2012/06/01 by E. Elhamifar, Guillermo Sapiro, René Vidal · 3 citations
Engineering · Computer Science · Mathematics · #Sparse and Compressive Sensing Techniques #Image and Signal Denoising Methods #Remote-Sensing Image Classification #Outlier #Computer science #Automatic summarization #Convex hull #Rank (graph theory) #Data point #Point (geometry) #Sparse matrix #Data mining #Pattern recognition (psychology) #Artificial intelligence #Algorithm #Regular polygon #Mathematics #Combinatorics
paper · doi:10.1109/cvpr.2012.6247852
openalex publication_date 2012/06/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29
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 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 efficiently deal with new observations and large datasets. The proposed framework and theoretical foundations are illustrated with examples in video summarization and image classification using representatives.