Text and document classification: In classifying substantial documents, the features used might be normalized occurrence frequencies of particular words (or word classes) and punctuation. Especially for shorter texts, various discrete features may be included as well, such as 0, 1-valued functions indicating the presence or absence of certain key words or structural features. In this way documents are represented as numerical vectors, with values  in a high-dimensional space, with separate classes presumably forming somewhat separate clusters in that space. A variety of classical pattern recognition techniques are applicable to the problem of learning to assign new documents (as vectors) to the appropriate class (e.g., Sebestyen 1962; Duda and Hart 1973). Perhaps the simplest approach (most easily applied when features are binary) is a naïve Bayesian one, which assumes that each class generates feature values that are independent of one another. The generative frequencies are estimated from the training data, and class membership probabilities for an unknown document (vector) are computed via Bayes' rule (which can be done using successive updates of the prior class probabilities).  Choosing the class with the highest resultant posterior probability then provides a decision criterion. A common generative model for real-valued features, allowing for feature interactions, views the known members of any given class as a sample of a multivariate normal (Gaussian) random variable. Learning in this case consists of estimating the mean and covariance matrix of each class (an example of maximum likelihood estimation).