Abstract. We consider low-rank reconstruction of a matrix using a subset of its columns and we present asymptotically optimal algorithms for both spectral norm and Frobenius norm reconstruction. The main tools we introduce to obtain our results are: (i) the use of fast approximate SVD-like decompositions for column-based matrix reconstruction, and (ii) two deterministic algorithms for selecting rows from matrices with orthonormal columns, building upon the sparse representation theorem for decompositions of the identity that appeared in [1].

Abstract. We consider low-rank reconstruction of a matrix using a subset of its columns and we present asymptotically optimal algorithms for both spectral norm and Frobenius norm reconstruction. The main tools we introduce to obtain our results are: (i) the use of fast approximate SVD-like decompositions for column-based matrix reconstruction, and (ii) two deterministic algorithms for selecting rows from matrices with orthonormal columns, building upon the sparse representation theorem for decompositions of the identity that appeared in [1].

Abstract. In this paper, we present an efficient algorithm for finding overlapping communities in social networks. Our algorithm does not rely on the contents of the messages and uses the communication graph only. The knowledge of the structure of the communities is important for the analysis of social behavior and evolution of the society as a whole, as well as its individual members. This knowledge can be helpful in discovering groups of actors that hide their communications, possibly for malicious reasons. Although the idea of using communication graphs for identifying clusters of actors is not new, most of the traditional approaches, with the exception of the work by Baumes et al, produce disjoint clusters of actors, de facto postulating that an actor is allowed to belong to at most one cluster. Our algorithm is significantly more efficient than the previous algorithm by Baumes et al; it also produces clusters of a comparable or better quality.

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