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• W4224880062 abstract "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." @default.
• W4224880062 created "2022-04-27" @default.
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• W4224880062 date "2022-07-01" @default.
• W4224880062 modified "2023-09-25" @default.
• W4224880062 title "Deep Isometric Maps" @default.
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• W4224880062 doi "https://doi.org/10.1016/j.imavis.2022.104461" @default.
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