Research On K - Center Plane Clustering Model And Algorithm

Clustering is the process of grouping data points into clusters, so that data points within a cluster have high similarity but are very dissimilar to data points in the other clusters. Being an useful tool for unsupervised machine learning, clustering has been studied and applied in many research areas. Instead of clustering data points to the center point in k-means, k-plane clustering(kPC) clusters data points to the center plane, which has received extensive attention by the academic community and become a new research focus. In this paper, we study about kPC and has done the following two aspects work.The first aspect, because of kPC only consider similarity within the same cluster,and does not care about the similarity of the data points from separated clusters. In this paper, we propose a novel plane-based clustering, called k-proximal plane clustering(kPPC). As in kPC, kPPC also leads to solve the eigenvalue problems. Compared with kPC, the main characteristics of our kPPC are:(1) Our kPPC minimizes the difference of within-cluster and maximizes the difference of between-cluster, which makes clustering plane is not only close to the objective points but also far away from the others.(2) Different from the random initialization in kPC, kPPC constructs a Laplace graph to give the efficient initial points.(3) By introducing kernel function, our kPPC has also been extended to nonlinear clustering.The second aspect, because of the cluster center plane constructed by kPC and kPPC is infinitely extending, which will affect the clustering performance on some cases.In this paper, we propose a local k-proximal plane clustering(LkPPC) by bringing kmeans into kPPC which will force the data points to center around some prototypes. The characteristics of our LkPPC are as follows:(1) LkPPC introduces localized representations of the data points to construct cluster center plane, which can prevent the center plane extending infinitely.(2) Different from kPPC, our LkPPC constructs cluster center plane that makes the data points of the same cluster close to both the same center plane and the prototype, and meanwhile far away from the other clusters to some extent.(3) The experimental results on several artificial datasets and benchmark datasets show the performance of our kPPC and LkPPC are better than kPC. kPPC can achievesbetter performance for the nonlinear datasets, and LkPPC has a better performance for the local structure of the datasets.