Multi-level optimization of the canonical polyadic tensor decomposition at large-scale: Application to the stratification of social networks through deflation

Tensors are multi-dimensional mathematical objects that allow to model complex relationships and perform decompositions for analytical purpose. They used in a wide range of data mining applications. In social network analysis, tensor give interesting insights by taking into consideration multiple characteristics data. However, the power-law distribution such forces decomposition reveal only strong signals hide information interest having lighter intensity. To hidden information, we propose method stratify signal, gathering clusters similar intensity each stratum. It is an iterative process, which CANDECOMP/PARAFAC (CP) applied its result deflate tensor, i.e., removing from found with decomposition. As CP computationally demanding, it also necessary optimize algorithm, apply on large-scale reasonable execution time, even several executions needed process stratification. Therefore, algorithm uses both dense sparse structures leverages coarse fine grained optimizations addition incremental computations order achieve large scale Our implementation outperforms baseline libraries orders magnitude. We validate our stratification optimized Twitter dataset about COVID vaccines. • Improvement at scale. Optimization Alternating Least Squares algorithm. Stratification through deflation. Application