Life-cycle assessment (LCA) and input-output analysis (IOA) are two data-intensive approaches whose reliability and applicability are dependent on the quality of the data. The difficulty is that not all data is available due to technical or cost reasons. However, the processes producing similar commodities have similar data structures in LCA, while the sectors of the historical surveyed years in IOA have similar input structures as the sectors of the objective year. These features imply that the data usually has low-rank or approximately low-rank structures which enables us to apply the emerging techniques of low-rank matrix completion to recover the missing data. Since the data should be nonnegative in LCA and IOA if we ignore the minor by-product issue, we propose two models for nonnegative matrix completion to recover the missing information of LCA and IOA. The alternating direction method of multipliers is then applied to solve them. The applicability and efficiency of our methods are demonstrated in an application to the widely used database "Ecoinvent" for the life-cycle assessment. Recovering results show that our approaches are helpful.
Key words:Missing data recovery, Nonnegative matrix completion, Life-cycle assessment, Input-output analysis, Alternating direction method of multipliers