP) method and the random weighting method, we propose a PP random weighting method, and set up the asymptotic distribution theory and strong limit theorem of PP random weighting empirical process. Applying this method, we obtain two kinds of goodness-of-fit test for a multivariate distribution function, i. e., we get the random weighting approximations of PP Kolmogorov Smirnov statistics (PPKS) and PP Smirnov Cramer Von Mises statistics (PPSC), we prove that the asymptotic distribution of PPKS and PPSC are the same as those of their respective random weighting approximations.

DIMENSION-REDUCTION TYPE TESTFOR LINEARITY OF ASTOCHASTIC REGRESSION MODEL

This article investigates the test for linearity of a multivariate stochastic regression model.The use of nonparametric regression procedures for developing regression diagnostics has beenthe subject of several recent research efforts. However, when the dimension of the regressor islarge, some traditional nonparametric methods, such as kernel estimation, may be inefficient.We in this article suggest two test statistics based on projection pursuit technique and kernelmethod. The tests proposed are consistent against all fixed smooth alternatives to linearityand are asymptotically distribution-free for the distribution of the error. Furthermore, the testsare applied to an example of real-life data and some simulated data sets to demonstrate theavailability of the tests proposed.