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Dark-Point Component Analysis: Nonnegative Blind Source Separation Based on Jaccard Index

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Abstract

A simplicial cone can be employed in nonnegative blind source separation (N-BSS). Nevertheless, the coordinate origin may not be a dark-point, and in this case, it is challenging to implement N-BSS with a simplicial cone. We propose an algorithm for finding dark-points based on the minimum Jaccard index (MJI) criterion-dark-point component analysis (DCA). This method only needs to assume source boundedness and nonnegativity instead of local dominance, full additivity, and sparsity. On the other hand, mixing data scatter plots are usually confined as tear-drop-shaped or deltoid. However, DCA does not need such restrictions. DCA can also be applied to blind source separation (BSS) in which the sources are strictly positive, and the result is the same as that of N-BSS.

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Data Availability Statement

In the manuscript entitled ‘Dark-Point Component Analysis: Nonnegative Blind Source Separation Based on Jaccard Index’, all the authors agree that the data that support the findings of this study are available from the authors upon reasonable request.

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Acknowledgements

This work is supported by National Key Research and Development Program(Grant No. 2017YFB1002804): Multimodal Data Interaction Intention Understanding in Cloud Fusion and Major Project of National Social Science Foundation of China (Grant No.17ZDA331): Methodology Research on Thinking of Chinese Medicine (2017-2022). This work is also supported by Hebei Province technology innovation guidance program - Winter Olympics with science and technology special funding project: Research on high precision positioning technology of ice and snow emergencies under 5G VR scene (project number: 20470302d).

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Authors and Affiliations

  1. School of Computer and Communication Engineering, University of Science and Technology Beijing, Beijing, 100083, China

    Mingzhan Zhao, Zhiliang Wang & Zhimin Zhang

  2. Information Engineering College Of Hebei University Of Architecture, Hebei University Of Architecture, Zhangjiakou, 075000, China

    Mingzhan Zhao & Xinyue Chang

  3. School of Information Engineering, Shanghai Open University, Shanghai, 201400, China

    Wei Zhao

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  1. Mingzhan Zhao
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Correspondence to Zhimin Zhang.

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Zhao, M., Wang, Z., Chang, X. et al. Dark-Point Component Analysis: Nonnegative Blind Source Separation Based on Jaccard Index. Circuits Syst Signal Process 41, 3985–4003 (2022). https://doi.org/10.1007/s00034-022-01969-w

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