See all by looking at a few: Sparse modeling for finding representative objects

We consider the problem of finding a few representatives for a dataset, i.e., a subset of data points that efficiently 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 finding 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 lowrank 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 ef...

• Type: Journal
• Year: 2012
• Where: CVPR
• Authors: Ehsan Elhamifar, Guillermo Sapiro, René Vidal
• Keywords: Computer Vision, Convex Optimization, Cvpr 2012, Vector Problem, Video Summarization