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Towards efficient prospective detection of multiple
spatio-temporal clusters
Bráulio Veloso, Andréa Iabrudi and Thais Correa.Universidade Federal de Ouro Preto – UFOPNovember, 2013, Campos do Jordão, SP – Brazil
XIV Brazilian Symposium on GeoInformatics
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Content
• Introduction• Method– STCD– Problem– STCD-Sim
• Metrics• Simulated Datasets• Results• Final Considerations
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Introduction
• Technique to efficiently detect multiple emergent clusters in a space-time point process
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
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Introduction
• Technique to efficiently detect multiple emergent clusters in a space-time point process– Surveillance Systems;• On-line;• Prospective;
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
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Introduction
• Technique to efficiently detect multiple emergent clusters in a space-time point process– Surveillance Systems;– Applications:
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
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Introduction
• Technique to efficiently detect multiple emergent clusters in a space-time point process– Surveillance Systems;– Applications:• Epidemic surveillance;
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
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Introduction
• Technique to efficiently detect multiple emergent clusters in a space-time point process– Surveillance Systems;– Applications:• Epidemic surveillance;• Criminology behavior;
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
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Introduction
• Technique to efficiently detect multiple emergent clusters in a space-time point process– Surveillance Systems;– Applications:• Epidemic surveillance;• Criminology behavior;• Traffic control;
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
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Introduction
• Technique to efficiently detect multiple emergent clusters in a space-time point process– Surveillance Systems;– Applications:• Epidemic surveillance;• Criminology behavior;• Traffic control;• Social networks behavior;
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
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Introduction
• Technique to efficiently detect multiple emergent clusters in a space-time point process– Spatio-temporal data are more available;
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
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Introduction
• Technique to efficiently detect multiple emergent clusters in a space-time point process– Spatio-temporal data are more available;– Process with more then one cluster;
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
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Introduction
• Technique to efficiently detect multiple emergent clusters in a space-time point process– Spatio-temporal data are more available;– Process with more then one cluster;– Need of computationally efficient approaches.
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
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Introduction
• STCD– Point Process;
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
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Introduction
• STCD– Point Process;– Earlier identification;
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
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Introduction
• STCD– Point Process;– Earlier identification;– Fast Execution;
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
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Introduction
• STCD– Point Process;– Earlier identification;– Fast Execution;– Efficient detection;
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
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Introduction
• STCD– Point Process;– Earlier identification;– Fast Execution;– Efficient detection;
– But identifies only one cluster.
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
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The Space-Time Cluster Detection
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
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STCD – Space Time Cluster Detection
• Renato Assunção and Thais Correa. Surveillance to detect emerging space-time clusters. Computational Statistics and Data Analysis, 53(8):2817-2830, 2009.
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
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STCD – Space Time Cluster Detection
• Surveillance Systems
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
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STCD – Space Time Cluster Detection
• Surveillance Systems– Process: Under Control vs. Out of Control;– System: try to detected earlier a change in the
process
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
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STCD – Space Time Cluster Detection
• Surveillance Systems;• Spatio-Temporal Events – Tuple: (id, x, y, t);– Order by time.
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
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STCD – Space Time Cluster Detection
• Surveillance Systems;• Spatio-Temporal Events;• Alarm– Evidence that the process changed from in control
to out of control.
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
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STCD – Space Time Cluster Detection
• Surveillance Systems;• Spatio-Temporal Events;• Alarm;• Space-Time Cluster– Cylindrical shape• Circular base in space• Temporal Height
Space
Time
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
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STCD – Space Time Cluster Detection
• Surveillance Systems;• Spatio-Temporal Events;• Alarm;• Space-Time Cluster ;• Prospective Detection– Live Cluster
Space
Time
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
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STCD – Space Time Cluster Detection
• Surveillance Systems;• Spatio-Temporal Events;• Alarm;• Space-Time Cluster ;• Prospective Detection– Live Cluster
Space
Time
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
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STCD – Space Time Cluster Detection
• Surveillance Systems;• Spatio-Temporal Events;• Alarm;• Space-Time Cluster ;• Prospective Detection– Live Cluster
Space
Time
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
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STCD – Space Time Cluster Detection– Ck,n : candidate cylinder to be a cluster, beginning
(centered) in event k and ending in the last event
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
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STCD – Space Time Cluster Detection– Ck,n : candidate cylinder to be a cluster, beginning
(centered) in event k and ending in the last event;
– Lk : likelihood of the space-time Poisson process when there is a cluster Ck,n;
– L ∞ : likelihood of the space-time Poisson process when there is no cluster.
