Hard c-Means Clustering Using Quadratic Penalty-Vector Regularization for Uncertain Data

Abstract

Clustering,in which information on a real space is transformed to data in a pattern space is one of the unsupervised classification techniques of the data analysis. However, the data cannot be often represented by a point because of uncertainty of the data,e.g., measurement error margin and loss of values in data. In this paper, we introduce quadratic penalty-vector regularization to handle such uncertain data. First, we propose a new clustering algorithm called hard c-means clustering using quadratic penalty-vector regularizationfor uncertain data (HCMP). Second, we propose seqential extraction hard c-means using penalty-vector regularization (SHCMP) to handle datasets of which the cluster number is unknown. Moreover we verify the effectiveness of our proposed algorithms through some numerical examples.