Modern applications in engineering and data science are increasingly based on multidimensional data of exceedingly high volume, variety, and structural richness. However, standard machine learning and data mining algorithms typically scale exponentially with data volume and complexity of cross-modal couplings - the so called curse of dimensionality - which is prohibitive to the analysis of such large-scale, multi-modal and multi-relational datasets. Given that such data are often conveniently represented as multiway arrays or tensors, it is therefore timely and valuable for the...
Modern applications in engineering and data science are increasingly based on multidimensional data of exceedingly high volume, variety, and struct...
This monograph builds on Tensor Networks for Dimensionality Reduction and Large-scale Optimization: Part 1 Low-Rank Tensor Decompositions by discussing tensor network models for super-compressed higher-order representation of data/parameters and cost functions, together with an outline of their applications in machine learning and data analytics. A particular emphasis is on elucidating, through graphical illustrations, that by virtue of the underlying low-rank tensor approximations and sophisticated contractions of core tensors, tensor networks have the ability to perform distributed...
This monograph builds on Tensor Networks for Dimensionality Reduction and Large-scale Optimization: Part 1 Low-Rank Tensor Decompositions by discussin...