• a
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
LLk
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STCD – Space Time Cluster Detection• Cumulative Sum Statistic
n
knk
n
k
kn L
L=R1
,1
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
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STCD – Space Time Cluster Detection• Cumulative Sum Statistic
n
knk
n
k
kn L
L=R1
,1
)(exp1 ,)(
,,
nkCN
nk Cεε+ nk
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
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STCD – Space Time Cluster Detection
• Each parcel k is related to a candidate cluster.
)(exp1 ,1
)( ,nk
n
=k
CNn Cεε+=R nk
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
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STCD – Space Time Cluster Detection
• Each parcel k is related to a candidate cluster.
– ε: increase in the intensity inside the cluster Ck,n;
)(exp1 ,1
)( ,nk
n
=k
CNn Cεε+=R nk
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
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STCD – Space Time Cluster Detection
• Each parcel k is related to a candidate cluster.
– ε: increase in the intensity inside the cluster Ck,n;
– N(Ck,n): number of events inside Ck,n;
)(exp1 ,1
)( ,nk
n
=k
CNn Cεε+=R nk
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
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STCD – Space Time Cluster Detection
• Each parcel k is related to a candidate cluster.
– ε: increase in the intensity inside the cluster Ck,n;
– N(Ck,n): number of events inside Ck,n;
– μ(Ck,n): expected number of events inside Ck,n.• non parametric estimate for μ(Ck,n).
)(exp1 ,1
)( ,nk
n
=k
CNn Cεε+=R nk
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
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STCD – Space Time Cluster Detection
• Each parcel k is related to a candidate cluster.
– ε: increase in the intensity inside the cluster Ck,n;
– N(Ck,n): number of events inside Ck,n;
– μ(Ck,n): expected number of events inside Ck,n.• non parametric estimate for μ(Ck,n).
)(exp1 ,1
)( ,nk
n
=k
CNn Cεε+=R nk
n
ttANttkBNC nkn
nk
],(.],(),()(ˆ 0
,
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
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STCD – Space Time Cluster Detection
• Alarm or not?
– A and‘
ARn
n
knkn =R
1,
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
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STCD – Space Time Cluster Detection
Space
Timetactual
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
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STCD – Space Time Cluster Detection
Space
Timetactual
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
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STCD – Space Time Cluster Detection
Space
Timetactual
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
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STCD – Space Time Cluster Detection
Space
Timetactual
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
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STCD – Space Time Cluster Detection
Space
Timetactual
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
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STCD – Space Time Cluster Detection
Space
Timetactual
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
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STCD – Space Time Cluster Detection
Space
Timetactual
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
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STCD – Space Time Cluster Detection
Space
Timetactual
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
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STCD – Space Time Cluster Detection
Space
Timetactual
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
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STCD – Space Time Cluster Detection
tactual
Space
Time
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
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STCD – Space Time Cluster Detection
Space
Timetactual
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
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STCD – Space Time Cluster Detection
Space
Timetactual
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
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STCD – Space Time Cluster Detection
Space
Timetactual
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
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STCD – Space Time Cluster Detection
Space
Timetactual
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
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STCD – Space Time Cluster Detection
Space
Timetactual
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
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STCD – Space Time Cluster Detection• Parameters: – Spatial Radius (ρ)• Used in the definition of spatial neighborhood for each
event
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
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STCD – Space Time Cluster Detection• Parameters: – Spatial Radius (ρ)• ρ
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
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STCD – Space Time Cluster Detection• Parameters: – Spatial Radius (ρ)• ρ ↑
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
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STCD – Space Time Cluster Detection• Parameters: – Spatial Radius (ρ)• ρ ↑↑
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
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STCD – Space Time Cluster Detection• Parameters: – Spatial Radius (ρ)– Increase in the intensity inside the cluster (ε);
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
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STCD – Space Time Cluster Detection• Parameters: – Spatial Radius (ρ);– Increase in the intensity inside the cluster (ε)• ε
