From: Review and classification of variability analysis techniques with clinical applications
Domain Assumptions | Features | Feature Assumptions | Transformation used | References |
---|---|---|---|---|
The information is held in those properties of the time series that are invariant-i.e. not supposed to change over either time or space. | Allan scaling exponent | The time series is modeled as a point process, and the ratio between the second order moment of the difference between the number of events of two successive windows and the mean number of events has scale-invariant properties | Point process | |
 | Detrended fluctuation analysis | The standard deviation of the detrended cumulative time series has scale-invariant properties |  | |
 | Diffusion Entropy | The time series is modeled as a family of diffusion processes, which Shannon entropies has scale-invariant properties |  | |
 | Embedding scaling exponent | The variance of the attractor at different embedding dimensions has scale-invariant properties | Phase space representation | [98] |
 | Fano scaling exponent | The time series is modeled as a point process, and the variance of the number of events divided by the mean number of events has scale-invariant properties | Point process | |
 | Higuchi's algorithm | The length of the time series at different windows has scale-invariant properties |  | |
 | Index of variability | The time series is modeled as a point process, and the variance of the number of events has scale-invariant properties | Point process | [2] |
 | Multifractal exponents | Multiple scaling exponents characterize the time series | Wavelet transform | |
 | Power spectrum scaling exponent | Stationarity, the power spectrum follows a 1/fb like behaviour | Power spectrum | [92] |
 | Probability distribution scaling exponent | The distribution of the data has scale--invariant properties | Bin transformation | |
 | Rescaled detrended range analysis | The range (difference between maximum and minimum value) of a time series has scale-invariant properties |  | [92] |
 | Scaled windowed variance | The standard deviation of the detrended time series has scale-invariant properties |  | [92] |
 | Correlation dimension | The time series is extracted from a dynamical system, and the number of points in the phase space that are closer than a certain threshold has scale-invariant properties | Phase space representation | |
 | Finite growth rates | The time series is extracted from a dynamical system, which is described by its dependence on the initial conditions (how two points that are close in space and time separate after a certain amount of time)-the ratio between the final and the initial time is an invariant of the system | Phase space representation | [86] |
 | Kolmogorov-Sinai entropy | The time series is extracted from a dynamical system, and it is possible to predict which part of the phase space the dynamics will visit at a time t+1, given the trajectories up to time t | Phase space representation | |
 | Largest Lyapunov exponent | The time series is extracted from a dynamical system, which is described by its dependence on the initial conditions (how two points that are close in space and time separate after a certain amount of time)-the distance grows on average exponentially in time, and the exponent is an invariant of the system | Phase space representation |