Table 2.

Characteristics of the methodological approaches for the three different categories of research questions. Different methods for answering the three type of broad research questions (study aims) are listed together with the analytical category they stem from, a short description of each method as well as the considered categories of input path-signals and important references

Study aim	Method	Analytical category	Description	Input signal	References
Movement pattern description	Thresholding	Topology-based	Applies thresholding schemes (cut-off values) to separate relocations into different groups based on single or multiple path parameters (e.g., short- vs. Long-range movements)	Primary and secondary signals	[45, 80, 84, 127]
	Supervised Classification	Topology-based	Relocations (steps) of a trajectory are assigned to certain classes of movement behavior based on a classification scheme fitted with a training dataset	Primary and secondary signals, additional information like activity data	[129–131]
	Clustering	Topology-based	Unsupervised classification for identifying distinctive groups within a multivariate set of path-signals	Primary and secondary signals, additional information like activity data	[21, 132]
	Bayesian Partitioning of Markov Models (BPMM)	Topology- and time- series based	Classification algorithm for determining the number and sequence of homogenous classes within a sequential path-signal (time series)	Primary and secondary signals	[35, 91, 92]
Change-point detection	Line Simplification	Topology- or time-series based	Tests whether reducing the number of vertices in a trajecotry significantly impacts path topology to determine change points (can also be applied with graphs of sequential path-signals)	Primitive signals (spatial position)	[12, 133]
	Change Point Test	Topology-based	Detects significant changes in the observed movement direction (orientation) between the starting point and an attraction point of a trajectory	Primitive signals (spatial position)	[86, 134]
	Spatio-Temporal Criteria Segmentation	Topology-based	Special type of thresholding seeking optimal segmentation of a trajectory based on monotone criteria: relocations are included in a segment as long as they fullfill certain predefined requirements	Primitive, primary and secondary signals	[32, 87]
	Piecewise Regression	Time-series analysis	Splits time-series model into representative segments based on a signficant change-point (fits a polynomial model for each segment)	Primary and secondary signals	[86, 87]
	Penalized Contrast Method (PCM)	Time-series analysis	Non-parametric segmentation of a path-signal: the unknown number of segments is estimated by minimizing a penalized contrast function	Mostly secondary signals	[31, 40, 135]
	Behavioral Change Point Analysis (BCPA)	Time-series analysis	Likelihood-based method for detecting significant change points; applies moving window over continuous autocorrelated time series of a path-signal	Mostly secondary signals	[28, 35]
	Pruned Exact Linear Time (PELT) Algorithm	Time-series analysis	Search method for detecting optimal number and locations of change points minimizing different cost and penalty functions	primary and secondary signals	[42, 136, 137]
	Behavioral Movement Segmentation (BMS)	Time-series analysis	Combined search algorithm which optimizes segmentation based on parsimony and subsequent clustering for assigning segments to similar behaviors	primary and secondary signals, additional information like activity data	[43]
Process identification	Hidden-Markov Models (HMM)	State-space models	Estimate the sequence and composition of a predifined number of discrete states (e.g., movement behaviors) as well as the switching-probabilities between these states	Primary signals, additional information like activity data	[33, 49, 53–55]
	State-Space Models with Location Filtering	State-space models	More complex models which can model hidden movement states and also correct for errors in the observation process (e.g., GPS errors)	Primitive (spatial position) and primary signals, additional information like activity data	[51, 52, 65, 88, 90, 138]
	Hierarchical State-Space Models	State-space models	Hierarchical models accounting for variability of number and composition of movement states between individuals (further making inferences at population level)	Primary signals	[48, 52, 89]
	Bayesian Partitioning of Markov Models (BPMM)	Topology- and time- series based	Can also be used as partitioning algorithm determining the number and sequence of homogenous models (“states”) within a sequential path-signal	primary and secondary signals	[35, 91, 92]