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
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STCD – Space Time Cluster Detection• Parameters: – Spatial Radius (ρ);– Increase in the intensity inside the cluster (ε)• ε ↑
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
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STCD – Space Time Cluster Detection• Parameters: – Spatial Radius (ρ);– Increase in the intensity inside the cluster (ε)• ε ↑↑
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
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STCD – Space Time Cluster Detection• Parameters: – Spatial Radius (ρ);– Increase in the intensity inside the cluster (ε);– Threshold (A)
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
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STCD – Space Time Cluster Detection• Parameters: – Spatial Radius (ρ);– Increase in the intensity inside the cluster (ε);– Threshold (A)• A↓• Faster Detection
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
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STCD – Space Time Cluster Detection• Parameters: – Spatial Radius (ρ);– Increase in the intensity inside the cluster (ε);– Threshold (A)• A↓↓• Increase the number of false alarms
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
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STCD – Space Time Cluster Detection• Parameters: – Spatial Radius (ρ);– Increase in the intensity inside the cluster (ε);– Threshold (A)• A ↑• Slower Detection
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
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STCD – Space Time Cluster Detection• Parameters: – Spatial Radius (ρ);– Increase in the intensity inside the cluster (ε);– Threshold (A)• A ↑↑• No Detection
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
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STCD – Space Time Cluster Detection• Parameters: – Spatial Radius (ρ);– Increase in the intensity inside the cluster (ε);– Threshold (A)• How much events the user wants to wait before a false alarm.
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
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STCD – Space Time Cluster Detection• Operations at time i:
i
Space
Time
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
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STCD – Space Time Cluster Detection• Operations at time i:
i
Space
Time
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
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STCD – Space Time Cluster Detection• Operations at time i:
N(C1,12)
i
Space
Time
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
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STCD – Space Time Cluster Detection• Operations at time i:
μ(C1,12)
i
Space
Time
N(C1,12)
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
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STCD – Space Time Cluster Detection• Operations at time i:
i
Space
Time
μ(C2,12)
N(C2,12)
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
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STCD – Space Time Cluster Detection• Operations at time i:
i
Space
Time
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
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STCD – Space Time Cluster Detection• Operations at time i:
i
Space
Time
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
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STCD – Space Time Cluster Detection• Operations at time i:
i
Space
Time
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
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STCD – Space Time Cluster Detection• Operations at time i:
i
Space
Time
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
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STCD – Space Time Cluster Detection• Operations at time i:
i
Space
Time
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
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STCD – Space Time Cluster Detection• Operations at time i:
i
Space
Time
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
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STCD – Space Time Cluster Detection• Operations at time i:
i
Space
Time
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
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STCD – Space Time Cluster Detection• Operations at time i:
i
Space
Time
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
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STCD – Space Time Cluster Detection• Operations at time i:
i
Space
Time
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
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STCD – Space Time Cluster Detection• Operations at time i:
i
Space
Time
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
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STCD – Space Time Cluster Detection• Operations at time i:
i
Space
Time
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
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STCD – Space Time Cluster Detection
• Alarm!
– A
ARn
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
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STCD – Space Time Cluster Detection
• Alarm!
– A
• Identifying the cluster– a
– Cylinder:
ARn
nknknk 1,max ,*,
nkC *,
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
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STCD – Space Time Cluster Detection• Operations at time i:
Space
Time
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
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Problem• Is there more than one cluster?
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
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Problem• Is there more than one cluster?
Space
Time
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
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Problem• Is there more than one cluster?
