2021/10/26 by Beheshteh T. Rakhshan, Rakhshan, Beheshteh T., Guillaume Rabusseau +1 · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Image and Video Retrieval Techniques #Algorithm #Artificial intelligence #Combinatorics #Computer science #Dimension (graph theory) #Eigenvalues and eigenvectors #Embedding #FOS: Computer and information sciences #Gaussian #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Mathematics #Physics #Projection (relational algebra) #Pure mathematics #Random matrix #Random projection #Rank (graph theory) #Sparse and Compressive Sensing Techniques #Tensor (intrinsic definition) #Tensor decomposition and applications #Tensor product #cs.LG #stat.ML
paper · pdf · doi:10.48550/arxiv.2110.13970
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2021/10/26 · arxiv created 2022/02/03 · arxiv updated 2022/02/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Random projection (RP) have recently emerged as popular techniques in the machine learning community for their ability in reducing the dimension of very high-dimensional tensors. Following the work in [30], we consider a tensorized random projection relying on Tensor Train (TT) decomposition where each element of the core tensors is drawn from a Rademacher distribution. Our theoretical results reveal that the Gaussian low-rank tensor represented in compressed form in TT format in [30] can be replaced by a TT tensor with core elements drawn from a Rademacher distribution with the same embedding size. Experiments on synthetic data demonstrate that tensorized Rademacher RP can outperform the tensorized Gaussian RP studied in [30]. In addition, we show both theoretically and experimentally, that the tensorized RP in the Matrix Product Operator (MPO) format is not a Johnson-Lindenstrauss transform (JLT) and therefore not a well-suited random projection map