Intrinsic Isometric Manifold Learning with Application to Localization
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Data living on manifolds commonly appear in many applications. We show that under certain conditions, it is possible to construct an intrinsic and isometric data representation, which respects an underlying latent intrinsic manifold geometry. Namely, instead of learning the structure of the observed manifold, we view the observed data only as a proxy and learn the structure of a latent unobserved intrinsic manifold. For this purpose, we build a new metric and propose a method for robust estimation by assuming mild statistical priors and by using artificial neural networks as a mechanism for metric regularization and parameterization. We show successful application to unsupervised indoor localization in ad-hoc sensor networks. Specifically, we show that our proposed method facilitates accurate localization of a moving agent from imaging data it collects. Importantly, our method is applied in the same way to two different imaging modalities, thereby demonstrating its intrinsic capabilities.
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