Space
Time
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
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Space
Time
Problem• How to identify these two clusters
simultaneously?
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
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STCD-Sim
Our extension
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
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STCD-Sim• Our extension:– Simultaneous Space-Time Clusters Detection
(STCD-Sim);
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
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STCD-Sim• Our extension:– Simultaneous Space-Time Clusters Detection
(STCD-Sim);– Same parameters and data type;
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
![Page 93: Towards efficient prospective detection of multiple spatio -temporal clusters](https://reader035.vdocuments.site/reader035/viewer/2022081520/56816216550346895dd24391/html5/thumbnails/93.jpg)
STCD-Sim• Our extension:– Simultaneous Space-Time Clusters Detection
(STCD-Sim);– Same parameters and data type;– Automatically identifies as many clusters as there
are in the database.
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
![Page 94: Towards efficient prospective detection of multiple spatio -temporal clusters](https://reader035.vdocuments.site/reader035/viewer/2022081520/56816216550346895dd24391/html5/thumbnails/94.jpg)
STCD-Sim• a
– N(Ck*,n): number of events inside the detected cluster;
– μ(Ck*,n): number of events expected in detected cluster.
)(exp1 *,)(
*,*,
nkCN
nk Cεε+ nk
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
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STCD-Sim• a
– N(Ck*,n): number of events inside the detected cluster;
– μ(Ck*,n): number of events expected in detected cluster.
• Excess of events
)(exp1 *,)(
*,*,
nkCN
nk Cεε+ nk
)()()( *,*,*, nknknk CCNC
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
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STCD-Sim• Excess of events– A ;)()()( *,*,*, nknknk CCNC
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
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STCD-Sim• Excess of events– A ;
• Delete excess of events inside Ck*,n – Random way;
)()()( *,*,*, nknknk CCNC
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
![Page 98: Towards efficient prospective detection of multiple spatio -temporal clusters](https://reader035.vdocuments.site/reader035/viewer/2022081520/56816216550346895dd24391/html5/thumbnails/98.jpg)
STCD-Sim• Excess of events– A ;
• Delete excess of events inside Ck*,n – Random way;
• Adjusted threshold– A ;
)()()( *,*,*, nknknk CCNC
)(' *,nkCAA
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
![Page 99: Towards efficient prospective detection of multiple spatio -temporal clusters](https://reader035.vdocuments.site/reader035/viewer/2022081520/56816216550346895dd24391/html5/thumbnails/99.jpg)
STCD-Sim• Excess of events– A ;
• Delete excess of events inside Ck*,n – Random way;
• Adjusted threshold– A ;
• Re-run the method with the reduced database and adjusted threshold A’ (same ρ and ε).
)()()( *,*,*, nknknk CCNC
)(' *,nkCAA
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
![Page 100: Towards efficient prospective detection of multiple spatio -temporal clusters](https://reader035.vdocuments.site/reader035/viewer/2022081520/56816216550346895dd24391/html5/thumbnails/100.jpg)
Evaluation Metrics
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
![Page 101: Towards efficient prospective detection of multiple spatio -temporal clusters](https://reader035.vdocuments.site/reader035/viewer/2022081520/56816216550346895dd24391/html5/thumbnails/101.jpg)
Evaluation Metrics
• For an unique cluster case– No Alarm– Incorrect Alarm– Correct Alarm
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
![Page 102: Towards efficient prospective detection of multiple spatio -temporal clusters](https://reader035.vdocuments.site/reader035/viewer/2022081520/56816216550346895dd24391/html5/thumbnails/102.jpg)
Evaluation Metrics
