Data-driven recognition of uncertainty by integrating matrix factorization and kernel smoothing methods

Recognizing uncertainty from complex data sets plays a fundamental role in solving many decision-making problems arising from learning systems and cognitive sciences, especially by data-driven robust optimization approaches. In this paper, a novel recognition method is proposed to characterize data distribution with complicated features by fusing different learning techniques, so as to construct a disjunctive data-driven uncertainty set by concurrent identification of clustering features and distribution information underlying in data. Boundary constraints are employed to further tighten the uncertainty set by removing the empty regions. Based on such an uncertainty set, a data-driven static robust optimization framework is proposed, and its computationally tractable robust counterpart is presented. A column-and-constraint generation based algorithm is also developed for solving the uncertainty set-induced data-driven two-stage robust optimization model. Efficiency and superiority of the proposed robust methods in this paper are illustrated by numerical tests involving the solution of a linear uncertain problem and a pre-inventory and reallocation problem under emergencies.