A novel model of fuzzy clustering using kernel methods is proposed. This model is called kernel modified possibilistic c-means （KMPCM） model. The proposed model is an extension of the modified possibilistic c-means ...A novel model of fuzzy clustering using kernel methods is proposed. This model is called kernel modified possibilistic c-means （KMPCM） model. The proposed model is an extension of the modified possibilistic c-means （MPCM） algorithm by using kernel methods. Different from MPCM and fuzzy c-means （FCM） model which are based on Euclidean distance, the proposed model is based on kernel-induced distance. Furthermore, with kernel methods the input data can be mapped implicitly into a high-dimensional feature space where the nonlinear pattern now appears linear. It is unnecessary to do calculation in the high-dimensional feature space because the kernel function can do it. Numerical experiments show that KMPCM outperforms FCM and MPCM.展开更多
A novel model of fuzzy clustering, i.e. an allied fuzzy c means （AFCM） model is proposed based on the combination of advantages of fuzzy c means （FCM） and possibilistic c means （PCM） clustering. PCM is sensitive...A novel model of fuzzy clustering, i.e. an allied fuzzy c means （AFCM） model is proposed based on the combination of advantages of fuzzy c means （FCM） and possibilistic c means （PCM） clustering. PCM is sensitive to initializations and often generates coincident clusters. AFCM overcomes this shortcoming and it is an ex tension of PCM. Membership and typicality values can be simultaneously produced in AFCM. Experimental re- suits show that noise data can be well processed, coincident clusters are avoided and clustering accuracy is better.展开更多
Traditional Fuzzy C-Means(FCM)and Possibilistic C-Means(PCM)clustering algorithms are data-driven,and their objective function minimization process is based on the available numeric data.Recently,knowledge hints have ...Traditional Fuzzy C-Means(FCM)and Possibilistic C-Means(PCM)clustering algorithms are data-driven,and their objective function minimization process is based on the available numeric data.Recently,knowledge hints have been introduced to formknowledge-driven clustering algorithms,which reveal a data structure that considers not only the relationships between data but also the compatibility with knowledge hints.However,these algorithms cannot produce the optimal number of clusters by the clustering algorithm itself;they require the assistance of evaluation indices.Moreover,knowledge hints are usually used as part of the data structure(directly replacing some clustering centers),which severely limits the flexibility of the algorithm and can lead to knowledgemisguidance.To solve this problem,this study designs a newknowledge-driven clustering algorithmcalled the PCM clusteringwith High-density Points(HP-PCM),in which domain knowledge is represented in the form of so-called high-density points.First,a newdatadensitycalculation function is proposed.The Density Knowledge Points Extraction(DKPE)method is established to filter out high-density points from the dataset to form knowledge hints.Then,these hints are incorporated into the PCM objective function so that the clustering algorithm is guided by high-density points to discover the natural data structure.Finally,the initial number of clusters is set to be greater than the true one based on the number of knowledge hints.Then,the HP-PCM algorithm automatically determines the final number of clusters during the clustering process by considering the cluster elimination mechanism.Through experimental studies,including some comparative analyses,the results highlight the effectiveness of the proposed algorithm,such as the increased success rate in clustering,the ability to determine the optimal cluster number,and the faster convergence speed.展开更多
Fuzzy c-means(FCM) clustering algorithm is sensitive to noise points and outlier data, and the possibilistic fuzzy c-means(PFCM) clustering algorithm overcomes the problem well, but PFCM clustering algorithm has some ...Fuzzy c-means(FCM) clustering algorithm is sensitive to noise points and outlier data, and the possibilistic fuzzy c-means(PFCM) clustering algorithm overcomes the problem well, but PFCM clustering algorithm has some problems: it is still sensitive to initial clustering centers and the clustering results are not good when the tested datasets with noise are very unequal. An improved kernel possibilistic fuzzy c-means algorithm based on invasive weed optimization(IWO-KPFCM) is proposed in this paper. This algorithm first uses invasive weed optimization(IWO) algorithm to seek the optimal solution as the initial clustering centers, and introduces kernel method to make the input data from the sample space map into the high-dimensional feature space. Then, the sample variance is introduced in the objection function to measure the compact degree of data. Finally, the improved algorithm is used to cluster data. The simulation results of the University of California-Irvine(UCI) data sets and artificial data sets show that the proposed algorithm has stronger ability to resist noise, higher cluster accuracy and faster convergence speed than the PFCM algorithm.展开更多
基金Project supported by the 15th Plan for National Defence Preventive Research Project (Grant No.413030201)
文摘A novel model of fuzzy clustering using kernel methods is proposed. This model is called kernel modified possibilistic c-means （KMPCM） model. The proposed model is an extension of the modified possibilistic c-means （MPCM） algorithm by using kernel methods. Different from MPCM and fuzzy c-means （FCM） model which are based on Euclidean distance, the proposed model is based on kernel-induced distance. Furthermore, with kernel methods the input data can be mapped implicitly into a high-dimensional feature space where the nonlinear pattern now appears linear. It is unnecessary to do calculation in the high-dimensional feature space because the kernel function can do it. Numerical experiments show that KMPCM outperforms FCM and MPCM.