• For an unique cluster case– No Alarm• a
– Incorrect Alarm– Correct Alarm
niARi ,..,1
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
![Page 103: Towards efficient prospective detection of multiple spatio -temporal clusters](https://reader035.vdocuments.site/reader035/viewer/2022081520/56816216550346895dd24391/html5/thumbnails/103.jpg)
Evaluation Metrics
• For an unique cluster case– No Alarm– Incorrect Alarm• A and
– Correct Alarm niARi ,..,1 TRUEik CC *,
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
![Page 104: Towards efficient prospective detection of multiple spatio -temporal clusters](https://reader035.vdocuments.site/reader035/viewer/2022081520/56816216550346895dd24391/html5/thumbnails/104.jpg)
Evaluation Metrics
• For an unique cluster case– No Alarm– Incorrect Alarm– Correct Alarm• A and niARi ,..,1 TRUEik CC *,
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
![Page 105: Towards efficient prospective detection of multiple spatio -temporal clusters](https://reader035.vdocuments.site/reader035/viewer/2022081520/56816216550346895dd24391/html5/thumbnails/105.jpg)
Evaluation Metrics
• For an unique cluster case
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
![Page 106: Towards efficient prospective detection of multiple spatio -temporal clusters](https://reader035.vdocuments.site/reader035/viewer/2022081520/56816216550346895dd24391/html5/thumbnails/106.jpg)
Evaluation Metrics
• For an unique cluster case
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
![Page 107: Towards efficient prospective detection of multiple spatio -temporal clusters](https://reader035.vdocuments.site/reader035/viewer/2022081520/56816216550346895dd24391/html5/thumbnails/107.jpg)
Evaluation Metrics
• For two simultaneous clusters case– No Alarm– Single Alarm– Double Alarm
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
![Page 108: Towards efficient prospective detection of multiple spatio -temporal clusters](https://reader035.vdocuments.site/reader035/viewer/2022081520/56816216550346895dd24391/html5/thumbnails/108.jpg)
Evaluation Metrics
• For two simultaneous clusters case– No Alarm• a
– Single Alarm– Double Alarm
ARi
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
![Page 109: Towards efficient prospective detection of multiple spatio -temporal clusters](https://reader035.vdocuments.site/reader035/viewer/2022081520/56816216550346895dd24391/html5/thumbnails/109.jpg)
Evaluation Metrics
• For two simultaneous clusters case– No Alarm– Single Alarm• A and
– Double AlarmARi '' AR i
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
![Page 110: Towards efficient prospective detection of multiple spatio -temporal clusters](https://reader035.vdocuments.site/reader035/viewer/2022081520/56816216550346895dd24391/html5/thumbnails/110.jpg)
Evaluation Metrics
• For two simultaneous clusters case– No Alarm– Single Alarm– Double Alarm• A andARi '' AR i
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
![Page 111: Towards efficient prospective detection of multiple spatio -temporal clusters](https://reader035.vdocuments.site/reader035/viewer/2022081520/56816216550346895dd24391/html5/thumbnails/111.jpg)
Evaluation Metrics
• For two simultaneous clusters case– No Alarm– Single Alarm• Correct• Incorrect
– Double Alarm• Correct• Incorrect• Half-Correct
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
![Page 112: Towards efficient prospective detection of multiple spatio -temporal clusters](https://reader035.vdocuments.site/reader035/viewer/2022081520/56816216550346895dd24391/html5/thumbnails/112.jpg)
Evaluation Metrics
• For two simultaneous clusters case– No Alarm– Single Alarm• Correct• Incorrect
– Double Alarm• Correct• Incorrect• Half-Correct
No Alarm
Incorrect Alarm
IncompleteAlarm
Complete Alarm
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
![Page 113: Towards efficient prospective detection of multiple spatio -temporal clusters](https://reader035.vdocuments.site/reader035/viewer/2022081520/56816216550346895dd24391/html5/thumbnails/113.jpg)
Evaluation Metrics
• For two simultaneous clusters case– No Alarm– Single Alarm• Correct• Incorrect
