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Era of Big Data Processing: A New Approach via Tensor Networks and Tensor Decompositions

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arxiv 1403.2048 v4 pith:P4KQEHX3 submitted 2014-03-09 cs.ET

Andrzej Cichocki This is my paper · ORCID
classification cs.ET
keywords tensordataanalysisdecompositionsmultidimensionalproducttensorsapproximations
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Many problems in computational neuroscience, neuroinformatics, pattern/image recognition, signal processing and machine learning generate massive amounts of multidimensional data with multiple aspects and high dimensionality. Tensors (i.e., multi-way arrays) provide often a natural and compact representation for such massive multidimensional data via suitable low-rank approximations. Big data analytics require novel technologies to efficiently process huge datasets within tolerable elapsed times. Such a new emerging technology for multidimensional big data is a multiway analysis via tensor networks (TNs) and tensor decompositions (TDs) which represent tensors by sets of factor (component) matrices and lower-order (core) tensors. Dynamic tensor analysis allows us to discover meaningful hidden structures of complex data and to perform generalizations by capturing multi-linear and multi-aspect relationships. We will discuss some fundamental TN models, their mathematical and graphical descriptions and associated learning algorithms for large-scale TDs and TNs, with many potential applications including: Anomaly detection, feature extraction, classification, cluster analysis, data fusion and integration, pattern recognition, predictive modeling, regression, time series analysis and multiway component analysis. Keywords: Large-scale HOSVD, Tensor decompositions, CPD, Tucker models, Hierarchical Tucker (HT) decomposition, low-rank tensor approximations (LRA), Tensorization/Quantization, tensor train (TT/QTT) - Matrix Product States (MPS), Matrix Product Operator (MPO), DMRG, Strong Kronecker Product (SKP).

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. AMPED: Accelerating MTTKRP for Billion-Scale Sparse Tensor Decomposition on Multiple GPUs

    cs.DC 2025-07 conditional novelty 6.0 of 10

    AMPED partitions sparse tensors by output-mode index to run MTTKRP on multiple GPUs, reporting a 5.1x geometric mean speedup over single-GPU baselines on billion-scale tensors.

  2. Tensorization is a powerful but underexplored tool for compression and interpretability of neural networks

    cs.LG 2025-05 conditional novelty 4.0 of 10

    The paper makes the case that tensorized neural networks offer valuable compression, scaling, and interpretability advantages that the deep learning community has not yet fully exploited.

  3. Deep Tree Tensor Networks

    cs.CV 2025-02 conditional novelty 4.0 of 10

    DTTN is a multilinear, activation-free architecture built from antisymmetric interaction modules that reaches 82.4% top-1 accuracy on ImageNet-1k and is claimed to unfold into a tree tensor network.

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