Ehsan Elhamifar presents the "Sparse Modeling Representative Selection (SMRS) is an algorithm based on sparse multiple-measurement-vector recovery theory for selecting a subset of data points as the representatives." The attendant paper is: See All by Looking at A Few: Sparse Modeling for Finding Representative Objects by Ehsan Elhamifar, Rene Vidal. The abstract reads:

We propose an algorithm called Sparse Manifold Clustering and Embedding (SMCE) for simultaneous clustering and dimensionality reduction of data lying in multiple nonlinear manifolds. Similar to most dimensionality reduction methods, SMCE ﬁnds a small neighborhood around each data point and connects each point to its neighbors with appropriate weights. The key difference is that SMCE ﬁnds both the neighbors and the weights automatically. This is done by solving a sparse optimization problem, which encourages selecting nearby points that lie in the same manifold and approximately span a low-dimensional afﬁne subspace. The optimal solution encodes information that can be used for clustering and dimensionality reduction using spectral clustering and embedding. Moreover, the size of the optimal neighborhood of a data point, which can be different for different points, provides an estimate of the dimension of the manifold to which the point belongs. Experiments demonstrate that our method can effectively handle multiple manifolds that are very close to each other, manifolds with non-uniform sampling and holes, as well as estimate the intrinsic dimensions of the manifolds.

The code is here.

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