– Double Alarm• Correct• Incorrect• Half-Correct
No Alarm
Incorrect Alarm
IncompleteAlarm
Complete Alarm
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
![Page 114: Towards efficient prospective detection of multiple spatio -temporal clusters](https://reader035.vdocuments.site/reader035/viewer/2022081520/56816216550346895dd24391/html5/thumbnails/114.jpg)
Evaluation Metrics
• For two simultaneous clusters case– No Alarm– Single Alarm• Correct• Incorrect
– Double Alarm• Correct• Incorrect• Half-Correct
No Alarm
Incorrect Alarm
IncompleteAlarm
Complete Alarm
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
![Page 115: Towards efficient prospective detection of multiple spatio -temporal clusters](https://reader035.vdocuments.site/reader035/viewer/2022081520/56816216550346895dd24391/html5/thumbnails/115.jpg)
Evaluation Metrics
• For two simultaneous clusters case– No Alarm– Single Alarm• Correct• Incorrect
– Double Alarm• Correct• Incorrect• Half-Correct
No Alarm
Incorrect Alarm
IncompleteAlarm
Complete Alarm
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
![Page 116: Towards efficient prospective detection of multiple spatio -temporal clusters](https://reader035.vdocuments.site/reader035/viewer/2022081520/56816216550346895dd24391/html5/thumbnails/116.jpg)
Evaluation Metrics
• For two simultaneous clusters case– No Alarm– Single Alarm• Correct• Incorrect
– Double Alarm• Correct• Incorrect• Half-Correct
No Alarm
Incorrect Alarm
IncompleteAlarm
Complete Alarm
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
![Page 117: Towards efficient prospective detection of multiple spatio -temporal clusters](https://reader035.vdocuments.site/reader035/viewer/2022081520/56816216550346895dd24391/html5/thumbnails/117.jpg)
Evaluation Metrics
• For two simultaneous clusters case– No Alarm– Single Alarm• Correct• Incorrect
– Double Alarm• Correct• Incorrect• Half-Correct
No Alarm
Incorrect Alarm
IncompleteAlarm
Complete Alarm
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
![Page 118: Towards efficient prospective detection of multiple spatio -temporal clusters](https://reader035.vdocuments.site/reader035/viewer/2022081520/56816216550346895dd24391/html5/thumbnails/118.jpg)
Evaluation Metrics
• Delay Time
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
![Page 119: Towards efficient prospective detection of multiple spatio -temporal clusters](https://reader035.vdocuments.site/reader035/viewer/2022081520/56816216550346895dd24391/html5/thumbnails/119.jpg)
Evaluation Metrics
• Delay Time– elapsed time between the cluster start and its
actual identification;
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
![Page 120: Towards efficient prospective detection of multiple spatio -temporal clusters](https://reader035.vdocuments.site/reader035/viewer/2022081520/56816216550346895dd24391/html5/thumbnails/120.jpg)
Evaluation Metrics
• Delay Time– elapsed time between the cluster start and its
actual identification;
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
Delay Delay
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Datasets
Simulated Databases
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
![Page 122: Towards efficient prospective detection of multiple spatio -temporal clusters](https://reader035.vdocuments.site/reader035/viewer/2022081520/56816216550346895dd24391/html5/thumbnails/122.jpg)
Simulated databases
• Homogeneous Poisson Point Process– Space:• X: [0, 10];• Y: [0, 10];
– Time:• T: [0, 10];
– Databases with one and two clusters.
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
![Page 123: Towards efficient prospective detection of multiple spatio -temporal clusters](https://reader035.vdocuments.site/reader035/viewer/2022081520/56816216550346895dd24391/html5/thumbnails/123.jpg)
• Clusters:– ε = 1.0, 3.0 e 10.0;– ρ = 0.5, 1.0, 1.5 e 2.0;– Δt = [5, 10], [7, 10] e [8, 10];• The process begin under control in time 0 and one or
two clusters start at time 5, for example.
• Running the STCD:– Input parameters (equal to the true values);– A = n (total number of events).
