Incremental Hierarchical Tucker Decomposition
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913622743056384 |
|---|---|
| author | Aksoy, Doruk Gorodetsky, Alex A. |
| author_facet | Aksoy, Doruk Gorodetsky, Alex A. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_16544 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Incremental Hierarchical Tucker Decomposition Aksoy, Doruk Gorodetsky, Alex A. Numerical Analysis Signal Processing 15A23, 65-04, 15A69, 65F55 G.4; G.1.3 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. |
| title | Incremental Hierarchical Tucker Decomposition |
| topic | Numerical Analysis Signal Processing 15A23, 65-04, 15A69, 65F55 G.4; G.1.3 |
| url | https://arxiv.org/abs/2412.16544 |