Using the Trace Norm Prior to Extend Mixture of Subspace Models

A popular approach for both classification and clustering is to assume that data is generated by a mixture model. Support of the mixture model for classification has waned as discriminative models have gained popularity. However, the mixture model is a valuable element of statistics and remains useful for clustering. Furthermore, reasoning about mixture models is often relatively simple, so they may still provide valuable intuition for the development of classification models. A mixture model assumes that each datum is generated via a two-stage process. First, a class is selected according to a multinomial distribution. Second, a datum is generated for the selected class. Typically, class models have a common form, but different parameter settings. In this work, we will discuss mixture models where the individual class models generated data in a low-dimensional subspace. This type of model is sometimes called a “mixture of subspaces” model.