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Using Partially Labeled Data For Normal Mixture Identification With Application To Class Definition

In this paper, we address the problem of estimating the parameters of a normal mixture density when in addition to the unlabeled samples, sets of partially labeled samples are available.We model the density of the multi-dimensional feature space with a normal mixture and assume that the set of components of the mixture can be partitioned into several classes and that training samples are available from each class. Each class can contain one or more components. Since for any training sample the class of origin is known but the exact component of origin within the corresponding class is unknown, we refer to the training samples as partially labeled. We have derived the EM iterative equations for estimating the parameters of the normal mixture in presence of partially labeled samples. These equations can be used to combine the supervised and non-supervised learning processes.