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Deep reconstruction of 1D ISOMAP representations

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A Correction to this article was published on 18 June 2021

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Abstract

This paper proposes a deep learning priors-based data reconstruction method of 1D isometric feature mapping (ISOMAP) representations. ISOMAP is a classical algorithm of nonlinear dimensionality reduction (NLDR) or manifold leaning (ML), which is devoted to questing for the low dimensional structure of high dimensional data. The reconstruction of ISOMAP representations, or the inverse problem of ISOMAP, reestablishes the high dimensional data from its low dimensional ISOMAP representations, and owns a bright future in data representation, generation, compression and visualization. Due to the fact that the dimension of ISOMAP representations is far less than that of the original high dimensional data, the reconstruction of ISOMAP representations is ill-posed or undetermined. Hence, the residual learning of deep convolutional neural network (CNN) is employed to boost reconstruction performance, via achieving the priors between the low-quality result of general ISOMAP reconstruction method and its residual relative to the original data. In the situation of 1D representations, it is evaluated by the experimental results that the proposed method outbalances the state-of-the-art methods, such as nearest neighbor (NN), discrete cosine transformation (DCT) and sparse representation (SR), in reconstruction performance of video data. In summary, the proposed method is suitable for low-bitrate and high-performance applications of data reconstruction.

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Acknowledgements

We would very much like to express our deep thanks to professor Maria Trocan from Institut Supérieur d'Électronique de Paris (ISEP) for her invaluable guidance and discussion on the theory and applications of deep learning.

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Authors and Affiliations

  1. School of Information Engineering, Yangzhou University, Yangzhou, 225127, China

    Honggui Li

  2. Laboratoire d’Informatique de Paris 6, Sorbonne University, Paris, 75020, France

    Dimitri Galayko

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  1. Honggui Li
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  2. Dimitri Galayko
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Correspondence to Honggui Li.

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The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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Communicated by Y. Zhang.

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Li, H., Galayko, D. Deep reconstruction of 1D ISOMAP representations. Multimedia Systems 27, 503–518 (2021). https://doi.org/10.1007/s00530-021-00750-4

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