Towards efficient prospective detection of multiple spatio-temporal clusters Bráulio Veloso, Andréa Iabrudi and Thais Correa. Universidade Federal de Ouro Preto – UFOP November, 2013, Campos do Jordão, SP – Brazil XIV Brazilian Symposium on GeoInformatics

Content Introduction Method – STCD – Problem – STCD-Sim Metrics Simulated Datasets Results Final Considerations

Introduction Technique to efficiently detect multiple emergent clusters in a space-time point process | Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |

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 |

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 |

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 |

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 |

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 |

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 |

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 |

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 |

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 |

Introduction STCD – Point Process; | Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |

Introduction STCD – Point Process; – Earlier identification; | Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |

Introduction STCD – Point Process; – Earlier identification; – Fast Execution; | Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |

Introduction STCD – Point Process; – Earlier identification; – Fast Execution; – Efficient detection; | Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |

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 |

The Space-Time Cluster Detection | Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |

STCD – Space Time Cluster Detection Renato Assunção and Thais Correa. Surveillance to detect emerging space-time clusters. Computational Statistics and Data Analysis, 53(8): , | Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |

STCD – Space Time Cluster Detection Surveillance Systems | Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |

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 |

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 |

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 |

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 |

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 |

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 |

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 |

STCD – Space Time Cluster Detection – C k,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 |

STCD – Space Time Cluster Detection – C k,n : candidate cylinder to be a cluster, beginning (centered) in event k and ending in the last event; – L k : likelihood of the space-time Poisson process when there is a cluster C k,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 |

STCD – Space Time Cluster Detection Cumulative Sum Statistic | Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |

STCD – Space Time Cluster Detection Cumulative Sum Statistic | Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |

STCD – Space Time Cluster Detection Each parcel k is related to a candidate cluster. | Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |

STCD – Space Time Cluster Detection Each parcel k is related to a candidate cluster. – ε: increase in the intensity inside the cluster C k,n ; | Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |

STCD – Space Time Cluster Detection Each parcel k is related to a candidate cluster. – ε: increase in the intensity inside the cluster C k,n ; – N(C k,n ): number of events inside C k,n ; | Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |

STCD – Space Time Cluster Detection Each parcel k is related to a candidate cluster. – ε: increase in the intensity inside the cluster C k,n ; – N(C k,n ): number of events inside C k,n ; – μ(C k,n ): expected number of events inside C k,n. non parametric estimate for μ(C k,n ). | Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |

STCD – Space Time Cluster Detection Each parcel k is related to a candidate cluster. – ε: increase in the intensity inside the cluster C k,n ; – N(C k,n ): number of events inside C k,n ; – μ(C k,n ): expected number of events inside C k,n. non parametric estimate for μ(C k,n ). | Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |

STCD – Space Time Cluster Detection Alarm or not? – A and ‘ | Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |

STCD – Space Time Cluster Detection Space Time t actual | Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |

STCD – Space Time Cluster Detection Space Time t actual | Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |

STCD – Space Time Cluster Detection Space Time t actual | Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |

STCD – Space Time Cluster Detection Space Time t actual | Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |

STCD – Space Time Cluster Detection Space Time t actual | Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |

STCD – Space Time Cluster Detection Space Time t actual | Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |

STCD – Space Time Cluster Detection Space Time t actual | Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |

STCD – Space Time Cluster Detection Space Time t actual | Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |

STCD – Space Time Cluster Detection Space Time t actual | Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |

STCD – Space Time Cluster Detection t actual Space Time | Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |

STCD – Space Time Cluster Detection Space Time t actual | Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |

STCD – Space Time Cluster Detection Space Time t actual | Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |

STCD – Space Time Cluster Detection Space Time t actual | Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |

STCD – Space Time Cluster Detection Space Time t actual | Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |

STCD – Space Time Cluster Detection Space Time t actual | Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |

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 |

STCD – Space Time Cluster Detection Parameters: – Spatial Radius (ρ) ρ | Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |

STCD – Space Time Cluster Detection Parameters: – Spatial Radius (ρ) ρ ↑ | Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |

STCD – Space Time Cluster Detection Parameters: – Spatial Radius (ρ) ρ ↑↑ | Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |

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 |

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 |

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 |

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 |

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 |

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 |

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 |

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 |

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 |

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 |

STCD – Space Time Cluster Detection Operations at time i: i Space Time | Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |

STCD – Space Time Cluster Detection Operations at time i: i Space Time | Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |

STCD – Space Time Cluster Detection Operations at time i: N(C 1,12 ) i Space Time | Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |

STCD – Space Time Cluster Detection Operations at time i: μ(C 1,12 ) i Space Time N(C 1,12 ) | Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |

STCD – Space Time Cluster Detection Operations at time i: i Space Time μ(C 2,12 ) N(C 2,12 ) | Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |

STCD – Space Time Cluster Detection Operations at time i: i Space Time | Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |

STCD – Space Time Cluster Detection Operations at time i: i Space Time | Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |

STCD – Space Time Cluster Detection Operations at time i: i Space Time | Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |

STCD – Space Time Cluster Detection Operations at time i: i Space Time | Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |

STCD – Space Time Cluster Detection Operations at time i: i Space Time | Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |

STCD – Space Time Cluster Detection Operations at time i: i Space Time | Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |

STCD – Space Time Cluster Detection Operations at time i: i Space Time | Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |

STCD – Space Time Cluster Detection Operations at time i: i Space Time | Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |

