Sufficient conditions for uniqueness in Candecomp/Parafac and Indscal with random component matrices
Sufficient conditions for uniqueness in Candecomp/Parafac and Indscal with random component matrices
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DOI：
10.1007/11336-006-1278-2
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发表时间：
2006-06
期刊：
影响因子：
3
通讯作者：
A. Stegeman;J. F. Berge;L. D. Lathauwer
中科院分区：
文献类型：
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作者：
A. Stegeman;J. F. Berge;L. D. Lathauwer
Candecomp/Parafac分析三路阵列的一个关键特征是三线性分解的本质唯一性。我们研究的Candecomp/Parafac和Indscale分解的唯一性。在后者中，要分解的数组具有对称切片。我们考虑的情况下，两个组件矩阵随机抽样从一个连续的分布，第三个组件矩阵具有完整的列秩。在这种情况下，我们分别获得了Candecomp/Parafac和Indscal模型的几乎必然的充分唯一性条件，只涉及三路数组的顺序和分解中的组件的数量。这两个唯一性条件比Kruskal的经典唯一性条件更接近必然性。
A key feature of the analysis of three-way arrays by Candecomp/Parafac is the essential uniqueness of the trilinear decomposition. We examine the uniqueness of the Candecomp/Parafac and Indscal decompositions. In the latter, the array to be decomposed has symmetric slices. We consider the case where two component matrices are randomly sampled from a continuous distribution, and the third component matrix has full column rank. In this context, we obtain almost sure sufficient uniqueness conditions for the Candecomp/Parafac and Indscal models separately, involving only the order of the three-way array and the number of components in the decomposition. Both uniqueness conditions are closer to necessity than the classical uniqueness condition by Kruskal.