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Cluster-Centric Anomaly Detection and Characterization in Spatial Time Series

Cluster-Centric Anomaly Detection and Characterization in Spatial Time Series. Dr. Hesam Izakian October 2014. Outline. Spatial time series Problem formulation Anomaly detection in spatial time series- questions Overall scheme of the proposed method Time series segmentation

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Cluster-Centric Anomaly Detection and Characterization in Spatial Time Series

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  1. Cluster-Centric Anomaly Detection and Characterization in Spatial Time Series Dr. Hesam Izakian October 2014

  2. Outline • Spatial time series • Problem formulation • Anomaly detection in spatial time series- questions • Overall scheme of the proposed method • Time series segmentation • Spatial time series clustering • Assigning anomaly scores to clusters • Visualizing the propagation of anomalies • An outbreak detection scenario • Application • Conclusions

  3. Spatial time series • Structure of data • A set of spatial coordinates • One or more time series for each point • Examples • Daily average temperature in different climate stations • Stock market indexes in different countries • Number of absent students in different schools • Number emergency department visits in different hospitals • Measured signals in different parts of brain

  4. Problem formulation There are N spatial time series Objective: Find a spatial neighborhood of data In a time interval Containing a high level of unexpected changes

  5. Anomaly detection in spatial time series- questions • Spatial neighborhood of data • Size of neighborhood • Overlapping neighborhoods • Unexpected changes (anomalies) • What kind of changes are expected/not expected • How to evaluate the level of unexpected changes • Anomaly visualization • Anomaly characterization • What was the source of anomaly • How the anomaly is propagated over time

  6. Overall scheme of the proposed method Spatial time series data Spatial time series data Sliding window Anomaly scores Spatial time series clustering Fuzzy relations Revealing the structure of data in various time intervals Comparing the revealed structures

  7. Time series part segmentation • Sliding window • Spatio-temporal subsequences • Local view of time series part

  8. Overall scheme of the proposed method Spatial time series data Sliding window Anomaly scores Spatial time series clustering Fuzzy relations Revealing the structure of data in various time intervals Comparing the revealed structures

  9. Fuzzy C-Means clustering- visual illustration

  10. Fuzzy C-Means clustering- visual illustration

  11. Fuzzy C-Means clustering… • Partitions N data • Into clusters • Result: • Objective function: • Minimization:

  12. Spatial time series clustering • Reveals available structure within data • In form of partition matrices • Challenges • Different sources: Spatial part vs. temporal part • Different dimensionality in each part • Different structure within each part

  13. Spatial time series clustering… • In spatial time series, we define • Adopted FCM objective function • Characteristics • When λ=0: Only spatial part of data in clustering • A higher value of λ : a higher impact of time series part in clustering • Optimal value of λ: Optimal impact of each part in clustering

  14. Spatial-time series clustering- Optimal value of λ

  15. Overall scheme of the proposed method Spatial time series data Sliding window Anomaly scores Spatial time series clustering Fuzzy relations Revealing the structure of data in various time intervals Comparing the revealed structures

  16. Assigning anomaly scores to clusters in different time windows Assign an anomaly score to each single subsequence based on historical data Aggregating anomaly scores inside revealed clusters

  17. Overall scheme of the proposed method Spatial time series data Sliding window Anomaly scores Spatial time series clustering Fuzzy relations Revealing the structure of data in various time intervals Comparing the revealed structures

  18. Visualizing the propagation of anomalies- Fuzzy relations • Objective: quantifying relations between clusters

  19. Visualizing the propagation of anomalies… • Objective function to construct relation • Optimization

  20. Example • An outbreak • In southern part of Alberta • Using NAADSM for 100 days

  21. Example… • A sliding window is used • Length : 20 • Movement: 10 • Generated spatio-temporal subsequences:

  22. Example…

  23. Example…

  24. Example…

  25. Example…

  26. Application • Implemented for Agriculture and Rural Development (Government of Alberta) • Using KNIME (Konstanz Information Miner) • Animal health surveillance in Alberta • Anomaly detection • Data visualization

  27. Conclusions • A framework for anomaly detection and characterization in spatial time series is developed • A sliding window to generate a set of spatio-temporal subsequences is considered • Clustering is used to discover the available structure within the spatio-temporal subsequences • An anomaly score assigned to each revealed spatio-temporal cluster • A fuzzy relation technique is proposed to quantify the relations between clusters in successive time steps

  28. Thank you

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