We develop several kernel methods for classification of longitudinal data and apply them to detect cognitive decline in the elderly. We first develop mixed-effects models, a type of hierarchical empirical Bayes generative models, for the time series. After demonstrating their utility in likelihood ratio classifiers (and the improvement over standard regression models for such classifiers), we develop novel Fisher kernels based on mixture of mixed-effects models and use them in support vector machine classifiers. The hierarchical generative model allows us to handle variations in sequence length and sampling interval gracefully. We also give nonparametric kernels not based on generative models, but rather on the reproducing kernel Hilbert space. We apply the methods to detecting cognitive decline from longitudinal clinical data on motor and neuropsychological tests. The likelihood ratio classifiers based on the neuropsychological tests perform better than than classifiers based on the motor behavior. Discriminant classifiers performed better than likelihood ratio classifiers for the motor behavior tests.

While clustering is usually an unsupervised operation, there are circumstances in which we believe (with varying degrees of certainty) that items A and B should be assigned to the same cluster, while items A and C should not. We would like such pairwise relations to influence cluster assignments of out-of-sample data in a manner consistent with the prior knowledge expressed in the training set. Our starting point is probabilistic clustering based on gaussian mixture models (GMM) of the data distribution. We express clustering preferences in a prior distribution over assignments of data points to clusters. This prior penalizes cluster assignments according to the degree with which they violate the preferences. The model parameters are fit with the expectation-maximization (EM) algorithm. Our model provides a flexible framework that encompasses several other semisupervised clustering models as its special cases. Experiments on artificial and real-world problems show that our model can consistently improve clustering results when pairwise relations are incorporated. The experiments also demonstrate the superiority of our model to other semisupervised clustering methods on handling noisy pairwise relations.