Semi-supervised Probabilistic Distance Clustering and the Uncertainty of Classification

Semi-supervised clustering is an attempt to reconcile clustering (unsupervised learning) and classification (supervised learning, using prior information on the data). These two modes of data analysis are combined in a parameterized model, the parameter θ ∈ [0, 1] is the weight attributed to the prior information, θ = 0 corresponding to clustering, and θ = 1 to classification. The results (cluster centers, classification rule) depend on the parameter θ, an insensitivity to θ indicates that the prior information is in agreement with the intrinsic cluster structure, and is otherwise redundant. This explains why some data sets (such as the Wisconsin breast cancer data, Merz and Murphy, UCI repository of machine learning databases, University of California, Irvine, CA) give good results for all reasonable classification methods. The uncertainty of classification is represented here by the geometric mean of the membership probabilities, shown to be an entropic distance related to the Kullback–Leibler divergence.