To classify a large number of unlabeled examples we combine a lim- ited number of labeled examples with a Markov random walk represen- tation over the unlabeled examples. We develop and compare several estimation criteria/algorithms suited to this representation. This includes in particular multi-way clas- sification with an average margin criterion which permits a closed form solution. The time scale of the random walk regularizes the representa- tion and can be set through a margin-based criterion favoring unambigu- ous classification. We also extend this basic regularization by adapting time scales for individual examples.

Representations based on random walks can exploit discrete data distributions for clustering and classification. We extend such representations from discrete to continuous distributions. Transition probabilities are now calculated using a diffusion equation with a diffusion coefficient that inversely depends on the data density. We relate this diffusion equation to a path integral and derive the corresponding path probability measure. The framework is useful for incorporating continuous data densities and prior knowledge.

To classify a large number of unlabeled examples we combine a limited number of labeled examples with a Markov random walk representation over the unlabeled examples.

To classify a large number of unlabeled examples we combine a limited number of labeled examples with a Markov random walk representation over the unlabeled examples.

To classify a large number of unlabeled examples we combine a limited numberof labeled examples with a Markov random walk representation overthe unlabeled examples.