Incremental Hierarchical Tucker Decomposition

TL;DR

This paper introduces two algorithms for efficient incremental and batch hierarchical Tucker tensor decompositions, enabling scalable data approximation and updating with theoretical guarantees and practical benefits.

Contribution

The paper presents novel algorithms for incremental and batch hierarchical Tucker tensor decompositions, improving efficiency and enabling online updates with theoretical guarantees.

Findings

Up to 6.2x compression and 3.7x faster than traditional methods.

Up to 3.1x compression and 3.2x faster than existing incremental tensor train algorithms.

Effective on physical and cyber-physical data.

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.