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Scalability of correlation clustering

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Abstract

The problem of scalability of correlation clustering (CC) is addressed by reducing the number of variables involved in the SDP formulation. A nonlinear programming formulation is obtained instead of SDP formulation, which reduces the number of variables. The new formulation is solved through limited memory Broyden Fletcher Goldfarb Shanno method. We demonstrate the potential of the nonlinear formulation on large graph datasets having more than ten thousand vertices and nine million edges. The proposed scalable formulation is experimentally shown not to compromise on quality of the obtained clusters. We compare the scalable formulation results with those of the original CC formulation. We compare the scalable formulation results with the original CC formulation, a constrained spectral clustering method which uses edge labels of the graph and differs only in the way clusters are obtained by defining the cut on the given graph and with a variant of constraint spectral clustering known as self-taught spectral clustering.

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Notes

  1. In maximization problem a \(\lambda\)-approximation algorithm A for the problem with cost function c is an algorithm such that, for every input I, the solution A(I) to satisfy \(c(A(I))\ge \lambda \mathrm{max}_S c(S)\) for some \(\lambda \le 1\).

  2. Approximation value(\(\lambda\)) in the case of a maximization problem is the ratio between the cost of an optimal solution to the cost of the solution produced by the approximation algorithm, in maximization problem \(\lambda \le 1\) and in minimization problem \(\lambda \ge 1.\)

  3. By large dataset we mean graph with large number of nodes as well as edges.

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Authors and Affiliations

  1. Computer Science and Engineering, Indian Institute of Technology Guwahati, Assam, 781 039, India

    Mamata Samal, V. Vijaya Saradhi & Sukumar Nandi

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  1. Mamata Samal
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  2. V. Vijaya Saradhi
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  3. Sukumar Nandi
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Correspondence to Mamata Samal.

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Samal, M., Saradhi, V.V. & Nandi, S. Scalability of correlation clustering. Pattern Anal Applic 21, 703–719 (2018). https://doi.org/10.1007/s10044-017-0598-7

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  • DOI: https://doi.org/10.1007/s10044-017-0598-7

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