SGD_Tucker: A Novel Stochastic Optimization Strategy for Parallel Sparse Tucker Decomposition

Understand

Sparse Tucker Decomposition (STD) algorithms learn a core tensor and a group of factor matrices to obtain an optimal low-rank representation feature for the \underline{H}igh-\underline{O}rder, \underline{H}igh-\underline{D}imension, and \underline{S}parse \underline{T}ensor (HOHDST).

• However, existing STD algorithms face the problem of intermediate variables explosion which results from the fact that the formation of those variables, i.e., matrices Khatri-Rao product, Kronecker product, and matrix-matrix multiplication, follows the whole elements in sparse tensor.
• The above problems prevent deep fusion of efficient computation and big data platforms.
• To overcome the bottleneck, a novel stochastic optimization strategy (SGD$\_$Tucker) is proposed for STD which can automatically divide the high-dimension intermediate variables into small batches of intermediate matrices.