Near-Isometric Properties of Kronecker-Structured Random Tensor Embeddings

Qijia Jiang

Keywords: Structured non-symmetric rank-1 tensor, Uniform deviation bound, Applications of random tensor embeddings

Abstract: We give uniform concentration inequality for random tensors acting on rank-1 Kronecker structured signals, which parallels a Gordon-type inequality for this class of tensor structured data. Two variants of the random embedding are considered, where the embedding dimension depends on explicit quantities characterizing the complexity of the signal. As applications of the tools developed herein, we illustrate with examples from signal recovery and optimization.