Some Theory on Non-negative Tucker Decomposition
Some Theory on Non-negative Tucker Decomposition
复制标题
非负Tucker分解的一些理论
DOI：
10.1007/978-3-319-53547-0_15
复制
发表时间：
2017
影响因子：
8.4
通讯作者：
Nicolas Gillis
中科院分区：
文献类型：
--
作者：
Jeremy E. Cohen;P. Comon;Nicolas Gillis
本文讨论了非负系数张量降维所带来的一些理论困难。给出了低非负秩张量允许具有相同非负秩核的非负Tucker分解的充要条件。此外，我们还提供了证据，证明了使特征空间的维度最小，并且能够保证非负核具有低非负阶的唯一算法需要在每个模式上识别一个可能具有非常多极值射线的锥体。为了说明我们的观察结果，我们描述了一些计算非负Tucker分解的现有算法，并在合成数据上进行了测试。
Some theoretical difficulties that arise from dimensionality reduction for tensors with non-negative coefficients is discussed in this paper. A necessary and sufficient condition is derived for a low non-negative rank tensor to admit a non-negative Tucker decomposition with a core of the same non-negative rank. Moreover, we provide evidence that the only algorithm operating mode-wise, minimizing the dimensions of the features spaces, and that can guarantee the non-negative core to have low non-negative rank requires identifying on each mode a cone with possibly a very large number of extreme rays. To illustrate our observations, some existing algorithms that compute the non-negative Tucker decomposition are described and tested on synthetic data.