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Provable Convex Co-clustering of Tensors
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<span title="2020-10-23">2020</span>
<i >
arXiv
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<span class="release-stage" >pre-print</span>
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<span title="2018-03-17">2018</span>
<span class="release-stage" >pre-print</span>
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1803.06518v1">arXiv:1803.06518v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/dkfew6nribfeti6q3axeuds7tq">fatcat:dkfew6nribfeti6q3axeuds7tq</a> </span>
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1803.06518v1">arXiv:1803.06518v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/dkfew6nribfeti6q3axeuds7tq">fatcat:dkfew6nribfeti6q3axeuds7tq</a> </span>
Cluster analysis is a fundamental tool for pattern discovery of complex heterogeneous data. Prevalent clustering methods mainly focus on vector or matrix-variate data and are not applicable to general-order tensors, which arise frequently in modern scientific and business applications. Moreover, there is a gap between statistical guarantees and computational efficiency for existing tensor clustering solutions due to the nature of their non-convex formulations. In this work, we bridge this gap
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<a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1803.06518v2">arXiv:1803.06518v2</a>
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... developing a provable convex formulation of tensor co-clustering. Our convex co-clustering (CoCo) estimator enjoys stability guarantees and its computational and storage costs are polynomial in the size of the data. We further establish a non-asymptotic error bound for the CoCo estimator, which reveals a surprising "blessing of dimensionality" phenomenon that does not exist in vector or matrix-variate cluster analysis. Our theoretical findings are supported by extensive simulated studies. Finally, we apply the CoCo estimator to the cluster analysis of advertisement click tensor data from a major online company. Our clustering results provide meaningful business insights to improve advertising effectiveness.
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