Aligning Manifolds of Double Pendulum Dynamics Under the Influence of Noise

Aziz, Fakhra; Wong, Anthony; Welsh, James S.; Chalup, Stephan K.

doi:10.1007/978-3-030-04239-4_7

Cited by 1 publication

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“…Only MAGG-feat and PDAE produced the expected visualisation, comprising six spheres that represented the snapshots we selected in the motion data on S 2 × S 2 . The outcome of MAGG-feat was also supported by our case study [47]. For the remaining experiments, random noise was added to the data in several stages as described in Section 5.2.1.…”

Section: Results Of 3-manifold Alignmentmentioning

confidence: 64%

Semi-Supervised Manifold Alignment Using Parallel Deep Autoencoders

2019

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The aim of manifold learning is to extract low-dimensional manifolds from high-dimensional data. Manifold alignment is a variant of manifold learning that uses two or more datasets that are assumed to represent different high-dimensional representations of the same underlying manifold. Manifold alignment can be successful in detecting latent manifolds in cases where one version of the data alone is not sufficient to extract and establish a stable low-dimensional representation. The present study proposes a parallel deep autoencoder neural network architecture for manifold alignment and conducts a series of experiments using a protein-folding benchmark dataset and a suite of new datasets generated by simulating double-pendulum dynamics with underlying manifolds of dimensions 2, 3 and 4. The dimensionality and topological complexity of these latent manifolds are above those occurring in most previous studies. Our experimental results demonstrate that the parallel deep autoencoder performs in most cases better than the tested traditional methods of semi-supervised manifold alignment. We also show that the parallel deep autoencoder can process datasets of different input domains by aligning the manifolds extracted from kinematics parameters with those obtained from corresponding image data.

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Section: Results Of 3-manifold Alignmentmentioning

confidence: 64%