First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. Summary: This paper presents a provable guarantee under what conditions the convex optimization procedure (COP) can successfully recover the correct clustering solutions. The main result is: if the samples are drawn from two cubes, each being a cluster, then COP can obtain the correct clustering solution provided the distance between two cubes is larger than a threshold value that linearly depends on the cube size and the ratio of numbers of samples in each cluster. The proof is based on the idea of lifting, which projects the problem into a higher dimensional space that transforms the original formulation into a separable form (separating the regularization term into the sum of l_2 norm of each row). After constructing the optimal dual solution through some algebraic operations, the primal optimal solution can be obtained.

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In this paper, we present theoretical analysis of SON~--~a convex optimization procedure for clustering using a sum-of-norms (SON) regularization recently proposed in \cite{ICML2011Hocking_419,SON, Lindsten650707, pelckmans2005convex}. In particular, we show if the samples are drawn from two cubes, each being one cluster, then SON can provably identify the cluster membership provided that the distance between the two cubes is larger than a threshold which (linearly) depends on the size of the cube and the ratio of numbers of samples in each cluster. To the best of our knowledge, this paper is the first to provide a rigorous analysis to understand why and when SON works. We believe this may provide important insights to develop novel convex optimization based algorithms for clustering.

In this paper, we present theoretical analysis of SON - a convex optimization procedure for clustering using a sum-of-norms (SON) regularization recently proposed in [8, 10, 11, 17]. In particular, we show if the samples are drawn from two cubes, each being one cluster, then SON can provably identify the cluster membership provided that the distance between the two cubes is larger than a threshold which (linearly) depends on the size of the cube and the ratio of numbers of samples in each cluster. To the best of our knowledge, this paper is the first to provide a rigorous analysis to understand why and when SON works. We believe this may provide important insights to develop novel convex optimization based algorithms for clustering.

In this paper, we present theoretical analysis of SON - a convex optimization procedure for clustering using a sum-of-norms (SON) regularization recently proposed in [8, 10, 11, 17]. In particular, we show if the samples are drawn from two cubes, each being one cluster, then SON can provably identify the cluster membership provided that the distance between the two cubes is larger than a threshold which (linearly) depends on the size of the cube and the ratio of numbers of samples in each cluster. To the best of our knowledge, this paper is the first to provide a rigorous analysis to understand why and when SON works. We believe this may provide important insights to develop novel convex optimization based algorithms for clustering.

In this paper, we present theoretical analysis of SON -- a convex optimization procedure for clustering using a sum-of-norms (SON) regularization recently proposed in \cite{ICML2011Hocking_419,SON, Lindsten650707, pelckmans2005convex}. In particular, we show if the samples are drawn from two cubes, each being one cluster, then SON can provably identify the cluster membership provided that the distance between the two cubes is larger than a threshold which (linearly) depends on the size of the cube and the ratio of numbers of samples in each cluster. To the best of our knowledge, this paper is the first to provide a rigorous analysis to understand why and when SON works. We believe this may provide important insights to develop novel convex optimization based algorithms for clustering. Papers published at the Neural Information Processing Systems Conference.

In this paper, we present theoretical analysis of SON~--~a convex optimization procedure for clustering using a sum-of-norms (SON) regularization recently proposed in \cite{ICML2011Hocking_419,SON, Lindsten650707, pelckmans2005convex}. In particular, we show if the samples are drawn from two cubes, each being one cluster, then SON can provably identify the cluster membership provided that the distance between the two cubes is larger than a threshold which (linearly) depends on the size of the cube and the ratio of numbers of samples in each cluster. To the best of our knowledge, this paper is the first to provide a rigorous analysis to understand why and when SON works. We believe this may provide important insights to develop novel convex optimization based algorithms for clustering.