文摘A novel model of fuzzy clustering, i.e. an allied fuzzy c means （AFCM） model is proposed based on the combination of advantages of fuzzy c means （FCM） and possibilistic c means （PCM） clustering. PCM is sensitive to initializations and often generates coincident clusters. AFCM overcomes this shortcoming and it is an ex tension of PCM. Membership and typicality values can be simultaneously produced in AFCM. Experimental re- suits show that noise data can be well processed, coincident clusters are avoided and clustering accuracy is better.
基金supported by the National Key Research and Development Program of China(No.2022YFB3304400)the National Natural Science Foundation of China(Nos.6230311,62303111,62076060,61932007,and 62176083)the Key Research and Development Program of Jiangsu Province of China(No.BE2022157).
文摘Traditional Fuzzy C-Means(FCM)and Possibilistic C-Means(PCM)clustering algorithms are data-driven,and their objective function minimization process is based on the available numeric data.Recently,knowledge hints have been introduced to formknowledge-driven clustering algorithms,which reveal a data structure that considers not only the relationships between data but also the compatibility with knowledge hints.However,these algorithms cannot produce the optimal number of clusters by the clustering algorithm itself;they require the assistance of evaluation indices.Moreover,knowledge hints are usually used as part of the data structure(directly replacing some clustering centers),which severely limits the flexibility of the algorithm and can lead to knowledgemisguidance.To solve this problem,this study designs a newknowledge-driven clustering algorithmcalled the PCM clusteringwith High-density Points(HP-PCM),in which domain knowledge is represented in the form of so-called high-density points.First,a newdatadensitycalculation function is proposed.The Density Knowledge Points Extraction(DKPE)method is established to filter out high-density points from the dataset to form knowledge hints.Then,these hints are incorporated into the PCM objective function so that the clustering algorithm is guided by high-density points to discover the natural data structure.Finally,the initial number of clusters is set to be greater than the true one based on the number of knowledge hints.Then,the HP-PCM algorithm automatically determines the final number of clusters during the clustering process by considering the cluster elimination mechanism.Through experimental studies,including some comparative analyses,the results highlight the effectiveness of the proposed algorithm,such as the increased success rate in clustering,the ability to determine the optimal cluster number,and the faster convergence speed.
文摘Fuzzy c-means(FCM) clustering algorithm is sensitive to noise points and outlier data, and the possibilistic fuzzy c-means(PFCM) clustering algorithm overcomes the problem well, but PFCM clustering algorithm has some problems: it is still sensitive to initial clustering centers and the clustering results are not good when the tested datasets with noise are very unequal. An improved kernel possibilistic fuzzy c-means algorithm based on invasive weed optimization(IWO-KPFCM) is proposed in this paper. This algorithm first uses invasive weed optimization(IWO) algorithm to seek the optimal solution as the initial clustering centers, and introduces kernel method to make the input data from the sample space map into the high-dimensional feature space. Then, the sample variance is introduced in the objection function to measure the compact degree of data. Finally, the improved algorithm is used to cluster data. The simulation results of the University of California-Irvine(UCI) data sets and artificial data sets show that the proposed algorithm has stronger ability to resist noise, higher cluster accuracy and faster convergence speed than the PFCM algorithm.
