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The Tucker tensor decomposition is a natural extension of the singular value decomposition (SVD) to multiway data. We propose to accelerate Tucker tensor decomposition algorithms by using randomization and parallelization. We present two algorithms that scale to large data and many processors, significantly reduce both computation and communication cost compared to previous deterministic and randomized approaches, and obtain nearly the same approximation errors. The key idea in our algorithms is to perform randomized sketches with Kronecker-structured random matrices, which reduces computation compared to unstructured matrices and can be implemented using a fundamental tensor computational kernel. We provide probabilistic error analysis of our algorithms and implement a new parallel algorithm for the structured randomized sketch. Our experimental results demonstrate that our combination of randomization and parallelization achieves accurate Tucker decompositions much faster than alternative approaches. We observe up to a 16X speedup over the fastest deterministic parallel implementation on 3D simulation data.
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Distributed-Memory Randomized Algorithms for Sparse Tensor CP Decomposition
Candecomp / PARAFAC (CP) decomposition, a generalization of the matrix singular value decomposition to higher-dimensional tensors, is a popular tool for analyzing multidimensional sparse data. On tensors with billions of nonzero entries, computing a CP decomposition is a computationally intensive task. We propose the first distributed-memory implementations of two randomized CP decomposition algorithms,CP-ARLS-LEV and STS-CP, that offer nearly an order-of-magnitude speedup at high decomposition ranks over well-tuned non-randomized decomposition packages. Both algorithms rely on leverage score sampling and enjoy strong theoretical guarantees, each with varying time and accuracy tradeoffs. We tailor the communication schedule for our random sampling algorithms, eliminating expensive reduction collectives and forcing communication costs to scale with the random sample count. Finally, we optimize the local storage format for our methods, switching between analogues of compressed sparse column and compressed sparse row formats. Experiments show that our methods are fast and scalable,producing 11x speedup over SPLATT by decomposing the billion-scale Reddit tensor on 512 CPU cores in under two minutes.
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- Award ID(s):
- 2004763
- PAR ID:
- 10511301
- Publisher / Repository:
- ACM
- Date Published:
- Journal Name:
- Annual ACM Symposium on Parallelism in Algorithms and Architectures
- ISSN:
- 1548-6109
- Format(s):
- Medium: X
- Location:
- Nantes, France
- Sponsoring Org:
- National Science Foundation
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