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Component preserving laplacian eigenmaps for data reconstruction and dimensionality reduction

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Abstract

Laplacian Eigenmaps (LE) is a widely used dimensionality reduction and data reconstruction method. When the data has multiple connected components, the LE method has two obvious deficiencies. First, it might reconstruct each component as a single point, resulting in loss of information within the component. Second, it only focuses on local features but ignores the location information between components, which might cause the reconstructed components to overlap or to completely change their relative positions. To solve these two problems, this article first modifies the optimization objective of the LE method, by characterizing the relative positions between components of data with the similarity between high-density core points, and then solves the optimization problem by using a gradient descent method to avoid the over-compression of data points in the same connected component. A series of experiments on synthetic data and real-world data verify the effectiveness of the proposed method.

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Data availability and access

The datasets generated and analysed during the current study are available from the corresponding author on reasonable request.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China [grant numbers 11871353, 12231007, 61806170], the National Key Research and Development Program of China [grant number 2019YFB1706104], and the Fundamental Research Funds for the Central Universities [grant numbers 2682022ZTPY082, 2682023ZTPY027]. We would also like to thank the anonymous reviewers for their helpful comments and suggestions to improve the article.

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Authors and Affiliations

  1. School of Mathematics, Southwest Jiaotong University, Chengdu, Sichuan, 611756, China

    Hua Meng, Hanlin Zhang, Yu Ding & Shuxia Ma

  2. School of Computing and Artificial Intelligence, Southwest Jiaotong University, Chengdu, Sichuan, 611756, China

    Zhiguo Long

Authors
  1. Hua Meng
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  2. Hanlin Zhang
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  3. Yu Ding
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  4. Shuxia Ma
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Contributions

Hua Meng: Conceptualization, Methodology, Supervision, Writing - Reviewing and Editing. Hanlin Zhang: Software, Visualization, Data curation, Investigation, Validation, Writing-Reviewing and Editing. Yu Ding: Visualization, Data curation. Shuxia Ma: Supervision, Project administration, Writing-Reviewing and Editing. Zhiguo Long: Conceptualization, Formal analysis, Supervision, Writing-Original Draft, Funding acquisition.

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Correspondence to Zhiguo Long.

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The authors declare that they have no competing interest to this work.

Ethical and informed consent for data used

The data used in this article are either from public datasets or generated by the authors. The research in this article does not involve humans or animals.

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Meng, H., Zhang, H., Ding, Y. et al. Component preserving laplacian eigenmaps for data reconstruction and dimensionality reduction. Appl Intell 53, 28570–28591 (2023). https://doi.org/10.1007/s10489-023-05012-6

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