Is walking a random walk? Evidence for long-range correlations in stride interval of human gait

1995 ◽  
Vol 78 (1) ◽  
pp. 349-358 ◽  
Author(s):  
J. M. Hausdorff ◽  
C. K. Peng ◽  
Z. Ladin ◽  
J. Y. Wei ◽  
A. L. Goldberger
Keyword(s):  
Time Series ◽  
Random Walk ◽  
Long Range ◽  
Power Law ◽  
Unknown Origin ◽  
Power Spectral Analysis ◽  
Gait Pattern ◽  
Human Gait ◽  
Long Range Correlations ◽  
Stride Interval

Complex fluctuations of unknown origin appear in the normal gait pattern. These fluctuations might be described as being 1) uncorrelated white noise, 2) short-range correlations, or 3) long-range correlations with power-law scaling. To test these possibilities, the stride interval of 10 healthy young men was measured as they walked for 9 min at their usual rate. From these time series, we calculated scaling indexes by using a modified random walk analysis and power spectral analysis. Both indexes indicated the presence of long-range self-similar correlations extending over hundreds of steps; the stride interval at any time depended on the stride interval at remote previous times, and this dependence decayed in a scale-free (fractallike) power-law fashion. These scaling indexes were significantly different from those obtained after random shuffling of the original time series, indicating the importance of the sequential ordering of the stride interval. We demonstrate that conventional models of gait generation fail to reproduce the observed scaling behavior and introduce a new type of central pattern generator model that successfully accounts for the experimentally observed long-range correlations.

Fractal dynamics of human gait: stability of long-range correlations in stride interval fluctuations

1996 ◽  
Vol 80 (5) ◽  
pp. 1448-1457 ◽  
Author(s):  
J. M. Hausdorff ◽  
P. L. Purdon ◽  
C. K. Peng ◽  
Z. Ladin ◽  
J. Y. Wei ◽  
...  
Keyword(s):  
Long Range ◽  
Healthy Subjects ◽  
Fractal Property ◽  
Dynamical Analysis ◽  
Human Gait ◽  
Locomotor System ◽  
Long Range Correlations ◽  
Power Law Decay ◽  
Stride Interval ◽  
The Stability

Fractal dynamics were recently detected in the apparently “noisy” variations in the stride interval of human walking. Dynamical analysis of these step-to-step fluctuations revealed a self-similar pattern: fluctuations at one time scale are statistically similar to those at multiple other time scales, at least over hundreds of steps, while healthy subjects walk at their normal rate. To study the stability of this fractal property, we analyzed data obtained from healthy subjects who walked for 1 h at their usual, slow, and fast paces. The stride interval fluctuations exhibited long-range correlations with power-law decay for up to 1,000 strides at all 3 walking rates. In contrast, during metronomically paced walking, these long-range correlations disappeared; variations in the stride interval were random (uncorrelated) and nonfractal. The long-range correlations observed during spontaneous walking were not affected by removal of drifts in the time series. Thus the fractal dynamics of spontaneous stride interval are normally quite robust and intrinsic to the locomotor system. Furthermore, this fractal property of neural output may be related to the higher nervous centers responsible for the control of walking rhythm.

Allometric Control of Human Gait

Fractals ◽  
1998 ◽  
Vol 06 (02) ◽  
pp. 101-108 ◽  
Author(s):  
Bruce J. West ◽  
Lori Griffin
Keyword(s):  
Time Series ◽  
Power Law ◽  
Relative Dispersion ◽  
Human Gait ◽  
Interval Time ◽  
Inverse Power Law ◽  
Time Correlations ◽  
Stride Interval ◽  
Interval Time Series ◽  
Long Time

The stride interval in normal human gait is not strictly constant, but fluctuates from step to step in a random manner. These fluctuations have traditionally been assumed to be uncorrelated random errors with normal statistics. Herein we show that, contrary to thes assumption these fluctuations have long-time correlations. Further, these long-time correlations are interpreted in terms of a scaling in the fluctuations indicating an allometric control process. To establish this result we measured the stride interval of a group of five healthy men and women as they walked for 5 to 15 minutes at their usual pace. From these time series we calculate the relative dispersion, the ratio of the standard deviation to the mean, and show by systematically aggregating the data that the correlation in the stride-interval time series is an inverse power law similar to the allometric relations in biology. The inverse power-law relative dispersion shows that the stride-interval time series scales indicating long-time self-similar correlations extending for hundreds of steps, which is to say that the underlying process is a random fractal. Furthermore, the power-law index is related to the fractal dimension of the time series. To determine if walking is a nonlinear process the stride-interval time series were randomly shuffled and the differences in the fractal dimensions of the surrogate time series from those of the original time series were determined to be statistically significant. This difference indicates the importance of the long-time correlations in walking.

