Abstract
Recovering a time sequence of events from multiple aggregated and possibly overlapping reports is a major challenge in historical data fusion. The goal is to reconstruct a higher resolution event sequence from a mixture of lower resolution samples as accurately as possible. For example, we may aim to disaggregate overlapping monthly counts of people infected with measles into weekly counts. In this paper, we propose a novel data disaggregation method, called HOMERUN, that exploits an alternative representation of the sequence and finds the spectrum of the target sequence. More specifically, we formulate the problem as so-called basis pursuit using the Discrete Cosine Transform (DCT) as a sparsifying dictionary and impose non-negativity and smoothness constraints. HOMERUN utilizes the energy compaction feature of the DCT by finding the sparsest spectral representation of the target sequence that contains the largest (most important) coefficients. We leverage the Alternating Direction Method of Multipliers to solve the resulting optimization problem with scalable and memory efficient steps. Experiments using real epidemiological data show that our method considerably outperforms the state-of-the-art techniques, especially when the DCT of the sequence has a high degree of energy compaction.