Lawrence Saul, Daniel Lee
We investigate a learning algorithm for the classiﬁcation of nonnegative data by mixture models. Multiplicative update rules are derived that directly optimize the performance of these models as classiﬁers. The update rules have a simple closed form and an intuitive appeal. Our algorithm retains the main virtues of the Expectation-Maximization (EM) algorithm—its guarantee of monotonic im- provement, and its absence of tuning parameters—with the added advantage of optimizing a discriminative objective function. The algorithm reduces as a spe- cial case to the method of generalized iterative scaling for log-linear models. The learning rate of the algorithm is controlled by the sparseness of the training data. We use the method of nonnegative matrix factorization (NMF) to discover sparse distributed representations of the data. This form of feature selection greatly accelerates learning and makes the algorithm practical on large problems. Ex- periments show that discriminatively trained mixture models lead to much better classiﬁcation than comparably sized models trained by EM.