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...ion Technological advances in tracking and navigation systems make it possible to capture, efficiently and cost-effectively, the trajectories of a wide range of moving objects, including human beings =-=[1, 2]-=-, animals [3–6], and vehicles [7, 8]. With access to an unprecedented wealth of accurate motion data, researchers today can apply pattern discovery techniques to moving object databases and generate k...

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...sive alignment procedure. At a given time, three corresponding QTC movement sequences (i.e., of the teacher and the two students) are aligned followed by a multiple alignment using a global alignment =-=[61]-=-. Fig 8 presents the results of the alignment of QTCB movement sequences. For clarity, the characters (i.e., transcoded QTCB relations) have been colour-coded. The row above the aligned sequences is u...

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...ng and navigation systems make it possible to capture, efficiently and cost-effectively, the trajectories of a wide range of moving objects, including human beings [1, 2], animals [3–6], and vehicles =-=[7, 8]-=-. With access to an unprecedented wealth of accurate motion data, researchers today can apply pattern discovery techniques to moving object databases and generate knowledge in a large member of discip...

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...ayed an important role in many research fields. In the early 1980s, biochemists began to use sequence alignment to analyse DNA sequences [39]. Later, social scientists, such as the sociologist Abbott =-=[46]-=-, have applied sequence alignment to the analysis of career patterns. More recently, sequence alignment methods have been used in fields including transportation [47–49], cartography [50], tourism [51...

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...ories, most studies have focused on the spatial dimension [17–20], whereas several studies have considered both spatial and temporal aspects [21–25]. However, despite extensive research in this field =-=[26, 27]-=-, certain aspects of moving object trajectories have received only scant attention to date. In this paper, instead of presenting a spatial or spatio-temporal similarity analysis of trajectories, we pr...

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...able to, for example, REMO and DTW. REMO is an approach that describes motion patterns by changes in the motion attributes of objects such as the speed and motion azimuth of individual MPOs over time =-=[6]-=-. DTW is an algorithm for measuring the similarity between two time series that may vary in time or speed [65]. Unlike traditional distance measures such as the Euclidean distance, DTW can calculate t...

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...vement Analysis PLOS ONE | DOI:10.1371/journal.pone.0132452 July 16, 2015 4 / 25 Trajectories and QTCMovement Sequences The trajectory of an MPO comprises a set of observations through space and time =-=[44, 45]-=-. A trajectory represents the movement of an individual MPO. The interactions between two MPOs during a time interval of movement can be expressed in the form of a QTC movement sequence– a chronologic...

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...y can apply pattern discovery techniques to moving object databases and generate knowledge in a large member of disciplines, including urban planning [9], event management [10, 11], crisis management =-=[12]-=-, traffic [13], and tourism [14]. In addition to their usefulness for processing large-scale movement data sets, data mining and knowledge discovery techniques can also be applied to small-scale movem...

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...ial Research Fund of Ghent University (BOF) for supporting the research. Competing Interests: The authors have declared that no competing interests exist. entity into another via a similarity measure =-=[16]-=-. In the context of movement, trajectories (i.e., representative paths that moving objects follow through space as a function of time) are typically considered to be the entities in similarity analysi...

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... interacting moving objects over time. Although SAMs have long been used in bioinformatics for the analysis of DNA strings [38], they have only recently been applied to the field of movement analysis =-=[39]-=-. In the current study, sequence alignment is used to assess the similarity between movement sequences of QTC relations for two reasons. First, SAMs allow us to visually distinguish movement patterns ...

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...46], have applied sequence alignment to the analysis of career patterns. More recently, sequence alignment methods have been used in fields including transportation [47–49], cartography [50], tourism =-=[51]-=-, and crowd behaviour analysis [52], among others. Sequence alignment is the process of aligning two or more character sequences based on a set of conventional operations. Specifically, dynamic progra...

