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Mihai Cucuringu (Oxford University) – "Laplacian-based methods for ranking and constrained clustering"

June 18, 2018 @ 2:00 pm - 3:15 pm
The Statistical Seminar: Every Monday at 2:00 pm.
Time: 2:00 pm – 3:15 pm
Date: 18th of June 2018
Place: Room 3001.
Mihai Cucuringu (Oxford University) – “Laplacian-based methods for ranking and constrained clustering

Abstract : We consider the classic problem of establishing a statistical ranking of a set of n items given a set of inconsistent and incomplete pairwise comparisons between such items. Instantiations of this problem occur in numerous applications in data analysis (e.g., ranking teams in sports data), computer vision, and machine learning. We formulate the above problem of ranking with incomplete noisy information as an instance of the group synchronization problem over the group SO(2) of planar rotations, whose usefulness has been demonstrated in numerous applications in recent years. Its least squares solution can be approximated by either a spectral or a semidefinite programming relaxation, followed by a rounding procedure. We perform extensive numerical simulations on both synthetic and real-world data sets, showing that our proposed method compares favorably to other algorithms from the recent literature. We also briefly discuss ongoing work on extensions and applications of the group synchronization framework to k-way synchronization, list synchronization, synchronization with heterogeneous information and partial rankings, and phase unwrapping.

We also present a simple spectral approach to the well-studied constrained clustering problem. It captures constrained clustering as a generalized eigenvalue problem with graph Laplacians. The algorithm works in nearly-linear time and provides concrete guarantees for the quality of the clusters, at least for the case of 2-way partitioning, via a generalized Cheeger inequality. In practice this translates to a very fast implementation that consistently outperforms existing spectral approaches both in speed and quality.