Clustering Trajectories of Moving Objects in an Uncertain World. Nikos Pelekis 1 , Ioannis Kopanakis 2 , Evangelos E. Kotsifakos 1 , Elias Frentzos 1 , Yannis Theodoridis 1. IEEE International Conference on Data Mining (ICDM 2009), Miami, FL, USA, 69 December, 2009. Outline. Related work
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Nikos Pelekis1, Ioannis Kopanakis2, Evangelos E. Kotsifakos1,
Elias Frentzos1, Yannis Theodoridis1
IEEE International Conference on Data Mining (ICDM 2009), Miami, FL, USA, 69 December, 2009
Pelekis et al. "Clustering Trajectories of Moving Objects in an Uncertain World"
Trajectory clustering
Pelekis et al. "Clustering Trajectories of Moving Objects in an Uncertain World"
ò World
t
t
d
(
(
t
),
(
t
))
dt
1
2
t
t
=
D
(
,
)

T
1
2
T

T

Which distance?distance between moving objects 1 and 2 at time t
Pelekis et al. "Clustering Trajectories of Moving Objects in an Uncertain World"
Kmeans
HACaverage
TOPTICS [Nanni & Pedreschi,
2006]
Reachability plot
(= objects reordering for distance distribution)
threshold
Pelekis et al. "Clustering Trajectories of Moving Objects in an Uncertain World"
TRACLUS: WorldA PartitionandGroup Framework
[Lee et al. 2007]
Discovers similar portions of trajectories (subtrajectories)
Two phases: partitioning and grouping
Pelekis et al. "Clustering Trajectories of Moving Objects in an Uncertain World"
Visual analytics for mobility data
[Andrienko et al. 2007]
Pelekis et al. "Clustering Trajectories of Moving Objects in an Uncertain World"
1) Trajectories sequences of “moves” between “places”
2) For each pair of “places”, compute the number of “moves”
3) Represent “moves” by arrows (with proportional widths)
Many small moves
Major flow
Minor variations
Pelekis et al. "Clustering Trajectories of Moving Objects in an Uncertain World"
Motivation World
Pelekis et al. "Clustering Trajectories of Moving Objects in an Uncertain World"
Our contribution World
Pelekis et al. "Clustering Trajectories of Moving Objects in an Uncertain World"
where
where
and
Pelekis et al. "Clustering Trajectories of Moving Objects in an Uncertain World"
Pelekis et al. "Clustering Trajectories of Moving Objects in an Uncertain World"
and a target dimension p << ni,
consists of p regions (i.e. sets of cells) crossed by Tiduring period pj
Pelekis et al. "Clustering Trajectories of Moving Objects in an Uncertain World"
A cell ck.l
ck.lε
Pelekis et al. "Clustering Trajectories of Moving Objects in an Uncertain World"
Pelekis et al. "Clustering Trajectories of Moving Objects in an Uncertain World"
where
and
Pelekis et al. "Clustering Trajectories of Moving Objects in an Uncertain World"
Assuming Worldtwo intuitionistic fuzzy sets on it, A= (MA, ΓA, ΠA)and B= (MB, ΓB, ΠΒ), with the same cardinality n, the similarity measure Z between A and B is given by the following equation:
where z(A’,B’) for fuzzy sets A' and B' (e.g. for MA, MB) is defined as:
and similarly for ΓA, ΓB and ΠA, ΠB.
Proposed similarity metric (2/2)Pelekis et al. "Clustering Trajectories of Moving Objects in an Uncertain World"
Pelekis et al. "Clustering Trajectories of Moving Objects in an Uncertain World"
Algorithm CenTra: An example World
T1
T2
Pelekis et al. "Clustering Trajectories of Moving Objects in an Uncertain World"
T3
The Cen Worldtroid Trajectory
T1
T2
Pelekis et al. "Clustering Trajectories of Moving Objects in an Uncertain World"
T3
Fuzzy CMeans algorithm World
and
Pelekis et al. "Clustering Trajectories of Moving Objects in an Uncertain World"
CenTRIFCM World algorithm
and
Ignore update centroid step
and instead use CenTra
Pelekis et al. "Clustering Trajectories of Moving Objects in an Uncertain World"
Pelekis et al. "Clustering Trajectories of Moving Objects in an Uncertain World"
“Round trips” clusters
“Linear” clusters
Pelekis et al. "Clustering Trajectories of Moving Objects in an Uncertain World"
Fix density threshold to δ=2% of the total number of trajectories
Pelekis et al. "Clustering Trajectories of Moving Objects in an Uncertain World"
Fix uncertainty to ε=1
Pelekis et al. "Clustering Trajectories of Moving Objects in an Uncertain World"
Pelekis et al. "Clustering Trajectories of Moving Objects in an Uncertain World"
Pelekis et al. "Clustering Trajectories of Moving Objects in an Uncertain World"
Representative Trajectories vs. Centroid Trajectories
cell size=1.3%, ε=0,δ=0.09
cell size=1.3%, ε=0,δ=0.09, cell size=2.8%, ε=0,δ=0.02
Pelekis et al. "Clustering Trajectories of Moving Objects in an Uncertain World"
Pelekis et al. "Clustering Trajectories of Moving Objects in an Uncertain World"
Pelekis et al. "Clustering Trajectories of Moving Objects in an Uncertain World"
Pelekis et al. "Clustering Trajectories of Moving Objects in an Uncertain World"
ε World
T
δt
Y
X
Examples of mobility patterns exploitationPelekis et al. "Clustering Trajectories of Moving Objects in an Uncertain World"
Pelekis et al. "Clustering Trajectories of Moving Objects in an Uncertain World"
Different time intervals can show different behaviours World
E.g.: objects that are close to each other within a time interval can be much distant in other periods of time
The time interval becomes a parameter
E.g.: rush hours vs. low traffic times
Already supported by the distance measure
Just compute D(1 , 2) T on a time interval T’ T
Problem: significant T’ are not always known a priori
An automated mechanism is needed to find them
Temporal focusingPelekis et al. "Clustering Trajectories of Moving Objects in an Uncertain World"
TRACLUS – representative trajectory World
Pelekis et al. "Clustering Trajectories of Moving Objects in an Uncertain World"
Pelekis et al. "Clustering Trajectories of Moving Objects in an Uncertain World"
Pelekis et al. "Clustering Trajectories of Moving Objects in an Uncertain World"
42
A={x, 0.4, 0.2}, B={x, 0.5, 0.3}, C={x, 0.5, 0.2}
Cis more similar to A than B
Pelekis et al. "Clustering Trajectories of Moving Objects in an Uncertain World"
Pelekis et al. "Clustering Trajectories of Moving Objects in an Uncertain World"