  Multidimensional data have become ubiquitous and are frequently encountered
in situations where the information is aggregated over multiple data atoms. The
aggregation can be over time or other features, such as geographical location.
We often have access to multiple aggregated views of the same data, each
aggregated in one or more dimensions, especially when data are collected or
measured by different agencies. For instance, item sales can be aggregated
temporally, and over groups of stores based on their location or affiliation.
However, data mining and machine learning models benefit from detailed data for
personalized analysis and prediction. Thus, data disaggregation algorithms are
becoming increasingly important in various domains. The goal of this paper is
to reconstruct finer-scale data from multiple coarse views, aggregated over
different (subsets of) dimensions. The proposed method, called PREMA, leverages
low-rank tensor factorization tools to fuse the multiple views and provide
recovery guarantees under certain conditions. PREMA can tackle challenging
scenarios, such as missing or partially observed data, double aggregation, and
even blind disaggregation (without knowledge of the aggregation patterns) using
a variant of PREMA called B-PREMA. To showcase the effectiveness of PREMA, the
paper includes extensive experiments using real data from different domains:
retail sales, crime counts, and weather observations.
