  In a series of recent works, we have generalised the consistency results in
the stochastic block model literature to the case of uniform and non-uniform
hypergraphs. The present paper continues the same line of study, where we focus
on partitioning weighted uniform hypergraphs---a problem often encountered in
computer vision. This work is motivated by two issues that arise when a
hypergraph partitioning approach is used to tackle computer vision problems:
(i) The uniform hypergraphs constructed for higher-order learning contain all
edges, but most have negligible weights. Thus, the adjacency tensor is nearly
sparse, and yet, not binary. (ii) A more serious concern is that standard
partitioning algorithms need to compute all edge weights, which is
computationally expensive for hypergraphs. This is usually resolved in practice
by merging the clustering algorithm with a tensor sampling strategy---an
approach that is yet to be analysed rigorously. We build on our earlier work on
partitioning dense unweighted uniform hypergraphs (Ghoshdastidar and Dukkipati,
ICML, 2015), and address the aforementioned issues by proposing provable and
efficient partitioning algorithms. Our analysis justifies the empirical success
of practical sampling techniques. We also complement our theoretical findings
by elaborate empirical comparison of various hypergraph partitioning schemes.
