Various Types of Objective Functions of Clustering for Uncertain Data

Whenever we classify a dataset into some clusters, we need to consider how to handle the uncertainty included into data. In those days, the ability of computers are very poor, and we could not help handling data with uncertainty as one point. However, the ability is now enough to handle the uncertainty of data, and we hence believe that we should handle the uncertain data as is. In this paper, we will show some clustering methods for uncertain data by two concepts of “tolerance” and “penalty-vector regularization”. The both concepts are more useful to model and handle the uncertainty of data and more flexible than the conventional methods for handling the uncertainty. By the way, we construct a clustering algorithm by putting one objective function. Hence, we can say that the whole clustering algorithm depends on its objective function. In this paper, we will thereby introduce various types of objective functions for uncertain data with the concepts of tolerance and penalty-vector regularization, and construct the clustering algorithms for uncertain data.