Analysis of Chaotic Behavior in Non-linear Dynamical Systems

Piórek, Michał

doi:10.1007/978-3-319-94887-4

Cited by 5 publications

(3 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The presented framework can have multiple areas of applicability for motion capture and motion tracks analysis including, but not limited to, human motion similarity comparison and analysis of large datasets, motion-based person recognition techniques, detection of anomalies in motion track as a result of disorder or disease. Quaternion-based clustering can be also used as a part of more complex algorithms, for example, analysis of chaotic behaviour (Piórek, 2018).…”

Section: Discussionmentioning

confidence: 99%

“…The main goal of this paper is to present a quaternion clustering methodology. The approach is an outcome of analysis of chaotic properties of processes described by quaternions presented in the work of Piórek (2018), where the initial idea of quaternion clustering appeared. Here this idea is enriched and wrapped up into a framework including the k-means algorithm generalization to the quaternion domain, a generalized set of methods to investigate clustering results, an automated procedure for estimation of the number of clusters and a test data generation framework.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A quaternion clustering framework

Piórek

Jablonski

2020

View full text Add to dashboard Cite

Data clustering is one of the most popular methods of data mining and cluster analysis. The goal of clustering algorithms is to partition a data set into a specific number of clusters for compressing or summarizing original values. There are a variety of clustering algorithms available in the related literature. However, the research on the clustering of data parametrized by unit quaternions, which are commonly used to represent 3D rotations, is limited. In this paper we present a quaternion clustering methodology including an algorithm proposal for quaternion based k-means along with quaternion clustering quality measures provided by an enhancement of known indices and an automated procedure of optimal cluster number selection. The validity of the proposed framework has been tested in experiments performed on generated and real data, including human gait sequences recorded using a motion capture technique.

show abstract

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A quaternion clustering framework

Piórek

Jablonski

2020

View full text Add to dashboard Cite

show abstract

“…While we could use the Euclidean distance in

, this would define a metric space that is not closed with respect to the quaternion algebra. We instead introduce the geodesic distance between two rotations

and

, which reads: 26

It corresponds to the minimum length of a geodesic line connecting the two quaternions on the 3‐sphere. 12 It can also be interpreted as the angle of the necessary rotation to obtain

from

.…”

Section: A Semi‐supervised Clustering Framework For Unit Quaternion T...mentioning

confidence: 99%

Semi‐supervised clustering of quaternion time series: Application to gait analysis in multiple sclerosis using motion sensor data

Drouin

Stamm

Chevreuil³

et al. 2022

Statistics in Medicine

View full text Add to dashboard Cite

Funding informationFondation pour l'Aide à la Recherche sur la Sclérose en Plaques Recent approaches in gait analysis involve the use of wearable motion sensors to extract spatio-temporal parameters that characterize multiple aspects of an individual's gait. In particular, the medical community could largely benefit from this type of devices as they could provide the clinicians with a valuable tool for assessing gait impairment. Motion sensor data are however complex and there is an urgent unmet need to develop sound statistical methods for analyzing such data and extracting clinically relevant information. In this article, we measure gait by following the hip rotation over time and the resulting statistical unit is a time series of unit quaternions. We explore the possibility to form groups of patients with similar walking impairment by taking into account their walking data and their global decease severity with semi-supervised clustering. We generalize a compromise-based method named hclustcompro to unit quaternion time series by combining it with the proper dissimilarity quaternion dynamic time warping. We apply this method on patients diagnosed with multiple sclerosis to form groups of patients with similar walking deficiencies while accounting for the clinical assessment of their overall disability. We also compare the compromise-based clustering approach with the method mergeTrees that falls into a sub-class of ensemble clustering named collaborative clustering. The results provide a first proof of both the interest of using wearable motion sensors for assessing gait impairment and the use of prior knowledge to guide the clustering process. It also demonstrates that compromise-based clustering is a more appropriate approach in this context.

show abstract