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...on attributes of objects such as the speed and motion azimuth of individual MPOs over time [6]. DTW is an algorithm for measuring the similarity between two time series that may vary in time or speed =-=[65]-=-. Unlike traditional distance measures such as the Euclidean distance, DTW can calculate the similarity between two time series that may feature some noise and displacements. The main difference betwe...

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...eras. It is used in a wide range of research fields. For example, MoCap has been used in sports sciences to capture the movement of athletes as part of rehabilitation, physical education and practice =-=[55, 56]-=-. In the medical sciences, physiotherapists, orthopaedists and neurologists may examine MoCap measurements of human gait in conjunction with biomechanical modelling to evaluate a patient’s status and ...

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...et of conventional operations. Specifically, dynamic programming algorithms are used to equate sequences with the goal of maximising a similarity measure or minimising a distance measure between them =-=[48, 53]-=-. Two of the most widely used SAMs are pairwise alignment and multiple alignment. Pairwise alignment is the comparison of two sequences, whereas multiple alignment is the comparison of more than two s...

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...i [28–31], with only a few studies presenting an integrated, spatio-temporal treatment of object movements. One notable example of an integrative approach is the Qualitative Trajectory Calculus (QTC) =-=[32]-=-. QTC reduces the complexity of interacting, real-world, continuously disjoint moving objects by representing the interaction in terms of qualitative relationships [33]. By converting relative motion ...

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...d interpreting movement data. Researchers have focused on different aspects in this area, including analysing the sequential aspects within the spatial and temporal dimensions of movement data (e.g., =-=[39, 52, 63, 64]-=-). For example, in [62], key parameters that characterise the movement of objects, the so-called movement parameters (MPs) such as speed, acceleration, direction, and derived from the trajectories of ...

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...et of conventional operations. Specifically, dynamic programming algorithms are used to equate sequences with the goal of maximising a similarity measure or minimising a distance measure between them =-=[48, 53]-=-. Two of the most widely used SAMs are pairwise alignment and multiple alignment. Pairwise alignment is the comparison of two sequences, whereas multiple alignment is the comparison of more than two s...

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...otion data, researchers today can apply pattern discovery techniques to moving object databases and generate knowledge in a large member of disciplines, including urban planning [9], event management =-=[10, 11]-=-, crisis management [12], traffic [13], and tourism [14]. In addition to their usefulness for processing large-scale movement data sets, data mining and knowledge discovery techniques can also be appl...

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...s notations A, B, C, and D respectively. Accordingly, the (A B C D)C relationship syntax has been proposed for the relation between two MPOs at each time stamp of the movement. In total, there are 81 =-=(34)-=- base relations for QTCC (Fig 2). QTCC relations thus reveal more detail of movement between two MPOs. SAM and Movement Analysis PLOS ONE | DOI:10.1371/journal.pone.0132452 July 16, 2015 4 / 25 Trajec...

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...vement Analysis PLOS ONE | DOI:10.1371/journal.pone.0132452 July 16, 2015 4 / 25 Trajectories and QTCMovement Sequences The trajectory of an MPO comprises a set of observations through space and time =-=[44, 45]-=-. A trajectory represents the movement of an individual MPO. The interactions between two MPOs during a time interval of movement can be expressed in the form of a QTC movement sequence– a chronologic...

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.... Global alignment forces the alignment to span the entire length of all sequences, whereas local alignments identifies regions of similarity in long sequences (for a detailed explanation, see, e.g., =-=[54]-=-). Pairwise alignment equates two sequences using four conventional operations: identity, substitution, insertion and deletion. Based on the scope of the research, each operation is associated with a ...

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...nce between a QTCB/QTCC relation and itself). The conceptual distance between ‘0’ and ‘+’ or ‘–’ is one. The conceptual distance between ‘–’ and ‘+’ equals two because direct transition is impossible =-=[60]-=-. The overall conceptual distances between two QTC relations can then be calculated by summing up the conceptual distance over all relation symbols and rescaling it to the interval [0 10]. Therefore, ...

