Quaternion Entropy for Analysis of Gait Data

Szczęsna, Agnieszka

doi:10.3390/e21010079

Cited by 13 publications

(9 citation statements)

References 31 publications

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“…Moreover, they showed a correlation between LLE values computed for time series consisting of (1) quaternion angles and (2) joint angles in a group of young individuals for hip, knee, and ankle joints in different variants of walking speed and ground inclination. The same set of experimental data was also analyzed using a new quaternion-based variant of the approximate entropy measure [25]. A systematic review of methodological approaches of the LLE quantification was prepared by Mehdizadeh [26].…”

Section: Methodsmentioning

confidence: 99%

Assessment of Local Dynamic Stability in Gait Based on Univariate and Multivariate Time Series

Josiński

Świtoński

Michalczuk

et al. 2019

Computational and Mathematical Methods in Medicine

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The ability of the locomotor system to maintain continuous walking despite very small external or internal disturbances is called local dynamic stability (LDS). The importance of the LDS requires constantly working on different aspects of its assessment method which is based on the short-term largest Lyapunov exponent (LLE). A state space structure is a vital aspect of the LDS assessment because the algorithm of the LLE computation for experimental data requires a reconstruction of a state space trajectory. The gait kinematic data are usually one- or three-dimensional, which enables to construct a state space based on a uni- or multivariate time series. Furthermore, two variants of the short-term LLE are present in the literature which differ in length of a time span, over which the short-term LLE is computed. Both a state space structure and the consistency of the observations based on values of both short-term LLE variants were analyzed using time series representing the joint angles at ankle, knee, and hip joints. The short-term LLE was computed for individual joints in three state spaces constructed on the basis of either univariate or multivariate time series. Each state space revealed walkers’ locally unstable behavior as well as its attenuation in the current stride. The corresponding conclusions made on the basis of both short-term LLE variants were consistent in ca. 59% of cases determined by a joint and a state space. Moreover, the authors present an algorithm for estimation of the embedding dimension in the case of a multivariate gait time series.

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Section: Methodsmentioning

confidence: 99%

Assessment of Local Dynamic Stability in Gait Based on Univariate and Multivariate Time Series

Josiński

Świtoński

Michalczuk

et al. 2019

Computational and Mathematical Methods in Medicine

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“…Another fundamental property of quaternion-valued learning is the Hamilton product, which has recently favored the proliferation of convolutional neural networks in the quaternion domain [ 35 , 36 , 37 , 38 ]. Due to their capabilities, quaternion-valued learning methods have been applied in several applications, including spoken language understanding [ 39 ], color image processing [ 40 , 41 ], 3D audio [ 42 , 43 ], speech recognition [ 44 ], image generation [ 45 ], quantum mechanics [ 46 ], risk diversification [ 47 ], gait data analysis [ 48 ].…”

Section: Introductionmentioning

confidence: 99%

An Information-Theoretic Perspective on Proper Quaternion Variational Autoencoders

Grassucci

Comminiello

Uncini

2021

Entropy

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Variational autoencoders are deep generative models that have recently received a great deal of attention due to their ability to model the latent distribution of any kind of input such as images and audio signals, among others. A novel variational autoncoder in the quaternion domain H, namely the QVAE, has been recently proposed, leveraging the augmented second order statics of H-proper signals. In this paper, we analyze the QVAE under an information-theoretic perspective, studying the ability of the H-proper model to approximate improper distributions as well as the built-in H-proper ones and the loss of entropy due to the improperness of the input signal. We conduct experiments on a substantial set of quaternion signals, for each of which the QVAE shows the ability of modelling the input distribution, while learning the improperness and increasing the entropy of the latent space. The proposed analysis will prove that proper QVAEs can be employed with a good approximation even when the quaternion input data are improper.

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“…The captured motion data is used in many analyses, such as inter alia: classification of motion capture human gait data ( Switonski, Josinski & Wojciechowski, 2019 ; Szczesna et al, 2018 ), identifying the presence of deterministic chaos in motion capture human gait data ( Piorek et al, 2017 ; Szczęsna, 2019 ), template generation and comparing based on motion capture data of karate athletes ( Hachaj, Piekarczyk & Ogiela, 2017 ).…”

Section: Introductionmentioning

confidence: 99%

Convolutional neural network in upper limb functional motion analysis after stroke

Szczęsna

Błaszczyszyn

Kawala-Sterniuk

2020

PeerJ

Self Cite

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In this work, implementation of Convolutional Neural Network (CNN) for the purpose of analysis of functional upper limb movement pattern was applied. The main aim of the study was to compare motion of selected activities of daily living of participants after stroke with the healthy ones (in similar age). The optical, marker-based motion capture system was applied for the purpose of data acquisition. There were some attempts made in order to find the existing differences in the motion pattern of the upper limb. For this purpose, the motion features of dominant and non-dominant upper limb of healthy participants were compared with motion features of paresis and non-paresis upper limbs of participants after stroke. On the basis of the newly collected data set, a new CNN application was presented to the classification of motion data in two different class label configurations. Analyzing individual segments of the upper body, it turned out that the arm was the most sensitive segment for capturing changes in the trajectory of the lifting movements of objects.

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Quaternion Entropy for Analysis of Gait Data

Cited by 13 publications

References 31 publications

Assessment of Local Dynamic Stability in Gait Based on Univariate and Multivariate Time Series

Assessment of Local Dynamic Stability in Gait Based on Univariate and Multivariate Time Series

An Information-Theoretic Perspective on Proper Quaternion Variational Autoencoders

Convolutional neural network in upper limb functional motion analysis after stroke

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