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Analyzing instability of industrial clustering techniques

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  • Studies on Industrial Ecology
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Abstract

The process life-cycle assessment (LCA) method has a crucial problem such that the LCA system boundary is freely decided by LCA practitioners, which consequently leads to truncation error and underestimation of life-cycle emission. This paper focuses on clustering methods (eigenvalue decomposition of the normalized Laplacian matrix and nonnegative matrix factorization of the normalized affinity matrix) which are useful in determining the LCA system boundary and investigates the instability of the clustering methods. The results indicate that, in cases involving a relatively small number of K-means repetitions (approximately 10), choosing the nonnegative matrix factorization method over the eigenvalue decomposition method yields smaller values of “normalized cut” value N cut (an indicator showing the goodness of network partitions), the benchmark indicating optimal cluster assignment. On the other hand, for a larger number of K-means repetitions (100 or more), neither method is universally superior to the other.

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Acknowledgments

An early version of this paper was prepared for the 24th Pan Pacific Association of Input–Output Studies, Nagoya, October 2013. I gratefully appreciate helpful comments received from Shunsuke Mori (Tokyo University of Science), Hiroshi Taguchi (Central Research Institute of Electric Power Industry), and Yuko Oshita (Kobe University) at the conference. In addition, I would like to express my gratitude to Shigemi Kagawa (Kyushu University) and Keiichiro Kanemoto (Kyushu University) for their penetrating opinions. I also want to express appreciation for the helpful comments and suggestions from the anonymous reviewer and the editor. This research has been supported by a Grant-in-Aid for Research Fellowship (No. 25·7261) of the Japan Society for the Promotion of Science.

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Authors and Affiliations

  1. Faculty of Economics, Kyushu University, 6-19-1 Hakozaki, Higashi-ku, Fukuoka, 812-8581, Japan

    Shunsuke Okamoto

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  1. Shunsuke Okamoto
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Correspondence to Shunsuke Okamoto.

Appendix

Appendix

See Table 2.

Table 2 Values of N cut obtained from a clustering method based on eigenvalue decomposition and those based on nonnegative matrix factorization
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Okamoto, S. Analyzing instability of industrial clustering techniques. Environ Econ Policy Stud 17, 389–406 (2015). https://doi.org/10.1007/s10018-014-0086-x

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