  Data collected at very frequent intervals is usually extremely sparse and has
no structure that is exploitable by modern tensor decomposition algorithms.
Thus the utility of such tensors is low, in terms of the amount of
interpretable and exploitable structure that one can extract from them. In this
paper, we introduce the problem of finding a tensor of adaptive aggregated
granularity that can be decomposed to reveal meaningful latent concepts
(structures) from datasets that, in their original form, are not amenable to
tensor analysis. Such datasets fall under the broad category of sparse point
processes that evolve over space and/or time. To the best of our knowledge,
this is the first work that explores adaptive granularity aggregation in
tensors. Furthermore, we formally define the problem and discuss what different
definitions of "good structure" can be in practice, and show that optimal
solution is of prohibitive combinatorial complexity. Subsequently, we propose
an efficient and effective greedy algorithm called IceBreaker, which follows a
number of intuitive decision criteria that locally maximize the "goodness of
structure", resulting in high-quality tensors. We evaluate our method on
synthetic, semi-synthetic and real datasets. In all the cases, our proposed
method constructs tensors that have very high structure quality.
