On optimizing distributed non-negative Tucker decomposition
On optimizing distributed non-negative Tucker decomposition
复制标题
关于优化分布式非负Tucker分解
DOI：
10.1145/3330345.3330367
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发表时间：
2019
期刊：
影响因子：
--
通讯作者：
Yogish Sabharwal
中科院分区：
文献类型：
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作者：
Venkatesan T. Chakaravarthy;Shivmaran S. Pandian;S. Raje;Yogish Sabharwal
Tucker分解将奇异值分解（SVD）推广到高维张量。它将一个给定的N维张量分解为一个小的核心张量和一组N个因子矩阵的乘积。非负塔克分解（NTD）是一种变体，它施加了核矩阵和因子矩阵的元素必须是非负的约束。从非负矩阵分解的域推广经典算法，Mørheimer等人。[19]通过乘法权重更新范例设计了NTD的程序。基于上述过程，我们提出了稀疏张量NTD的分布式实现。我们开发了三种算法，有效地执行程序。第一个是一个基线算法，适应策略从以前的工作塔克分解。另外两个是改进的算法，其基于NTD过程所特有的属性进行优化。我们在具有32至512个MPI等级的系统上对现实生活中的大型张量基准进行了实验评估。该研究表明，优化后的算法在执行时间上比基线高出6倍。分布式实现的扩展性很好，加速比高达12倍（而理想情况下是16倍）。
The Tucker decomposition generalizes singular value decomposition (SVD) to high dimensional tensors. It factorizes a given N-dimensional tensor as the product of a small core tensor and a set of N factor matrices. Non-negative Tucker Decomposition (NTD) is a variant that imposes the constraint that the entries of the core and the factor matrices must be non-negative. Generalizing a classical algorithm from the domain of non-negative matrix factorization, Mørup et al. [19] designed a procedure for NTD via the multiplicative weight update paradigm. Based on the above procedure, we present a distributed implementation of NTD for sparse tensors. We develop three algorithms for efficiently executing the procedure. The first is a baseline algorithm that adapts strategies from prior work on the Tucker decomposition. The other two are improved algorithms that are optimized based on properties unique to the NTD procedure. We present an experimental evaluation on a benchmark of large real-life tensors on a system with 32 to 512 MPI ranks. The study shows that the optimized algorithms outperform the baseline by a factor of up to 6x in execution time. The distributed implementation scales well with speedup up to 12x (as against an ideal factor of 16x).
稠密张量的并行非负 CP 分解
DOI：
10.1109/hipc.2018.00012
发表时间：
2018
期刊：
25th IEEE International Conference on High Performance Computing
影响因子：
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作者：
Ballard, Grey;Hayashi, Koby;Ramakrishnan, Kannan
通讯作者：
Ramakrishnan, Kannan