Simulated databases| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
![Page 124: Towards efficient prospective detection of multiple spatio -temporal clusters](https://reader035.vdocuments.site/reader035/viewer/2022081520/56816216550346895dd24391/html5/thumbnails/124.jpg)
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
Simulated databases
![Page 125: Towards efficient prospective detection of multiple spatio -temporal clusters](https://reader035.vdocuments.site/reader035/viewer/2022081520/56816216550346895dd24391/html5/thumbnails/125.jpg)
Results
Percentage of AlarmsDelays
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
![Page 126: Towards efficient prospective detection of multiple spatio -temporal clusters](https://reader035.vdocuments.site/reader035/viewer/2022081520/56816216550346895dd24391/html5/thumbnails/126.jpg)
Results – Alarms unique cluster
• No Alarm
• Incorrect Alarm
• Correct Alarm
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
![Page 127: Towards efficient prospective detection of multiple spatio -temporal clusters](https://reader035.vdocuments.site/reader035/viewer/2022081520/56816216550346895dd24391/html5/thumbnails/127.jpg)
Results – Alarms unique cluster
• No Alarm
• Incorrect Alarm
• Correct Alarm
General Mean:1.37%; 3.39%; 95.24%
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
![Page 128: Towards efficient prospective detection of multiple spatio -temporal clusters](https://reader035.vdocuments.site/reader035/viewer/2022081520/56816216550346895dd24391/html5/thumbnails/128.jpg)
Results – Alarms two clusters
• No Alarm
• Incorrect Alarm
• Incomplete Alarm
• Complete Alarm
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
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Results – Alarms two clusters
• No Alarm
• Incorrect Alarm
• Incomplete Alarm
• Complete Alarm
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
General Mean:• 1.00%• 1.69%• 63.68% • 33.63%
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Results – Alarms two clusters
• No Alarm
• Incorrect Alarm
• Incomplete Alarm
• Complete Alarm
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
General Mean:• 1.00%• 1.69%• 63.68% • 33.63%
Our extension reached a complete Alarm in 88.2% of cases in database
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Results – Delay
• Delay 1C.
• 2C. Delay 1st
• 2C. Delay C1
• 2C. Delay C2
• 2C. Delay Duplo
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
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Results – Delay
• Delay 1C.
• 2C. Delay 1st
• 2C. Delay C1
• 2C. Delay C2
• 2C. Delay Duplo
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
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Final Considerations
• Our extension for multiple cluster– Percentage of detection for both clusters around
88%;
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
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Final Considerations
• Our extension for multiple cluster– Percentage of detection for both clusters around
88%;– Delay for two clusters slightly larger than delay for
one cluster;
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
![Page 135: Towards efficient prospective detection of multiple spatio -temporal clusters](https://reader035.vdocuments.site/reader035/viewer/2022081520/56816216550346895dd24391/html5/thumbnails/135.jpg)
Final Considerations
• Our extension for multiple cluster– Percentage of detection for both clusters around
88%;– Delay for two clusters slightly larger than delay for
one cluster;– Promising method.
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
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Final Considerations
• Future works– Evaluate the impact of changing ρ and ε;
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
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Final Considerations
• Future works– Evaluate the impact of changing ρ and ε;– Apply to a real database and benchmark;
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
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Final Considerations
• Future works– Evaluate the impact of changing ρ and ε;– Apply to a real database and benchmark;– Compare with others approaches;
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
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Final Considerations
• Future works– Evaluate the impact of changing ρ and ε;– Apply to a real database and benchmark;– Compare with others approaches;– Remove the restriction of the cylindrical shape for
the cluster.
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |
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References[1] Renato Assunção and Thais Correa. Surveillance to detect emerging space-time clusters. Computational Statistics and Data Analysis, 53(8):2817-2830, June 2009.
[2] B. Veloso, A. Iabrudi and T. Correa. Localização em tempo real de acontecimentos através de vigilância espaço-temporal de microblogs. In IX Encontro Nacional de Inteligência Artificial, 12 pages, Curitiba - PR, Brazil, October 2012.
[3] C. Sonesson and D. Bock. A review and discussion of prospective statistical surveillance in public health. Journal of the Royal Statistical Society: Series A (Statistics in Society), 166(1):5–21 , 2003.
[4] M. Höhle. surveillance: An R package for the monitoring of infectious diseases. Computational Statistics, 22:571–582, 2007.
| Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |