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arXiv · 2412.16544

Incremental Hierarchical Tucker Decomposition

Doruk Aksoy·Alex A. Gorodetsky
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Abstract

We present two new algorithms for approximating and updating the hierarchical Tucker decomposition of tensor streams. The first algorithm, Batch Hierarchical Tucker - leaf to root (BHT-l2r), proposes an alternative and more efficient way of approximating a batch of similar tensors in hierarchical Tucker format. The second algorithm, Hierarchical Tucker - Rapid Incremental Subspace Expansion (HT-RISE), updates the batch hierarchical Tucker representation of an accumulated tensor as new batches of tensors become available. The HT-RISE algorithm is suitable for the online setting and never requires full storage or reconstruction of all data while providing a solution to the incremental Tucker decomposition problem. We provide theoretical guarantees for both algorithms and demonstrate their effectiveness on physical and cyber-physical data. The proposed BHT-l2r algorithm and the batch hierarchical Tucker format offers up to $6.2\times$ compression and $3.7\times$ reduction in time over the hierarchical Tucker format. The proposed HT-RISE algorithm also offers up to $3.1\times$ compression and $3.2\times$ reduction in time over a state of the art incremental tensor train decomposition algorithm.

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Doruk Aksoy, Alex A. Gorodetsky. 2024-12-21. Incremental Hierarchical Tucker Decomposition. https://arxiv.org/abs/2412.16544

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