scholarly journals Multimodal Few-Shot Learning for Gait Recognition

2020 ◽  
Vol 10 (21) ◽  
pp. 7619
Author(s):  
Jucheol Moon ◽  
Nhat Anh Le ◽  
Nelson Hebert Minaya ◽  
Sang-Il Choi
Keyword(s):  
Neural Network ◽  
Time Series ◽  
Gait Recognition ◽  
Gait Pattern ◽  
Recognition Problem ◽  
Human Gait ◽  
Training Dataset ◽  
Support Vector ◽  
Open Set ◽  
Latent Space

A person’s gait is a behavioral trait that is uniquely associated with each individual and can be used to recognize the person. As information about the human gait can be captured by wearable devices, a few studies have led to the proposal of methods to process gait information for identification purposes. Despite recent advances in gait recognition, an open set gait recognition problem presents challenges to current approaches. To address the open set gait recognition problem, a system should be able to deal with unseen subjects who have not included in the training dataset. In this paper, we propose a system that learns a mapping from a multimodal time series collected using insole to a latent (embedding vector) space to address the open set gait recognition problem. The distance between two embedding vectors in the latent space corresponds to the similarity between two multimodal time series. Using the characteristics of the human gait pattern, multimodal time series are sliced into unit steps. The system maps unit steps to embedding vectors using an ensemble consisting of a convolutional neural network and a recurrent neural network. To recognize each individual, the system learns a decision function using a one-class support vector machine from a few embedding vectors of the person in the latent space, then the system determines whether an unknown unit step is recognized as belonging to a known individual. Our experiments demonstrate that the proposed framework recognizes individuals with high accuracy regardless they have been registered or not. If we could have an environment in which all people would be wearing the insole, the framework would be used for user verification widely.

Analytical and empirical fluctuation functions of the EEG microstate random walk - Short-range vs. long-range correlations

NeuroImage ◽  
2016 ◽  
Vol 141 ◽  
pp. 442-451 ◽  
Author(s):  
F. von Wegner ◽  
E. Tagliazucchi ◽  
V. Brodbeck ◽  
H. Laufs
Keyword(s):  
Random Walk ◽  
Long Range ◽  
Short Range ◽  
Long Range Correlations

scholarly journals Long-Range Correlations and Characterization of Financial and Volcanic Time Series

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 441 ◽  
Author(s):  
Maria C. Mariani ◽  
Peter K. Asante ◽  
Md Al Masum Bhuiyan ◽  
Maria P. Beccar-Varela ◽  
Sebastian Jaroszewicz ◽  
...  
Keyword(s):  
Time Series ◽  
Long Range ◽  
Time Series Data ◽  
Financial Time Series ◽  
Seismic Station ◽  
Volcanic Eruptions ◽  
Series Data ◽  
Fluctuation Analysis ◽  
Scaling Properties ◽  
Long Range Correlations

In this study, we use the Diffusion Entropy Analysis (DEA) to analyze and detect the scaling properties of time series from both emerging and well established markets as well as volcanic eruptions recorded by a seismic station, both financial and volcanic time series data have high frequencies. The objective is to determine whether they follow a Gaussian or Lévy distribution, as well as establish the existence of long-range correlations in these time series. The results obtained from the DEA technique are compared with the Hurst R/S analysis and Detrended Fluctuation Analysis (DFA) methodologies. We conclude that these methodologies are effective in classifying the high frequency financial indices and volcanic eruption data—the financial time series can be characterized by a Lévy walk while the volcanic time series is characterized by a Lévy flight.

Detecting long-range correlations in time series of neuronal discharges

2003 ◽  
Vol 330 (3-4) ◽  
pp. 391-399 ◽  
Author(s):  
S. Blesić ◽  
S. Milošević ◽  
Dj. Stratimirović ◽  
M. Ljubisavljević
Keyword(s):  
Time Series ◽  
Long Range ◽  
Long Range Correlations
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