The second stage of this research focuses on the development of a trajectory decomposition method. For the sake of consistency, from this point on the de- composition method is referred as trajectory segmentation in this thesis, just as in Stage III, Research Paper 3. The aim of segmentation is to decrease the com- plexity of movement data in preparation of subsequent analyses. The method allows extraction of the local movement features that are essential for modeling, simulating, and analyzing movement as well as discovering movement patterns. Research Paper 2 presents the substance of this stage extensively (see Part II, Research Paper 2, page 97).
ä Research Paper 2:
Dodge, S., Weibel, R. and Forootan, E. (2009). Revealing the physics of movement: Comparing the similarity of movement characteristics of differ- ent types of moving objects. Computers, Environment and Urban Systems, Volume 33, Issue 6, November 2009, pages 419 – 434.
3.2.1 Objectives
This stage primarily pursues the Objectives 3 and 5(a)of this thesis (cf. chapter
1):
Objective 3: This research shall identify, and formalize important features char- acterizing the movement of objects from the parameters of movement. Quantitative methods shall be developed to extract such features from raw trajectory data, with the aim of transforming trajectories into a simpler structure, while still conveying the important movement features.
Objective 5: The applicability of the developed methods shall be evaluated in knowledge discovery tasks such as (a) trajectory classification, [...] in real movement datasets.
In order to investigate the applicability of the proposed feature extraction and segmentation methods, the Objective 5(a) is expanded as follows:
Objective 5(a): This research shall develop a trajectory classification tech-
nique using movement feature extraction. The developed classification tech- nique shall enable classifying movement data generated by unknown moving objects and assigning them to the known types of moving objects.
3.2.2 Methods and Results
In order to achieve the objectives of this stage, Research Paper 2 proposes a three-step methodology as illustrated in Figure 3.2. The key element of this methodology is the evolution function of the movement parameters (i.e. speed, acceleration, direction etc.) over time, called movement parameter profile (see Figure 3.3).
<Analysis of movement behavior of different MPOs using trajectory decomposition>
‘ Car
Motorcycle Bicycle Pedestrian Eye
Sinuosity Deviation (mp , t ) μ=mp time MP 0
Figure 3.3: Movement parameter profile: The evolution function of a move- ment parameter over time
The developed methodology consists of the following processes (see Part II, Research Paper 2, Figure 3.2):
(1) Trajectory data preparation: consists of data cleaning and preprocessing steps in order to remove effects of noise and positioning errors.
(2) Computation of global descriptors: involves the extraction of global move- ment properties of objects (i.e. computation of the movement parameters and their descriptive statistics over the entire trajectory). In order to de- tect possible interrelationships, correlation analysis between the movement parameters is recommended.
(3) Local feature extraction: a trajectory segmentation approach is proposed to partition the movement parameter profiles into sections of homogeneous movement features. Important movement features are identified as the fre- quency and amplitude of variations of movement parameters. The frequency of variations is quantified by the sinuosity of the MP profile, while the am- plitude of variations is measured by the deviation of the MP profile from the median (or mean) line (Figure 3.3). According to the magnitudes of sinuosity and deviation, each point of the MP profile is labeled with a certain sinuos- ity and deviation regime (later called movement parameter class in Research Paper 3). Here, four main MP regimes (or MP classes) representative of the local movement parameter features are distinguished, as seen in Figure 3.4 (the sequence of colored segments at the bottom of each graph):
• low sinuosity – low deviation • low sinuosity – high deviation • high sinuosity – low deviation • high sinuosity – high deviation
(a) Normalized and decomposed velocity profiles for the sample trajectories of bicycle (on the left) and eye movement (on the right)
(b) Normalized and decomposed acceleration profiles for the sample trajectories of bicycle (on the left) and eye movement (on the right)
0 50 100 150 200 250 300 0 0.2 0.4 0.6 0.8 1
1.2 Velocity for eye movement
time Velocity time 0 50 100 150 200 250 300 0 0.2 0.4 0.6 0.8 1
1.2 Acceleration for eye movement
Acceleration 0 50 100 150 200 250 300 0 0.2 0.4 0.6 0.8 1
1.2 Acceleration for bicycle
time Acceleration 0 50 100 150 200 250 300 0 0.2 0.4 0.6 0.8 1
1.2 Velocity for bicycle
time
Velocity
low sinuosity − low deviation high sinuosity − low deviation low sinuosity − high deviation high sinuosity − high deviation
Figure 3.4: Different MP profiles exhibit different characteristics: Speed and acceleration profiles of the bicycle and eye movements exhibit different amplitude and frequency variations.
In response to Objective 5.a, Research Paper 2 suggests a trajectory classi- fication strategy exploiting the results of the proposed feature extraction and segmentation methods. The classification strategy consists of feature selection and dimension reduction procedures using Principal Component Analysis (PCA) (Jolliffe, 1986), followed by supervised classification using Support Vector Ma- chines (SVM) (Cortes and Vapnik, 1995). In a set of experiments it is shown how the developed methods can be used to label trajectories of unknown objects by similarity to previously learned moving objects. As an example, the classi- fication strategy is applied on movement data from the transportation domain (e.g. pedestrians, motorcycles, bicycles, and cars) in order to extract the mode of transport of unknown trajectories.
3.2.3 Main Findings
• The proposed feature extraction and classification methods can be success- fully applied to detect the mode of transport from unknown trajectories of people using different transportation means.
• The experiments suggest that the movement characteristics of a mass-less process such as eye movement are very different from full-body movement of humans and vehicles (e.g. as speed profiles in Figure 3.4 show). Hence,
such virtual movement data can not be used as a proxy of the movement of massive objects that produce a continuous path. In contrast, eye movement data could potentially be considered as a proxy of the movement of objects with a stop-and-go behavior (e.g. bees, butterflies).
3.2.4 Contributions
This study can contribute to knowledge discovery, modeling, simulation, and analyzing of movement data in the following aspects:
(a) To decrease the complexity of movement data by segmenting trajectories into sections of homogeneous movement characteristics and hence to facilitate knowledge discovery of massive movement data. The segmented trajectories convey information about the frequency and amplitude of variations of move- ment parameters, which are recognized as the important movement features in this thesis.
(b) To assess the similarity of the movement characteristics of proxy and simu- lated data to the movement of real objects.
(c) To automatically identify trajectories of unknown objects by applying the available knowledge about the movement of similar known objects.