Minimally-supervised classification using multiple observation sets

We discuss building complex classifiers from a single labeled example and vast number of unlabeled observation sets, each derived from observation of a single process or object. When data can be measured by observation, it is often plentiful and it is often possible to make more than one observation of the state of a process or object. We discuss how to exploit the variability across such sets of observations of the same object to estimate class labels for unlabeled examples given a minimal number of labeled examples. In contrast to similar semisupervised classification procedures that define the likelihood that two observations share a label as a function of the embedded distance between the two observations, this method uses the Naive Bayes estimate of how often the two observations did result from the same observed process. Exploiting this additional source of information in an iterative estimation procedure can generalize complex classification models from single labeled observations. Some examples involving classification of tracked objects in a low-dimensional feature space given thousands of unlabeled observation sets are used to illustrate the effectiveness of this method.