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Deep Isometric Maps
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DOI：10.1016/j.imavis.2022.104461.png)
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Abstract
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Isometric feature mapping is an established time-honored algorithm in manifold learning and non-linear dimensionality reduction. Its prominence can be attributed to the output of a coherent global low-dimensional representation of data by preserving intrinsic distances. In order to enable an efficient and more applicable isometric feature mapping, a diverse set of sophisticated advancements have been proposed to the original algorithm to incorporate important factors like sparsity of computation, conformality, topological constraints and spectral geometry. However, a significant shortcoming of most approaches is the dependence on large-scale dense-spectral decompositions and the inability to generalize to points far away from the sampling of the manifold.In this paper, we explore an unsupervised deep learning approach for computing distance-preserving maps for non-linear dimensionality reduction. We demonstrate that our framework is general enough to incorporate all previous advancements and show a significantly improved local and non-local generalization of the isometric mapping. Our approach involves training with only a few landmark points and avoids the need for population of dense matrices as well as computing their spectral decomposition.(c) 2022 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http:// creativecommons.org/licenses/by/4.0/).
Keywords:
Multidimensional scaling
Manifold learning
Non-linear dimensionality reduction
Neural networks
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