Dimensionality reduction of collective motion by principal manifolds

Gajamannage, Kelum; Butail, Sachit; Porfiri, Maurizio; Bollt, Erik M.

doi:10.1016/j.physd.2014.09.009

Cited by 17 publications

(17 citation statements)

References 41 publications

(82 reference statements)

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“…For example, when a participant performed shoulder abduction to the right side of the body, 2 angles of the left Touch controller and only 1 angle of the right Touch controller were dubiously deemed salient. Potentially, nonlinear dimensionality reduction methods such as Isomap, diffusion maps, and principal manifolds could better identify sets of variables that distinguish one movement from another [ 94 - 96 ].…”

Section: Discussionmentioning

confidence: 99%

Data-Driven Classification of Human Movements in Virtual Reality–Based Serious Games: Preclinical Rehabilitation Study in Citizen Science

Ventura¹,

Hughes²,

Nov³

et al. 2022

JMIR Serious Games

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Background Sustained engagement is essential for the success of telerehabilitation programs. However, patients’ lack of motivation and adherence could undermine these goals. To overcome this challenge, physical exercises have often been gamified. Building on the advantages of serious games, we propose a citizen science–based approach in which patients perform scientific tasks by using interactive interfaces and help advance scientific causes of their choice. This approach capitalizes on human intellect and benevolence while promoting learning. To further enhance engagement, we propose performing citizen science activities in immersive media, such as virtual reality (VR). Objective This study aims to present a novel methodology to facilitate the remote identification and classification of human movements for the automatic assessment of motor performance in telerehabilitation. The data-driven approach is presented in the context of a citizen science software dedicated to bimanual training in VR. Specifically, users interact with the interface and make contributions to an environmental citizen science project while moving both arms in concert. Methods In all, 9 healthy individuals interacted with the citizen science software by using a commercial VR gaming device. The software included a calibration phase to evaluate the users’ range of motion along the 3 anatomical planes of motion and to adapt the sensitivity of the software’s response to their movements. During calibration, the time series of the users’ movements were recorded by the sensors embedded in the device. We performed principal component analysis to identify salient features of movements and then applied a bagged trees ensemble classifier to classify the movements. Results The classification achieved high performance, reaching 99.9% accuracy. Among the movements, elbow flexion was the most accurately classified movement (99.2%), and horizontal shoulder abduction to the right side of the body was the most misclassified movement (98.8%). Conclusions Coordinated bimanual movements in VR can be classified with high accuracy. Our findings lay the foundation for the development of motion analysis algorithms in VR-mediated telerehabilitation.

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Section: Discussionmentioning

confidence: 99%

Data-Driven Classification of Human Movements in Virtual Reality–Based Serious Games: Preclinical Rehabilitation Study in Citizen Science

Ventura¹,

Hughes²,

Nov³

et al. 2022

JMIR Serious Games

Self Cite

View full text Add to dashboard Cite

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“…In order to quantitatively analyze the embedding performance, we compute neighborhood preserving error [26], denoted by E δ . For that, first, we make an adjacency distance matrix…”

Section: Face Imagesmentioning

confidence: 99%

Bounded Manifold Completion

Gajamannage¹,

Paffenroth²

2019

Preprint

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Nonlinear dimensionality reduction or, equivalently, the approximation of high-dimensional data using a low-dimensional nonlinear manifold is an active area of research. In this paper, we will present a thematically different approach to detect the existence of a low-dimensional manifold of a given dimension that lies within a set of bounds derived from a given point cloud. A matrix representing the appropriately defined distances on a low-dimensional manifold is low-rank, and our method is based on current techniques for recovering a partially observed matrix from a small set of fully observed entries that can be implemented as a low-rank Matrix Completion (MC) problem. MC methods are currently used to solve challenging real-world problems, such as image inpainting and recommender systems, and we leverage extent efficient optimization techniques that use a nuclear norm convex relaxation as a surrogate for non-convex and discontinuous rank minimization. Our proposed method provides several advantages over current nonlinear dimensionality reduction techniques, with the two most important being theoretical guarantees on the detection of low-dimensional embeddings and robustness to non-uniformity in the sampling of the manifold. We validate the performance of this approach using both a theoretical analysis as well as synthetic and real-world benchmark datasets.

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“…Another disadvantage of LSE is that it embeds the data into a space where the distances in this space are not faithful to the distances on the manifold. The Principal Manifold Finding Algorithm (PMFA) is another NDR method that also uses cubic smoothing splines to represent the manifold and then quantifies the intrinsic distances of the points on the manifold as lengths of the splines [25]. However, this approach embeds high-dimensional data by reducing the reconstruction error over a two-dimensional space.…”

Section: Introductionmentioning

confidence: 99%

A nonlinear dimensionality reduction framework using smooth geodesics

Gajamannage

Paffenroth

Bollt

2019

Pattern Recognition

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Existing dimensionality reduction methods are adept at revealing hidden underlying manifolds arising from high-dimensional data and thereby producing a low-dimensional representation. However, the smoothness of the manifolds produced by classic techniques over sparse and noisy data is not guaranteed. In fact, the embedding generated using such data may distort the geometry of the manifold and thereby produce an unfaithful embedding. Herein, we propose a framework for nonlinear dimensionality reduction that generates a manifold in terms of smooth geodesics that is designed to treat problems in which manifold measurements are either sparse or corrupted by noise. Our method generates a network structure for given high-dimensional data using a nearest neighbors search and then produces piecewise linear shortest paths that are defined as geodesics. Then, we fit points in each geodesic by a smoothing spline to emphasize the smoothness. The robustness of this approach for sparse and noisy datasets is demonstrated by the implementation of the method on synthetic and real-world datasets.

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Dimensionality reduction of collective motion by principal manifolds

Cited by 17 publications

References 41 publications

Data-Driven Classification of Human Movements in Virtual Reality–Based Serious Games: Preclinical Rehabilitation Study in Citizen Science

Data-Driven Classification of Human Movements in Virtual Reality–Based Serious Games: Preclinical Rehabilitation Study in Citizen Science

Bounded Manifold Completion

A nonlinear dimensionality reduction framework using smooth geodesics

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