Expected Tensor Decomposition with Stochastic Gradient Descent
Expected Tensor Decomposition with Stochastic Gradient Descent
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DOI：
10.1609/aaai.v30i1.10292
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发表时间：
2016-02
影响因子：
1.9
通讯作者：
Takanori Maehara;K. Hayashi;K. Kawarabayashi
中科院分区：
文献类型：
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作者：
Takanori Maehara;K. Hayashi;K. Kawarabayashi
在这项研究中，我们研究了期望CP分解-CP分解的一种特殊情况，其中要分解的张量被给定为张量样本X（t）的总和或平均值，t = 1，.，T.为了确定这种分解，我们开发了随机梯度下降型算法，具有四个吸引人的功能：高效的内存使用，能够在在线环境中工作，参数调整的鲁棒性和简单性。我们的理论分析表明，解不发散到无穷大的任何初始值或步长。实验结果证实，我们的算法显着优于所有现有的方法在准确性方面。我们还表明，他们可以成功地分解一个大的张量，包含十亿规模的非零元素。
In this study, we investigate expected CP decomposition — a special case of CP decomposition in which a tensor to be decomposed is given as the sum or average of tensor samples X(t) for t = 1,...,T. To determine this decomposition, we develope stochastic-gradient-descent-type algorithms with four appealing features: efficient memory use, ability to work in an online setting, robustness of parameter tuning, and simplicity. Our theoretical analysis show that the solutions do not diverge to infinity for any initial value or step size. Experimental results confirm that our algorithms significantly outperform all existing methods in terms of accuracy. We also show that they can successfully decompose a large tensor, containing billion-scale nonzero elements.