Site : http://www.ee.duke.edu/faculty/guillermo-sapiro

We consider the problem of nding a few representatives for a big dataset, i.e., a subset of data points that efciently describes the entire dataset.

We assume that each data point can be expressed as a linear combination of the representatives  and formulate the problem of nding the representatives as a sparse  multiple measurement vector problem.

In our formulation, both the dictionary and the measurements are given by the data matrix, and the unknown sparse codes select the representatives via convex optimization.

In general,  we do not assume that the data are low rank or distributed around cluster centers. When the data do come from a collection of low-rank models, we show that our method automatically selects a few representatives from each
low-rank model. We also analyze the geometry of the representatives and discuss their relationship to the vertices of the convex hull of the data.

We show that our framework can be extended to detect and reject outliers in datasets, and to efciently deal with new observations and large datasets. The proposed framework and theoretical foundations are illustrated with examples in video summarization and image classication using representatives.

Extensions to active learning and learning from dissimilarities are mentioned as well.

Joint work with E. Elhamifar and R. Vidal