Semi-supervised point prototype clustering

This paper describes a class of models we call semi-supervised clustering. Algorithms in this category are clustering methods that use information possessed by labeled training data X-d subset of R-p as well as structural information that resides in the unlabeled data X-u subset of R-p. The labels are used in conjunction with the unlabeled data to help clustering algorithms partition X-u subset of R-p which then terminate without the capability to label other points in R-p. This is very different from supervised learning, wherein the training data subsequently endow a classifier with the ability to label every point in R-p. The methodology is applicable in domains such as image segmentation, where users may have a small set of labeled data, and can use it to semi-supervise classification of the remaining pixels in a single image. The model can be used with many different point prototype clustering algorithms. We illustrate how to attach it to a particular algorithm (fuzzy c-means). Then we give two numerical examples to show that it overcomes the failure of many point prototype clustering schemes when confronted with data that possess overlapping and/or non uniformly distributed clusters. Finally, the new method compares favorably to the fully supervised k nearest neighbor rule when applied to the Iris data.