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...d interpreting movement data. Researchers have focused on different aspects in this area, including analysing the sequential aspects within the spatial and temporal dimensions of movement data (e.g., =-=[39, 52, 63, 64]-=-). For example, in [62], key parameters that characterise the movement of objects, the so-called movement parameters (MPs) such as speed, acceleration, direction, and derived from the trajectories of ...

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...d wealth of accurate motion data, researchers today can apply pattern discovery techniques to moving object databases and generate knowledge in a large member of disciplines, including urban planning =-=[9]-=-, event management [10, 11], crisis management [12], traffic [13], and tourism [14]. In addition to their usefulness for processing large-scale movement data sets, data mining and knowledge discovery ...

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...f the two-dimensional movement of a pair of MPOs. Binary relations between two MPOs are evaluated based on the Euclidean distance [32]. QTCB relations are constructed from the following relationships =-=[36]-=-: Assume: MPOs k and l, and time point t k|t denotes the position of k at t l|t denotes the position of l at t d(u, v) denotes the Euclidean distance between two positions u and v A. Movement of k wit...

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...eras. It is used in a wide range of research fields. For example, MoCap has been used in sports sciences to capture the movement of athletes as part of rehabilitation, physical education and practice =-=[55, 56]-=-. In the medical sciences, physiotherapists, orthopaedists and neurologists may examine MoCap measurements of human gait in conjunction with biomechanical modelling to evaluate a patient’s status and ...

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...ion Technological advances in tracking and navigation systems make it possible to capture, efficiently and cost-effectively, the trajectories of a wide range of moving objects, including human beings =-=[1, 2]-=-, animals [3–6], and vehicles [7, 8]. With access to an unprecedented wealth of accurate motion data, researchers today can apply pattern discovery techniques to moving object databases and generate k...

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...ng and navigation systems make it possible to capture, efficiently and cost-effectively, the trajectories of a wide range of moving objects, including human beings [1, 2], animals [3–6], and vehicles =-=[7, 8]-=-. With access to an unprecedented wealth of accurate motion data, researchers today can apply pattern discovery techniques to moving object databases and generate knowledge in a large member of discip...

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...otion data, researchers today can apply pattern discovery techniques to moving object databases and generate knowledge in a large member of disciplines, including urban planning [9], event management =-=[10, 11]-=-, crisis management [12], traffic [13], and tourism [14]. In addition to their usefulness for processing large-scale movement data sets, data mining and knowledge discovery techniques can also be appl...

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...ttern discovery techniques to moving object databases and generate knowledge in a large member of disciplines, including urban planning [9], event management [10, 11], crisis management [12], traffic =-=[13]-=-, and tourism [14]. In addition to their usefulness for processing large-scale movement data sets, data mining and knowledge discovery techniques can also be applied to small-scale movement data sourc...

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...chniques to moving object databases and generate knowledge in a large member of disciplines, including urban planning [9], event management [10, 11], crisis management [12], traffic [13], and tourism =-=[14]-=-. In addition to their usefulness for processing large-scale movement data sets, data mining and knowledge discovery techniques can also be applied to small-scale movement data sources. For example, m...

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...umping, lifting, striking and swimming, can be investigated for various purposes. Investigating the movement of swimmers, for instance, might help coaches to analyse the performance of their swimmers =-=[15]-=-. Nonetheless, the specific techniques and methods chosen for extracting movement patterns from a data set depend on the context of the movement under examination. Among the wide range of research met...

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...ative Trajectory Calculus (QTC) [32]. QTC reduces the complexity of interacting, real-world, continuously disjoint moving objects by representing the interaction in terms of qualitative relationships =-=[33]-=-. By converting relative motion attributes (i.e., distance) into symbolic representations, QTC transforms quantitative data on movement (positional information) into qualitative data (QTC relations), ...