STCD – Space Time Cluster Detection Operations at time i: i Space Time | Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |

STCD – Space Time Cluster Detection Operations at time i: i Space Time | Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |

STCD – Space Time Cluster Detection Operations at time i: i Space Time | Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |

STCD – Space Time Cluster Detection Alarm! – A | Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |

STCD – Space Time Cluster Detection Alarm! – A Identifying the cluster – a – Cylinder: | Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |

STCD – Space Time Cluster Detection Operations at time i: Space Time | Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |

Problem Is there more than one cluster? | Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |

Problem Is there more than one cluster? Space Time | Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |

Problem Is there more than one cluster? Space Time | Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |

Space Time Problem How to identify these two clusters simultaneously? | Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |

STCD-Sim Our extension | Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |

STCD-Sim Our extension: – Simultaneous Space-Time Clusters Detection (STCD-Sim); | Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |

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 |

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 |

STCD-Sim a – N(C k*,n ): number of events inside the detected cluster; – μ(C k*,n ): number of events expected in detected cluster. | Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |

STCD-Sim a – N(C k*,n ): number of events inside the detected cluster; – μ(C k*,n ): number of events expected in detected cluster. Excess of events | Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |

STCD-Sim Excess of events – A; | Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |

STCD-Sim Excess of events – A; Delete excess of events inside C k*,n – Random way; | Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |

STCD-Sim Excess of events – A; Delete excess of events inside C k*,n – Random way; Adjusted threshold – A ; | Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |

STCD-Sim Excess of events – A; Delete excess of events inside C k*,n – Random way; Adjusted threshold – A ; Re-run the method with the reduced database and adjusted threshold A’ (same ρ and ε). | Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |

Evaluation Metrics | Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |

Evaluation Metrics For an unique cluster case – No Alarm – Incorrect Alarm – Correct Alarm | Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |

Evaluation Metrics For an unique cluster case – No Alarm a – Incorrect Alarm – Correct Alarm | Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |

Evaluation Metrics For an unique cluster case – No Alarm – Incorrect Alarm A and – Correct Alarm | Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |

Evaluation Metrics For an unique cluster case – No Alarm – Incorrect Alarm – Correct Alarm Aand | Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |

Evaluation Metrics For an unique cluster case | Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |

Evaluation Metrics For an unique cluster case | Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |

Evaluation Metrics For two simultaneous clusters case – No Alarm – Single Alarm – Double Alarm | Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |

Evaluation Metrics For two simultaneous clusters case – No Alarm a – Single Alarm – Double Alarm | Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |

Evaluation Metrics For two simultaneous clusters case – No Alarm – Single Alarm A and – Double Alarm | Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |

Evaluation Metrics For two simultaneous clusters case – No Alarm – Single Alarm – Double Alarm A and | Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |

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 |

Evaluation Metrics For two simultaneous clusters case – No Alarm – Single Alarm Correct Incorrect – Double Alarm Correct Incorrect Half-Correct No Alarm Incorrect Alarm Incomplet e Alarm Complete Alarm | Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |

Evaluation Metrics For two simultaneous clusters case – No Alarm – Single Alarm Correct Incorrect – Double Alarm Correct Incorrect Half-Correct No Alarm Incorrect Alarm Incomplet e Alarm Complete Alarm | Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |

Evaluation Metrics For two simultaneous clusters case – No Alarm – Single Alarm Correct Incorrect – Double Alarm Correct Incorrect Half-Correct No Alarm Incorrect Alarm Incomplet e Alarm Complete Alarm | Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |

Evaluation Metrics For two simultaneous clusters case – No Alarm – Single Alarm Correct Incorrect – Double Alarm Correct Incorrect Half-Correct No Alarm Incorrect Alarm Incomplet e Alarm Complete Alarm | Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |

Evaluation Metrics For two simultaneous clusters case – No Alarm – Single Alarm Correct Incorrect – Double Alarm Correct Incorrect Half-Correct No Alarm Incorrect Alarm Incomplet e Alarm Complete Alarm | Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |

Evaluation Metrics For two simultaneous clusters case – No Alarm – Single Alarm Correct Incorrect – Double Alarm Correct Incorrect Half-Correct No Alarm Incorrect Alarm Incomplet e Alarm Complete Alarm | Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |

Evaluation Metrics Delay Time | Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |

Evaluation Metrics Delay Time – elapsed time between the cluster start and its actual identification; | Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |

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

Datasets Simulated Databases | Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |

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 |

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 |

Simulated databases

Results Percentage of Alarms Delays | Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |

Results – Alarms unique cluster No Alarm Incorrect Alarm Correct Alarm | Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |

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 |

Results – Alarms two clusters No Alarm Incorrect Alarm Incomplete Alarm Complete Alarm | Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |

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%

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

Results – Delay Delay 1C. 2C. Delay 1 st 2C. Delay C1 2C. Delay C2 2C. Delay Duplo | Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |

Results – Delay Delay 1C. 2C. Delay 1 st 2C. Delay C1 2C. Delay C2 2C. Delay Duplo | Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |

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 |

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 |

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 |

Final Considerations Future works – Evaluate the impact of changing ρ and ε; | Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |

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 |

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 |

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 |

References [1] Renato Assunção and Thais Correa. Surveillance to detect emerging space- time clusters. Computational Statistics and Data Analysis, 53(8): , June [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 [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, [4] M. Höhle. surveillance: An R package for the monitoring of infectious diseases. Computational Statistics, 22:571–582, | Introduction | STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations |

Thank you!