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...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).展开更多
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 ...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.展开更多
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 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.展开更多
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 evalu...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.展开更多
基金Supported by the National Natural Science Foundation of China (No. 61003198, 60703108, 60703109, 60702062,60803098)the National High Technology Development 863 Program of China (No. 2008AA01Z125, 2009AA12Z210)+1 种基金the China Postdoctoral Science Foundation funded project (No. 20090460093)the Provincial Natural Science Foundation of Shaanxi, China (No. 2009JQ8016)
文摘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).
文摘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.
文摘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.
基金supported by the National Natural Science Foundation of China (No. 51575469)
文摘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.