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...nt and reason about moving objects. It expresses the spatio-temporal relationship between two disjoint moving point objects (MPOS). Different types of QTC have been developed, namely QTCB (QTC-Basic) =-=[40]-=-, QTCC (QTC-Double Cross) [41], QTCN (QTC-Network) [42], and QTCS (QTC-Shape) [43]. This paper will focus on QTCB and QTCC. In QTCB, qualitative relations are defined based on the Euclidean distance b...

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...ects. It expresses the spatio-temporal relationship between two disjoint moving point objects (MPOS). Different types of QTC have been developed, namely QTCB (QTC-Basic) [40], QTCC (QTC-Double Cross) =-=[41]-=-, QTCN (QTC-Network) [42], and QTCS (QTC-Shape) [43]. This paper will focus on QTCB and QTCC. In QTCB, qualitative relations are defined based on the Euclidean distance between two disjoint MPOs at ea...

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...atio-temporal relationship between two disjoint moving point objects (MPOS). Different types of QTC have been developed, namely QTCB (QTC-Basic) [40], QTCC (QTC-Double Cross) [41], QTCN (QTC-Network) =-=[42]-=-, and QTCS (QTC-Shape) [43]. This paper will focus on QTCB and QTCC. In QTCB, qualitative relations are defined based on the Euclidean distance between two disjoint MPOs at each time stamp of movement...

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...between two disjoint moving point objects (MPOS). Different types of QTC have been developed, namely QTCB (QTC-Basic) [40], QTCC (QTC-Double Cross) [41], QTCN (QTC-Network) [42], and QTCS (QTC-Shape) =-=[43]-=-. This paper will focus on QTCB and QTCC. In QTCB, qualitative relations are defined based on the Euclidean distance between two disjoint MPOs at each time stamp of movement (Fig 1A), while QTCC relat...

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...ogist Abbott [46], have applied sequence alignment to the analysis of career patterns. More recently, sequence alignment methods have been used in fields including transportation [47–49], cartography =-=[50]-=-, tourism [51], and crowd behaviour analysis [52], among others. Sequence alignment is the process of aligning two or more character sequences based on a set of conventional operations. Specifically, ...

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...t to the analysis of career patterns. More recently, sequence alignment methods have been used in fields including transportation [47–49], cartography [50], tourism [51], and crowd behaviour analysis =-=[52]-=-, among others. Sequence alignment is the process of aligning two or more character sequences based on a set of conventional operations. Specifically, dynamic programming algorithms are used to equate...

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...thopaedists and neurologists may examine MoCap measurements of human gait in conjunction with biomechanical modelling to evaluate a patient’s status and develop plans for treatment and rehabilitation =-=[57]-=-. Here, we examine some of the basic movements in two different types of dances, namely samba and tango. Samba is a rhythmical dance. Characterising the conformity of samba dance movements is highly m...

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...ncers. One way to visually recognise the periodicity in movement sequences is mapping sequences to dot plots. From a dot plot, certain sequence features (such as ‘repeats’) can be visually identified =-=[58]-=-. Dot plots are constructed using two sequences– one written along the top row and the second written along the leftmost column of a two-dimensional matrix. In a dot plot, each dot represents a point ...

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...equences, which is the alignment that minimises the overall distance between the two sequences. Two different scoring matrices for QTCB and QTCC relations are defined based on the conceptual distance =-=[59]-=- of QTC relations. The conceptual distance is defined as a measure of closeness of two QTC relations by counting the number of changes in the symbols of the QTC representation (A B)B and (A B C D)C [5...

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...and right hand over time, he could not manage to control the relative directions of his movements in a manner similar to that of the teacher. The results of this approach are comparable with those in =-=[62]-=-. Case 2: Tango dance. In this subsection, we present the results of our comparison for the most complete recorded tango data. Fig 14 shows a histogram in which the overall performances of beginners a...