For many classification problems, unlabeled training data are inexpensive and readily available, whereas labeling training data imposes costs. Semi-supervised classification algorithms aim at utilizing information contained in unlabeled data in addition to the (few) labeled data. Semi-supervised (for an example, see Seeger, 2001) has a long tradition in statistics (Cooper & Freeman, 1970); much early work has focused on Bayesian discrimination of Gaussians. The Expectation Maximization (EM) algorithm (Dempster, Laird, & Rubin, 1977) is the most popular method for learning generative models from labeled and unlabeled data. Model-based, generative learning algorithms find model parameters (e.g., the parameters of a Gaussian mixture model) that best explain the available labeled and unlabeled data, and they derive the discriminating classification hypothesis from this model. In discriminative learning, unlabeled data is typically incorporated via the integration of some model assumption into the discriminative framework (Miller & Uyar, 1997; Titterington, Smith, & Makov, 1985). The Transductive Support Vector Machine (Vapnik, 1998; Joachims, 1999) uses unlabeled data to identify a hyperplane that has a large distance not only from the labeled data but also from all unlabeled data. This identification results in a bias toward placing the hyperplane in regions of low density p(x). Recently, studies have covered graph-based approaches that rely on the assumption that neighboring instances are more likely to belong to the same class than remote instances (Blum & Chawla, 2001). A distinct approach to utilizing unlabeled data has been proposed by de Sa (1994), Yarowsky (1995) and Blum and Mitchell (1998). When the available attributes can be split into independent and compatible subsets, then multi-view learning algorithms can be employed. Multi-view algorithms, such as co-training (Blum & Mitchell, 1998) and co-EM (Nigam & Ghani, 2000), learn two independent hypotheses, which bootstrap by providing each other with labels for the unlabeled data. An analysis of why training two independent hypotheses that provide each other with conjectured class labels for unlabeled data might be better than EM-like self-training has been provided by Dasgupta, Littman, and McAllester (2001) and has been simplified by Abney (2002). The disagreement rate of two independent hypotheses is an upper bound on the error rate of either hypothesis. Multi-view algorithms minimize the disagreement rate between the peer hypotheses (a situation that is most apparent for the algorithm of Collins & Singer, 1999) and thereby the error rate. Semi-supervised learning is related to active learning. Active learning algorithms are able to actively query the class labels of unlabeled data. By contrast, semi-supervised algorithms are bound to learn from the given data.
Semi-supervised classification algorithms receive both labeled data and unlabeled data and return a classifier f: x → y; the unlabeled data is generally assumed to be governed by an underlying distribution p(x), and the labeled data by p(x,y) = p(y | x) p(x). Typically, the goal is to find a classifierthat minimizes the error rate with respect to p(x).