Some Theory on Non-negative Tucker Decomposition

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• 关键词：Non ; negative Tucker Decomposition ; Non ; negative Canonical Polyadic Decomposition ; Dimensionality reduction ; Non ; negative Matrix Factorization
• 刊名：Lecture Notes in Computer Science
• 出版年：2017
• 出版时间：2017
• 年：2017
• 卷：10169
• 期：1
• 页码：152-161
• 丛书名：Latent Variable Analysis and Signal Separation
• ISBN：978-3-319-53547-0
• 卷排序：10169

文摘

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.