Abstract
In biomedical engineering applications, high-order data, also known as tensors, are more and more popular and canonical polyadic decomposition (CPD) is one of the most powerful tool to analyze such high-dimensional high-order data. However, existing CPD algorithms suffer from a serious disadvantage: they are prone to stick into local minima and hence may result in unreasonable components that are hard to interpret. To overcome this problem, we proposed a new CPD algorithm that not only provides significantly improved stability but is also very suitable for parallel computing. The performance of the proposed algorithm was justified by using synthetic data and its applications in biomedical image denoising.
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Notes
Deflation means that one layer of \(\mathbf{a}_k^{\left( 1 \right) } \circ \mathbf{a}_k^{\left( 2 \right) } \circ \cdots \circ \mathbf{a}_k^{\left( N \right) } \) is estimated first and then is subtracted from the original tensor, and then the next layer of \(\mathbf{a}_{k+1}^{\left( 1 \right) } \circ \mathbf{a}_{k+1}^{\left( 2 \right) } \circ \cdots \circ \mathbf{a}_{k+1}^{\left( N \right) } \) will be estimated, and so on.
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Acknowledgements
The work was supported in part by the National Natural Science Foundation of China 61673124 and 61333013, the Guangdong Province Natural Science Foundation under Grant 2014A030308009 and 2014B090907010, the Foundation of Guangdong Provincial Department of Science and Technology under 15ZS0117.
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Xie, K., Yu, J. & Lu, C. A new canonical polyadic decomposition algorithm with improved stability and its applications to biomedical signal processing. Cluster Comput 20, 1449–1455 (2017). https://doi.org/10.1007/s10586-017-0858-8
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DOI: https://doi.org/10.1007/s10586-017-0858-8