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The paper categorizes and reviews the state-of-the-art approaches to the partially supervised learning (PSL) task. Special emphasis is put on the fields of pattern recognition and clustering involving partially (or, weakly) labeled data sets. The major instances of PSL techniques are categorized into the following taxonomy: (i) active learning for training set design, where the learning algorithm has control over the training data; (ii) learning from fuzzy labels, whenever multiple and discordant human experts are involved in the (complex) data labeling process; (iii) semi-supervised learning (SSL) in pattern classification (further sorted out into: self-training, SSL with generative models, semi-supervised support vector machines; SSL with graphs); (iv) SSL in data clustering, using additional constraints to incorporate expert knowledge into the clustering process; (v) PSL in ensembles and learning by disagreement; (vi) PSL in artificial neural networks. In addition to providing the reader with the general background and categorization of the area, the paper aims at pointing out the main issues which are still open, motivating the on-going investigations in PSL research.