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Data collected at very frequent intervals is usually extremely sparse and hasno structure that is exploitable by modern tensor decomposition algorithms.Thus the utility of such tensors is low, in terms of the amount ofinterpretable and exploitable structure that one can extract from them. In thispaper, we introduce the problem of finding a tensor of adaptive aggregatedgranularity that can be decomposed to reveal meaningful latent concepts(structures) from datasets that, in their original form, are not amenable totensor analysis. Such datasets fall under the broad category of sparse pointprocesses that evolve over space and/or time. To the best of our knowledge,this is the first work that explores adaptive granularity aggregation intensors. Furthermore, we formally define the problem and discuss what differentdefinitions of "good structure" can be in practice, and show that optimalsolution is of prohibitive combinatorial complexity. Subsequently, we proposean efficient and effective greedy algorithm called IceBreaker, which follows anumber of intuitive decision criteria that locally maximize the "goodness ofstructure", resulting in high-quality tensors. We evaluate our method onsynthetic, semi-synthetic and real datasets. In all the cases, our proposedmethod constructs tensors that have very high structure quality.

Adaptive Granularity in Tensors: A Quest for Interpretable Structure