## Nonnegative Tensor Factorization, Completely Positive Tensors and an Hierarchical Elimination Algorithm

**报告题目**：Nonnegative Tensor Factorization, Completely Positive Tensors and an Hierarchical Elimination Algorithm

**报告人**：祁力群教授(香港理工大学)

**时间****： **2013年6月18日（星期二）16:00-17:00

**地点：**理科楼数学系A304

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**摘要****： **Nonnegative tensor factorization has applications in statistics, computer vision, ex-ploratory multiway data analysis and blind source separation. A symmetric nonneg-ative tensor, which has a symmetric nonnegative factorization, is called a completely positive (CP) tensor. The H-eigenvalues of a CP tensor are always nonnegative. When the order is even, the Z-eigenvalue of a CP tensor are all nonnegative. When the or-der is odd, a Z-eigenvector associated with a positive (negative) Z-eigenvalue of a CP tensor is always nonnegative (nonpositive). The entries of a CP tensor obey some dominance properties. The CP tensor cone and the copositive tensor cone of the same order are dual to each other. We introduce strongly symmetric tensors and show that a symmetric tensor has a symmetric binary decomposition if and only if it is strongly symmetric. Then we show that a strongly symmetric, hierarchically dominated non-negative tensor is a CP tensor, and present a hierarchical elimination algorithm for checking this. Numerical examples are also given.

**联系人**：张立平